ml_ppcic_dim_reduc.ipynb

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      "name": "ml_ppcic_dim_reduc.ipynb",
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        "<a href=\"https://colab.research.google.com/github/MLRG-CEFET-RJ/ml-class/blob/master/ml_ppcic_dim_reduc.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
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        "id": "D9yeRGYWSEE4"
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      "source": [
        "# Introduction\n",
        "\n",
        "## Curse of dimensionality\n",
        "\n",
        "The term *curse of dimensionality* was coined by [Richard Bellman](https://en.wikipedia.org/wiki/Richard_E._Bellman) to denote the difficulty of manipulating data sets that have a very large number of attributes, or that is, they have a high dimensionality.\n",
        "\n",
        "In the context of ML, the curse of dimensionality, also known as the *Hughes phenomenon* states that, in a data set that contains a fixed amount of samples, say 1000, the more dimensions the samples have, the more difficult is to generate an ML model.\n",
        "\n",
        "For example, if the samples are two-dimensional, it is easy to train a decent predictive model with 1000 samples. However, when each sample contains 500 dimensions, then 1000 samples are not enough to train a decent model. This is because, to train a good predictive model, an ML algorithm has to be presented with a reasonable number of possible combinations of attribute values, in order to properly capture the patterns underlying the data. With more dimensions (i.e., more attributes), there are more possible combinations and therefore more samples are needed. The following figure illustrates this: the amount of training data needed to cover 20% of the attribute space grows exponentially with the number of dimensions.\n",
        "\n",
        "![alt text](https://www.visiondummy.com/wp-content/uploads/2014/04/curseofdimensionality.png)\n",
        "\n",
        "As the figure below illustrates, as the dimensionality of a data set increases, the performance of the prediction model increases until the ideal number of attributes is reached. However, further increasing the dimensionality without increasing the number of training samples results in a decrease in the performance of the model generated.\n",
        "\n",
        "![alt text](https://www.visiondummy.com/wp-content/uploads/2014/04/dimensionality_vs_performance.png)\n",
        "\n",
        "## Dimensionality reduction and attribute selection\n",
        "\n",
        "The choice of attributes (features) used to train a machine learning model has a great influence on the performance that can be achieved.\n",
        "\n",
        "Example (2D to 1D):\n",
        "\n",
        "![alt text](https://shapeofdata.files.wordpress.com/2013/04/projection.png)\n",
        "\n",
        "Example (3D to 2D):\n",
        "\n",
        "![alt text](https://i.stack.imgur.com/9ETLr.png)\n",
        "\n",
        "If the original data set contains a very large number of attributes, it is possible that there are dependencies between them. As a result, there will be more dimensions in the attribute space than the minimum required to perform any ML task. In addition, in classification or regression tasks, it is possible that there are attributes that are not relevant to infer the value of the target attribute.\n",
        "\n",
        "In the context described above, we can consider applying techniques of *dimensionality reduction* or *feature selection* on the original data set. The purpose of these families of techniques is to reduce the number of attributes to be used when adjusting some ML model.\n",
        "\n",
        "The difference between dimensionality reduction and attribute selection is that the set of attributes resulting from the application of the latter is a subset of the original set of attributes, while the set of attributes produced by dimensionality reduction does not need to be a subset (for example, example, the PCA reduces dimensionality by producing new attributes by linearly combining the original attributes, and then discarding the less important ones). In this way, we can understand the selection of attributes as a particular case of dimensionality reduction.\n",
        "\n",
        "In any case, both DR and AS can be used during the pre-processing phase for later application of an estimator (i.e., of some ML model)."
      ]
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      "source": [
        "# Dimensionality reduction\n",
        "\n",
        "DR's main objective is to compact a set of data, preserving most of the significant information. This compression corresponds to reducing the dimensions of the data set with minimal loss of information.\n",
        "\n",
        "Compression facilitates the process of understanding the data, as it is expected that the reduced data representation captures the dominant sources of variation more efficiently.\n",
        "\n",
        "The goal is to discover the \"hidden variables\" that can successfully expose the underlying structure of the data.\n",
        "\n",
        "The desired result is to design an attribute space in a smaller subspace that represents the data properly. A possible application would be in a classification task, in which we want to reduce the computational costs and the classification error, reducing the number of dimensions of the attribute space.\n"
      ]
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      "source": [
        "## Mean vector\n",
        "\n",
        "Consider a data set consisting of $m$ samples, each one an $n$-dimensional vector. That is, the corresponding data matrix $X$ contains in its rows $m$ vector columns (each with $n$ components) of the data set.\n",
        "\n",
        "Structure of a data matrix $X$:\n",
        "\n",
        "$$\n",
        "\\mathbf{X} = {\n",
        "  \\begin{bmatrix}\n",
        "    \\mathbf{x}^{(1)}\\\\\n",
        "    \\vdots \\\\\n",
        "    \\mathbf{x}^{(m)}\n",
        "  \\end{bmatrix}}^T = \n",
        "  {\\begin{bmatrix} \n",
        "    (\\mathbf{x}^{(1)})^T \\\\ \n",
        "    \\vdots \\\\ \n",
        "    (\\mathbf{x}^{(m)})^T \n",
        "  \\end{bmatrix}}\n",
        "$$\n",
        "\n",
        "Another way to interpret the above statement is to say that a data matrix $X$ contain the $m$ column vector as rows, and each column vector has $n$ components.\n",
        "\n",
        "$$\n",
        "\\mathbf{X} = {\\begin{bmatrix} (\\mathbf{x}^{(1)})^T \\\\ \\vdots \\\\ (\\mathbf{x}^{(m)})^T \\end{bmatrix}}\n",
        "$$\n",
        "\n",
        "We denote the entry in the $i$-th row and $j$-th column of $X$ by $x^{(i)}_j$. We define $\\mu_j$, the **mean** of the $j$-th column (feature) of $X$ as the following:\n",
        "\n",
        "$$\n",
        "{\\mu_j = \\displaystyle {\\frac {1}{m}}\\sum _{i=1}^{m}x_{j}^{(i)} } \n",
        "$$\n",
        "\n",
        "Notice that $\\mu_j \\in \\Re$. We can also think of $\\mathbf{\\mu} \\in \\Re^n$, the **sample mean vector** of a data matrix. The sample mean vector contains the average of the observations for each variable, and is written as the following:\n",
        "\n",
        "$$\n",
        "\\mathbf{\\mu} ={\\frac{1}{m}}\\sum _{i=1}^{m} \\mathbf{x}^{(i)} = {\\begin{bmatrix}{\\mu}_{1}\\\\\\vdots \\\\{\\mu}_{j}\\\\\\vdots \\\\{\\mu}_{n}\\end{bmatrix}}\n",
        "$$\n",
        "\n",
        "A data matrix is ​​said to be *centered* if all of its points (data vectors) have been transformed to subtract the corresponding mean vector. See the following example. Notice that centering the points in the original matrix results in them being just translated; the distances between them remain the same after the translation.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jn-T6VFBLnlg",
        "outputId": "6cd3673c-59bc-47f8-f858-b31fdc36ccba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        }
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "X = np.array([[0,0],[1/2,1/2],[0,1],[1,0],[1,1]])\n",
        "print('Original data matrix:\\n', X)\n",
        "\n",
        "X_centered = X - X.mean(axis=0)\n",
        "print('Centered data matrix:\\n', X_centered)"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Original data matrix:\n",
            " [[0.  0. ]\n",
            " [0.5 0.5]\n",
            " [0.  1. ]\n",
            " [1.  0. ]\n",
            " [1.  1. ]]\n",
            "Centered data matrix:\n",
            " [[-0.5 -0.5]\n",
            " [ 0.   0. ]\n",
            " [-0.5  0.5]\n",
            " [ 0.5 -0.5]\n",
            " [ 0.5  0.5]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kHV4y1FD4sEV",
        "outputId": "1a00aadb-5405-4240-85b6-b5340405db33",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
        "fig.suptitle('Data matrices before (left) and after (right) centering.')\n",
        "\n",
        "# plot data\n",
        "ax1.scatter(X[:, 0], X[:, 1])\n",
        "ax2.scatter(X_centered[:, 0], X_centered[:, 1])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f531709ab00>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        },
        {
          "output_type": "display_data",
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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CwHySm4jbLGI"
      },
      "source": [
        "## Variance and covariance\n",
        "\n",
        "Given two random variable $x$ and $y$, the covariance between $x$ and $y$ as follows:\n",
        "\n",
        "$$\n",
        "\\mathrm{cov}(x,y)=\\mathbf{E}{\n",
        "  \\begin{bmatrix}\n",
        "  (x-\\mathbf{\\mu}_x)(y-\\mathbf{\\mu}_y)\n",
        "  \\end{bmatrix}}=\\mathbf{E} \n",
        "  {\\begin{bmatrix}x y\\end{bmatrix}}-\\mathbf{\\mu}_{x}\\mathbf{\\mu}_{y}\n",
        "$$\n",
        "\n",
        "In the above expression, $\\mu_x$ and $\\mu_y$ are the means of $x$ and $y$, respectively, and $\\mathbf{E}[\\cdot]$ denotes the expected value.\n",
        "\n",
        "In the context of a data matrix, covariance measures the linear relationship (if any) between a pair of features. For example, suppose a data matrix has two features:\n",
        "\n",
        "* $x_j = \\text{number of hours of study}$\n",
        "* $x_k = \\text{final grade obtained}$ \n",
        "\n",
        "The value $\\mathrm{cov}(x_j,x_k)$ tells us whether those two variables are related, and, if so, what is the direction of such relationship.\n",
        "\n",
        "The covariance between a random variable and itself is the *variance* of this variable. This gives us a notion of the dispersion of the values of this variable around its mean. That is, variance is a measure of the deviation (from the mean) for points in one dimension. For example, we can compute the variance of the heights of a group of individuals to see how dispersed these values are.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "61G7pOT9bW2I"
      },
      "source": [
        "## Covariance matrix\n",
        "\n",
        "It is possible to organize the values of covariances between variables (features) of a $n$-dimensional data matrix into another matrix.The so called *covariance matrix* of a data matrix $X$ has order $n \\times n$. Given two attributes $x_j$ and $x_k$ in $X$, the entry $(j, k)$ in this matrix is ​​defined by the following:\n",
        "\n",
        "$$\n",
        "\\Sigma_{jk} = \\mathrm{cov}(x_j,x_k)\n",
        "$$\n",
        "\n",
        "Every covariance matrix is ​​symmetric with respect to the main diagonal, since $\\text{cov}(x_j,x_k) = \\text{cov}(x_k,x_j)$. The values ​​on the main diagonal of a covariance matrix correspond to the sample variances of each of the $n$ variables (features)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VvdbH38D20Ji"
      },
      "source": [
        "In a machine learning context, we will be working with [estimates of the covaviance matrix](https://en.wikipedia.org/wiki/Estimation_of_covariance_matrices), since we are going to build an approximation of the true covariance matriz considering only the samples from the data matrix $X$.\n",
        "\n",
        "$$\n",
        "\\Sigma_{jk} = {\\frac{1}{m-1}}\\sum _{i=1}^{m}\\left(x^{(i)}_{j}-{\\mu}_{j}\\right)\\left(x^{(i)}_{k}-{\\mu}_{k}\\right) \n",
        "$$\n",
        "\n",
        "The covariance matrix can be computed in a vectorized way:\n",
        "\n",
        "$$\n",
        "\\Sigma =\\frac{1}{m-1} X^T \\, X\n",
        "$$\n",
        "\n",
        "In the expression above, $X$ is the (*already centered*) data matrix.\n",
        "\n",
        "The code cell below shows how the sample covariance matrix of a data matrix $X$ can be computed."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5rvca_nNfOxD",
        "outputId": "b5cd23cb-28ea-4dff-9e33-57f758851097",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 242
        }
      },
      "source": [
        "X = np.array([[0, 2], [1, 1], [2, 0]])\n",
        "m =3\n",
        "print(X)\n",
        "\n",
        "X_centered = X - X.mean(axis=0)\n",
        "\n",
        "print('centered:')\n",
        "print(X_centered)\n",
        "\n",
        "print('cov:')\n",
        "temp = X_centered.T.dot(X_centered)\n",
        "temp = temp / (m-1)\n",
        "print(temp)\n",
        "\n",
        "from sklearn.covariance import EmpiricalCovariance\n",
        "\n",
        "cov = EmpiricalCovariance().fit(temp)\n",
        "\n",
        "print('Estimate of the covariance matrix:\\n', cov.covariance_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0 2]\n",
            " [1 1]\n",
            " [2 0]]\n",
            "centered:\n",
            "[[-1.  1.]\n",
            " [ 0.  0.]\n",
            " [ 1. -1.]]\n",
            "cov:\n",
            "[[ 1. -1.]\n",
            " [-1.  1.]]\n",
            "Estimate of the covariance matrix:\n",
            " [[ 1. -1.]\n",
            " [-1.  1.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1UHhJRcFmqqB"
      },
      "source": [
        "The code cell below ilustrates the difference between the real covariance matrix and the sample covariance matrix. Consider that the covariance matrix for these two variables is the following:\n",
        "\n",
        "\\begin{equation*} \n",
        "\t\\Sigma = \\begin{bmatrix} \\text{cov}(x,x) & \\text{cov}(x,y) \\\\[0.3em] \\text{cov}(y,x) & \\text{cov}(y,y) \\\\[0.3em] \\end{bmatrix}  = \\begin{bmatrix} 0.8 & 0.3 \\\\[0.3em] 0.3 & 0.4 \\\\[0.3em] \\end{bmatrix}\n",
        "\\end{equation*}\n",
        "\n",
        "The code cell below first build a sample of 500 pais of those two normally distributed random variables. The result is a data matrix with $n=2$ features and $m = 500$ examples. In the generated plot, notice how these two variable are somewhat positively correlated. After ploting the points, the class `EmpiricalCovariance` of Scikit-Learn is used to build an estimate of the covariance matriz using these points. By comparing the real covariance matrix and its estimate, you should conclude that the latter is a good approximation of the former. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_E6KjZxIUGby",
        "outputId": "a0e27483-023e-4975-80e5-ae2a42704582",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "import numpy as np\n",
        "from sklearn.covariance import EmpiricalCovariance\n",
        "from sklearn.datasets import make_gaussian_quantiles\n",
        "real_cov = np.array([[.8, .3],\n",
        "                     [.3, .4]])\n",
        "\n",
        "print('Real covariance matrix:\\n', real_cov)\n",
        "\n",
        "rng = np.random.RandomState(0)\n",
        "X = rng.multivariate_normal(mean=[0, 0], cov=real_cov, size=500)\n",
        "cov = EmpiricalCovariance().fit(X)\n",
        "\n",
        "plt.title('Data matrix $X$')\n",
        "plt.scatter(X[:, 0], X[:, 1])\n",
        "plt.show()\n",
        "\n",
        "print('Estimate of the covariance matrix:\\n', cov.covariance_)\n",
        "print('***')\n",
        "print('Estimate of the mean vector:\\n', cov.location_)"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Real covariance matrix:\n",
            " [[0.8 0.3]\n",
            " [0.3 0.4]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Estimate of the covariance matrix:\n",
            " [[0.75693565 0.28186631]\n",
            " [0.28186631 0.39288421]]\n",
            "***\n",
            "Estimate of the mean vector:\n",
            " [0.06228968 0.01937939]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hW8m5PrbdbP4"
      },
      "source": [
        "## Principal Component Analysis\n",
        "\n",
        "Principal Components Analysis (PCA) is the most popular algorithm to perform dimensionality reduction in a unsupervised way.\n",
        "\n",
        "Mathematically, PCA is defined as an orthogonal linear transformation that represents the data points in $X$ in a new coordinate system, so that the largest variance resides in the first coordinate (called the first principal component), the second largest variance resides in the second coordinate, and so on."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "czf0O_FvdmXe"
      },
      "source": [
        "### Projection error\n",
        "\n",
        "The new coordinate system is produced by the PCA in such a way as to minimize the **projection error** of the data on the smaller dimensional space.\n",
        "\n",
        "Mathematically, the projection error corresponds to the sum of the squares of the distances between each data point and the surface corresponding to the smaller dimensional space for which the points must be projected.\n",
        "\n",
        "To understand the concept of projection error, consider the following 2D data set:\n",
        "\n",
        "![alt text](https://i.stack.imgur.com/jPw90.png)\n",
        "\n",
        "The following animation ([source](https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues)) presents different lines of projections on which the set original data file (in 2D) can be designed. Each of these projection lines corresponds to a 1D dimensional space. For each projection line, each of the points located on it (points in red) corresponds to some point in the original space (points in blue).\n",
        "\n",
        "![alt text](https://i.stack.imgur.com/Q7HIP.gif)\n",
        "\n",
        "For a given projection line $R$, if we compute the square of the distance between each red point and the corresponding blue point (i.e., the lengths of the straight line segments in red) and add all these distances, we obtain the projection error related to the line $R$. In this example, note that\n",
        "\n",
        "* each projection line has its corresponding projection error.\n",
        "* each of these lines defines a new space determined by a vector (which defines the direction of the line).\n",
        "* the line that corresponds to the maximum data gap is the same that corresponds to the minimum projection error value.\n",
        "\n",
        "The objective of the PCA is to find the direction (s) of projection corresponding to the minimum possible projection error."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WWq9Fv5bdy81"
      },
      "source": [
        "### Formalization\n",
        "\n",
        "* 2 dimensions case $\\rightarrow$ 1 dimension: find a direction (i.e., a vector) on which to project the data, in such a way as to minimize the projection error.\n",
        "* (general case) $n$ dimensions $\\rightarrow$ $k$ dimensions: find $k$ directions (i.e., $k$ vectors) on which to project the data, in order to minimize the projection error."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nuavm0RUfJAl"
      },
      "source": [
        "### Pre-processing\n",
        "\n",
        "Before applying the PCA, it is necessary to centralize the data matrix $X$.\n",
        "\n",
        "Furthermore, if the scales of the various attributes in $ X $ are very different, *feature scaling* should be performed."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3r1MEkJjOPnN"
      },
      "source": [
        "### Linear Transformations\n",
        "\n",
        "Fundamental to understading PCA is the concept of linear transformations. Watch the video below to get a grasp on this subject."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qAMsQS-9OThx",
        "outputId": "06a9ef1e-e0f1-4633-8029-fca66a14de59",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 322
        }
      },
      "source": [
        "from IPython.display import YouTubeVideo\n",
        "YouTubeVideo('kYB8IZa5AuE')"
      ],
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "        <iframe\n",
              "            width=\"400\"\n",
              "            height=\"300\"\n",
              "            src=\"https://www.youtube.com/embed/kYB8IZa5AuE\"\n",
              "            frameborder=\"0\"\n",
              "            allowfullscreen\n",
              "        ></iframe>\n",
              "        "
            ],
            "text/plain": [
              "<IPython.lib.display.YouTubeVideo at 0x7f5317d01908>"
            ],
            "image/jpeg": 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\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 100
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dU-YkqZnmHMx"
      },
      "source": [
        "### Singular Values Decomposition ​​(SVD)\n",
        "\n",
        "By now, you should understand that linear tranformations are special functions that map one vector to another. You should also understand that a linear transformation can always be represented by a matrix in such a way that, when we multiply this matrix by a vector the resulting vector is produced.\n",
        "\n",
        "Formally, SVD is a way to factor a composite linear transformation represented by a matrix M into its component matrices. In particular, a matrix $M$ representing a composite linear transformatrion can be factorized: \n",
        "\n",
        "$$\n",
        "M = \\mathbf{U \\times \\Sigma \\times V}\n",
        "$$\n",
        "\n",
        "Intuitively, SVD produces a decomposition of the original matrix $M$ into matrices that either rotate or resize the input vectors. This way, applying $M$ to a vector $\\mathbf{v}$ is equivalent to applying the components matrices in sequence:\n",
        "\n",
        "$$\n",
        "M \\times \\mathbf{v}\\equiv U \\times (\\Sigma \\times (V \\times \\mathbf{v}))\n",
        "$$\n",
        "\n",
        "The following animation ([source](https://en.wikipedia.org/wiki/Singular_value_decomposition)) illustrates the mechanics of SVD. Two vectors are depicted (in yellow and red). You should see that the change in these vectors resulting from applying $M$ is the same obtained by applying $V$, $\\Sigma$ and $U$ (in this order) on them.\n",
        "\n",
        "![alt text](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Singular_value_decomposition.gif/280px-Singular_value_decomposition.gif)\n",
        "\n",
        "See also the following image.\n",
        "\n",
        "![alt text](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Singular-Value-Decomposition.svg/800px-Singular-Value-Decomposition.svg.png)\n",
        "\n",
        "NB: be aware of the chance in notation used in the above animation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ii2oY3N7fRKs"
      },
      "source": [
        "### Algorithm steps\n",
        "\n",
        "Consider using PCA to reduce the dimensionality of the (already centralized) $X$ data matrix from $n$ to $k$. To do this, the following steps should be performed:\n",
        "\n",
        "1. Compute $\\Sigma$, the covariance matrix of $X$:\n",
        "\n",
        "2. Compute the SVD decomposition of $\\Sigma$: $[U, S, V] := \\text{svd}(\\Sigma)$\n",
        "\n",
        "From this decomposition (step 2), the relevant matrix for PCA is ​​$U \\in \\Re^{n \\times n}$. This matrix contains the main components determined by PCA.\n",
        "\n",
        "$$\n",
        "U = \\begin{bmatrix}\n",
        "\\vert \t& \\vert \t& \t\t\t& \\vert \\\\ \n",
        "\\mathbf{u}^{(1)} & \\mathbf{u}^{(2)} & \\dots & \\mathbf{u}^{(n)}\\\\ \n",
        "\\vert \t& \\vert \t& \t\t\t& \\vert \n",
        "\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "After identifying the principal components, it is possible to reduce the size of the data set to $k$ dimensions, projecting it on the hyperplane defined by the first $k$ principal components. Selecting this hyperplane ensures that the projection will preserve the greatest possible variance. Consider the matrix $U_{redux}$ obtained from $U$: $U_{redux}$ contains the first $k$ columns of $U$:\n",
        "\n",
        "$$\n",
        "U_{redux} = \\begin{bmatrix}\n",
        "\\vert \t& \\vert \t& \t\t\t& \\vert \\\\ \n",
        "\\mathbf{u}^{(1)} & \\mathbf{u}^{(2)} & \\dots & \\mathbf{u}^{(k)}\\\\ \n",
        "\\vert \t& \\vert \t& \t\t\t& \\vert \n",
        "\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "To map the vector $\\mathbf{x}^{(i)} \\in \\Re^n$ to the vector $\\mathbf{z}^{(i)} \\in \\Re^k$, PCA computes:\n",
        "$$\n",
        "\\mathbf{z}^{(i)} = \\begin{bmatrix}\n",
        "\\vert \t& \\vert \t& \t\t\t& \\vert \\\\ \n",
        "\\mathbf{u}^{(1)} & \\mathbf{u}^{(2)} & \\dots & \\mathbf{u}^{(k)}\\\\ \n",
        "\\vert \t& \\vert \t& \t\t\t& \\vert \n",
        "\\end{bmatrix}^T \\, \\mathbf{x}^{(i)}\n",
        "$$\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1FSqTMLGbuJ0"
      },
      "source": [
        "### PCA: implementation with numpy and scipy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vzaOuhlXYWrW"
      },
      "source": [
        "import numpy as np\n",
        "from scipy import linalg as LA\n",
        "\n",
        "def pca(X, k):\n",
        "    # Data centering\n",
        "    mu = np.mean(X, axis = 0)\n",
        "    print('Mean vector: ' + str(mu))\n",
        "    centered_X = X - mu  \n",
        "    print('\\nCentered data matrix:\\n ' + str(centered_X))\n",
        "\n",
        "    C = np.cov(centered_X, rowvar = False)\n",
        "\n",
        "    # SVD decomposition on the covariance matrix\n",
        "    print('\\n***** SVD decomposition ****')\n",
        "    U, S, V = LA.svd(C)\n",
        "    print('U:\\n' + str(U))\n",
        "    print('S:\\n' + str(S))\n",
        "    print('V:\\n' + str(V))\n",
        "\n",
        "    # Verifying that the eigenvectors are unit vectors\n",
        "    print('\\nEigenvectors norms (columns of U):')\n",
        "    print(np.linalg.norm(U[:,0]), np.linalg.norm(U[:,1]), np.linalg.norm(U[:,2]))\n",
        "\n",
        "    print('\\nVariance percentages per component:\\n', str(S/np.sum(S) * 100))\n",
        "\n",
        "    # To project to k dimensions, we must compute U_redux\n",
        "    U_redux = U[:, 0:k]\n",
        "    print('\\nU_redux:\\n', str(U_redux))\n",
        "\n",
        "    # Now, we compute Z, the matrix of projected points in k-dimensional space.\n",
        "    Z = np.matmul(U_redux.T,X.T)\n",
        "    print('\\nProjected data matrix (k=' + str(k) + '):\\n' + str(Z.T))\n",
        "    \n",
        "    return U_redux, Z\n",
        "\n",
        "def restore(U_redux, Z):\n",
        "    print('\\nRestored data matrix:\\n' + str(np.matmul(U_redux, Z).T))"
      ],
      "execution_count": 99,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "100CG-X4YWra",
        "outputId": "d469c586-a185-47b2-b1ca-f70d269f772b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 777
        }
      },
      "source": [
        "X = np.array([\n",
        "        [0.387,  4878, 5.42],\n",
        "        [0.723, 12104, 5.25],\n",
        "        [1,     12756, 5.52],\n",
        "        [1.524,  6787, 3.94],\n",
        "    ])\n",
        "\n",
        "pca(X, 2)"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "**************\n",
            "Mean vector: [9.08500e-01 9.13125e+03 5.03250e+00]\n",
            "\n",
            "Centered data matrix:\n",
            " [[-5.21500e-01 -4.25325e+03  3.87500e-01]\n",
            " [-1.85500e-01  2.97275e+03  2.17500e-01]\n",
            " [ 9.15000e-02  3.62475e+03  4.87500e-01]\n",
            " [ 6.15500e-01 -2.34425e+03 -1.09250e+00]]\n",
            "\n",
            "***** SVD decomposition ****\n",
            "U:\n",
            "[[-1.21901390e-05  5.66460727e-01  8.24088736e-01]\n",
            " [-9.99999997e-01  5.32639789e-05 -5.14047691e-05]\n",
            " [-7.30130279e-05 -8.24088734e-01  5.66460725e-01]]\n",
            "S:\n",
            "[1.51872330e+07 6.70619604e-01 2.02485956e-02]\n",
            "V:\n",
            "[[-1.21901390e-05 -9.99999997e-01 -7.30130279e-05]\n",
            " [ 5.66460727e-01  5.32639789e-05 -8.24088734e-01]\n",
            " [ 8.24088736e-01 -5.14047691e-05  5.66460725e-01]]\n",
            "\n",
            "Eigenvectors norms (columns of U):\n",
            "0.9999999999999998 0.9999999999999997 0.9999999999999998\n",
            "\n",
            "Variance percentages per component:\n",
            " [9.99999955e+01 4.41567976e-06 1.33326424e-07]\n",
            "\n",
            "U_redux:\n",
            " [[-1.21901390e-05  5.66460727e-01]\n",
            " [-9.99999997e-01  5.32639789e-05]\n",
            " [-7.30130279e-05 -8.24088734e-01]]\n",
            "\n",
            "Projected data matrix (k=2):\n",
            "[[-4.87800039e+03 -3.98751895e+00]\n",
            " [-1.21040004e+04 -3.27220755e+00]\n",
            " [-1.27560004e+04 -3.30307377e+00]\n",
            " [-6.78700029e+03 -2.02212084e+00]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[-1.21901390e-05,  5.66460727e-01],\n",
              "        [-9.99999997e-01,  5.32639789e-05],\n",
              "        [-7.30130279e-05, -8.24088734e-01]]),\n",
              " array([[-4.87800039e+03, -1.21040004e+04, -1.27560004e+04,\n",
              "         -6.78700029e+03],\n",
              "        [-3.98751895e+00, -3.27220755e+00, -3.30307377e+00,\n",
              "         -2.02212084e+00]]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 98
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-o5WlQ7HYWre",
        "outputId": "4f198eb0-6f69-4e30-e388-1d39d5b15c07",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 743
        }
      },
      "source": [
        "X = np.array([\n",
        "        [1,  -2, -.05],\n",
        "        [2, 4, +.05],\n",
        "        [4, -8, -.1],\n",
        "        [8,  16, +.1],\n",
        "    ])\n",
        "U_redux, Z = pca(X, k=2)\n",
        "\n",
        "restore(U_redux, Z)"
      ],
      "execution_count": 101,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean vector: [3.75 2.5  0.  ]\n",
            "\n",
            "Centered data matrix:\n",
            " [[ -2.75  -4.5   -0.05]\n",
            " [ -1.75   1.5    0.05]\n",
            " [  0.25 -10.5   -0.1 ]\n",
            " [  4.25  13.5    0.1 ]]\n",
            "\n",
            "***** SVD decomposition ****\n",
            "U:\n",
            "[[-0.21011096  0.97765515  0.00661783]\n",
            " [-0.97764219 -0.21004099 -0.00992594]\n",
            " [-0.00831413 -0.00855542  0.99992884]]\n",
            "S:\n",
            "[1.09628348e+02 4.96292646e+00 3.92101053e-04]\n",
            "V:\n",
            "[[-0.21011096 -0.97764219 -0.00831413]\n",
            " [ 0.97765515 -0.21004099 -0.00855542]\n",
            " [ 0.00661783 -0.00992594  0.99992884]]\n",
            "\n",
            "Eigenvectors norms (columns of U):\n",
            "1.0000000000000002 1.0 0.9999999999999999\n",
            "\n",
            "Variance percentages per component:\n",
            " [9.56686915e+01 4.33096630e+00 3.42172398e-04]\n",
            "\n",
            "U_redux:\n",
            " [[-0.21011096  0.97765515]\n",
            " [-0.97764219 -0.21004099]\n",
            " [-0.00831413 -0.00855542]]\n",
            "\n",
            "Projected data matrix (k=2):\n",
            "[[  1.74558913   1.3981649 ]\n",
            " [ -4.33120641   1.11471857]\n",
            " [  6.98152512   5.59180404]\n",
            " [-17.32399421   4.45972983]]\n",
            "\n",
            "Restored data matrix:\n",
            "[[ 1.0001557  -2.00023352 -0.02647493]\n",
            " [ 1.99984429  4.00023354  0.02647331]\n",
            " [ 3.99996105 -7.99994158 -0.1058855 ]\n",
            " [ 8.00003891 15.99994164  0.10587902]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GsLdRiK_eEo0"
      },
      "source": [
        "### PCA on Scikit-Learn\n",
        "\n",
        "In Scikit-Learn, the class [sklearn.decomposition.PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) implements PCA. This class project point in the the input data matrix $X$ to a smaller dimensional space. The data matrix is ​​centralized, but its attributes are not resized, before applying the SVD decomposition.\n",
        "\n",
        "```\n",
        "from sklearn.decomposition import PCA\n",
        "pca = PCA(n_components = 2)\n",
        "X_reduced = pca.fit_transform(X)\n",
        "```\n",
        "\n",
        "Instead of specifying the number of principal components to be preserved, it is possible to define `n_components` as a number between 0.0 and 1.0, to indicate the proportion of variance to be maintained:\n",
        "\n",
        "```\n",
        "from sklearn.decomposition import PCA\n",
        "pca = PCA(ncomponents = 0.95)\n",
        "X_reduced = pca.fit_transform(X)\n",
        "```\n",
        "\n",
        "After applying the transformer to the $X$, the principal components are stored in the variable `components_`. This variable contains PCs as horizontal vectors. So, for example, the first major component is the same as `pca.components_.T [:, 0])`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "84F2YiA-RzjC"
      },
      "source": [
        "As an example of using the class [sklearn.decomposition.PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html), consider the following two-dimensional toy dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J5Kqq31EUtec",
        "outputId": "278f319a-0b87-4079-f5b5-1d72fb3fb0b0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "rng = np.random.RandomState(42)\n",
        "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
        "\n",
        "plt.scatter(X[:, 0], X[:, 1])\n",
        "plt.axis('equal');"
      ],
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD4CAYAAADxeG0DAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAcv0lEQVR4nO3dbYxcV3kH8P+z40kyGyjrkFVLJl5sUmqD49irbENafwAbilOclyUhccNLRflgIRWJROmiDVCctCBWWoUECaQqhaqtEgWHJCwhBjlBtoTq1inrrE1iYiPAsZMJFQvJhhdP8Hj36Yfdu7lz55z7MvfO3Jf5/yRL2Zmde8+Oss+cfc5zniOqCiIiyq++tAdARETxMJATEeUcAzkRUc4xkBMR5RwDORFRzq1I46YXXnihrl69Oo1bExHl1qFDh36lqoPex1MJ5KtXr8b09HQatyYiyi0ROWl6nKkVIqKcYyAnIso5BnIiopxjICciyjkGciKinEulaoWIKA+mZmqY3HscL87VcdFABWPb1mJ0uJr2sFowkBMRGUzN1HD7I0+j3pgHANTm6rj9kacBIHPBnKkVIiKDyb3Hl4O4o96Yx+Te4ymNyI6BnIjI4MW5eqTH08RATkRkcNFAJdLjaWIgJyIyGNu2FpVyqemxSrmEsW1rUxqRHRc7iYgMnAVNVq0QEeXY6HA1k4Hbi6kVIqKc44yciFKRl802ecBATkRdl6fNNnnA1AoRdV2eNtvkAQM5EXVdnjbb5AEDORF1XZ422+QBAzkRdV2eNtvkARc7iQoui9UhedpskwcM5EQFluXqkLxstskDplaICozVIb2BgZyowFgd0hsYyIkKjNUhvYGBnKjAwlSHTM3UsHliH9aM78HmiX2Ymql1e5gUExc7iQosqDoky4uhFB4DOVHB+VWH+C2GMpDnB1MrRD2Mi6HFwEBO1MO4GFoMDOREPcy2GLpl3SAXQHMkdo5cRFYB+E8AfwxAAdyrql+Oe10i6jzTYuiWdYN4+FCNC6A5Iqoa7wIibwLwJlV9SkReD+AQgFFV/bHtNSMjIzo9PR3rvkTUGZsn9qFmyJFXByo4ML41hRGRQ0QOqeqI9/HYqRVV/YWqPrX0378F8CwAfmwT5RQXQPMn0Ry5iKwGMAzgScNzO0VkWkSmZ2dnk7wtESWIC6D5k1ggF5HXAXgYwC2q+hvv86p6r6qOqOrI4OBgUrclooRF7RXOnaHpS2RDkIiUsRjE71fVR5K4JhGlI0qvcO4MzYYkqlYEwNcBPKuqX4o/JCJKW9he4dwZmg1JpFY2A/gIgK0icnjp3/sSuC4RZRwXRrMh9oxcVf8LgCQwFiLKmYsGKsZSRS6Mdhd3dhJR23iIcjaw+yERtY2HKGcDAzkRxcJDlNPH1AoRUc4xkBMR5RwDORFRzjGQExHlHAM5EVHOMZATEeUcyw+JPKZmah2ri+7ktTt57zTHTcEYyIlcOtnNL+janf4AaffnYofD7GNqhcjFr5tfJ6/tBMvaXB2K14JlUr294/xcnXxPKBkM5EQunezm53ftTgfLOD8XOxxmH1MrRC5JdfMzpUn8rt3pYBnn52KHw+zjjJzIJW43v6mZGjbd+Thu2X24JU2yZd2g9dqdPiczzs/FDofZx0BO5DI6XMUXr9+A6kAFAqA6UMEXr98QalHPyXPP1Rstz9Ub89h/bNZ67U4Hyzg/V5zXUneIqnb9piMjIzo9Pd31+xJ10uaJfcYUhEMAnJjYbn2+WyV+LCXMLxE5pKoj3seZIydKSFA+OyhN0o12sCwlLCamVogS4heos5JTZilhMTGQEyXElOcGgJX95czklFlKWExMrRAlJA/HnrGUsJg4IydK0OhwFQfGt+LuHZsAALfuPozNE/tC79Ccmqlh88Q+rBnfE+l1YbGUsJg4IyeKyVsFsmXdIB4+VIu8oBi3H8odjx5dLn1c2V/GrmvWt7wuD381UHQsPySKwRt8gcUyQ9NvVXWgggPjW43XmNx73Fq6aHud+/Vj3zyCxkLzXcslweQHNkYK0ixNzDaWHxJ1gKkKxDY1MgVq0weBV9BC5OTe4y1BHAAa84rJvceXA3FQkGZpYn4xkBNF4A2GfhuAvEoiLY+ZPgi8+kSwZnyPdYbsF+id58IEab/SRAbybONiJ1FIplazraHZbt6QxgxT9jev6tva1q/ixHkuTP04SxPzK5FALiL/JiK/FJFnkrgeURbZ0ihhg/nK/nLLY35B2DSDN23eGdu2FuW+1u8tl2S5GiVMkO504y7qnKRm5P8O4KqErkWUSbZgqEBTQ6n+svnXylRXYCsHvGfHJixYChG84xgdrmLyxo0YqLz2QbGyv9y00BkmSLM0Mb8SyZGr6g9EZHUS1yLKKltO3FtVsmZ8j/H1rxi6IvqVA9oqWUxBOahPy9i2tS2Lqt4gzdLE/Eqs/HApkD+mqpdant8JYCcADA0NXX7y5MlE7kvULaYKk0q51LL93tYFsSSCu24KXw5oul+5T/C681Zg7nSjJdCGqUphkM43W/lh1wK5G+vIKSndDk5h7udXUmgK/GHv94ZKGb8/cxaN+dd+Z53rAQj1IUP5xkBOhRN2hpyGz049jfsOnjI+F7TBx8Y2068upVrCpH0o37ghiAonq3XPUzM1PPDk89bnvQHXNssPW7Mepo6cii2RQC4iDwB4F4ALReQFALtU9etJXJvIptt1z2H6mTh/JZhqxh3uskLbRp3pky+19Guxbf0f6C+j/5wV7GrYw5KqWrk5iesQRdGNlqx+fVBePt3A2ENHAPjvjvRyB3nbXxUPPPl8y4eB7aPhd6+exfbL3tQU+AFz6SAXPIuJOzsptzpd9+zeyWnj9DNxhPlrwMlpT83UrNf2m9G3jGFBfQ92dph2ppp2ilL+MEdOudXpuucws2tgMSAO/9Pj2HXN+sD+K84HzdRMbXk2n4QX5+qBteRZXVOg+BjIKdc6eWBxlFy7k2bZ8eerWlIcTm676vqg2Tyxr6mMMIxKuYRzV/Qt5+jdgtJJfrN/LojmH1MrRBZRc+2N+eYUB7C4sOkN4kD44FkSaUqV3HHt+sjpJCelYsMF0fzjjJzIwrStPYiT4gBgrUbZf2zWunDpNa/a8iEAREsn+aWI2EulGBjIiSyc4Hjnd47i5dOt6QyToLax9x88FTqIO7y9w6Omk/xm/1nYPEXxMbVCtMR08PHocBX954Sb75RLgi3rBq07MAF7CWEQU/vasGypk+pAhUG8IBjIieBfmhcmn91f7lte6IxyalAU7S5Ksj1t8TG1QoUQd6OLX2lemCPdFILHjvwiUj49qnYXJdmetvgYyCn3kjg02G+7/907NuHW3Yd90yL1xnxbQbzcJ4AgsBQx7gy6k2WalD6mVij3wpxH6WdqpoY+w7FqwOIseHS4ig9dORTpfM4wSiKYvHEjJj+wsWlH5j07NuGeHZt8d2kSuXFGTrnXTvMsdw8VWzMq9yz486MbMPLmC6x9V9qxoLocnE1BmoGbwmIgp9zza55lyp0DzTXepiBeEmmZBTvpiamZGm7ZfTiRcRMlgakVyj1TVYYAWP3GCsYeOtJUiTL20BHc8ejRwHy2e7bsNTpcbTrouB3uE+6J4uKMnHJvdLiK6ZMvNW22UQAHfvZSy/c25tXYq8SrTwRrxvcsz+KnT7603Fq2JIIr37IST516pa0FzvPPKeEL72fOm5KT2FFvUfCoN0qa3yacuPoEWDD8mmy+5AI89+s6Xlya8duURLCgiosGKtiybhD7j82yDJDaYjvqjakVKoSom2VMqRig+fQehymIA8DBn7+MA+NbcWJiu++9bn7HKpyY2I6xbWuXNwyxHzgliYGcCiHKwuFApdxyCMPdOzbhuYntWIjwF6r78Ieqz/0fPlRbXnSNUyZJZMMcOaXGW1ESJ+1g6lRY7hPMqzbNqMt9gjuuXW/dIBNmF6fDPXsf27YWYw8dMW7sqTfmccejR/GKJTfPfuAUFwM5pcK0G/O+g6eWn4+6O9O2Dd30mPf4M++HifdgCFuO/Mq3rGy6v/tgZq+5egMDlXJbh0IE4TmcxMVOSkXYxcnqQAUHxrd2ZAyfnXq6pa1spVzCDZdXW/4y+Ob0KWMVjEMECPpVWtlfxquNhZYDkuPs2vR+ICZxTcouLnZSpoRNJ8RNO5ha0zqPm3qDOyfYe2e3z/06oGlWiPnQ3OlG4AHJUX8O5t0JYGqFUhI2F+1NO0RJI/g105rce9xaMugsYrq/P4k8drspFL+fo532BFQ8nJFTKky7Mb28Hf/8eoab+M1WwwY6dyvbOCrlErasG4w0fkdQi10Tbv/vLQzklIrR4WpLmuHDVw75ph2iphH8ZqsD/eG32L84Vw/1weO2sr/c8rPsPzbbVhrE7+fgoREEMLVCKYrSI3tqxn7yTm2ujs0T+1rKF8slwRlDOaAC+EOErfVOK1sAobofVsol7LpmfcvPdqul0VbQXwd+TcF4aAQBDOSUA05KxY+pfNHP6cZCqHu7Z7fuD54P/ev/GKtYBirl5Tp1L7+A7MdUI28bF/WmRAK5iFwF4MsASgC+pqoTSVyXCDCnVDplZX8Z/eesaKlF33Tn48s14OefU8Lvz9jHYwuqQQE56HqcdZNN7EAuIiUAXwXwVwBeAPBDEXlUVX8c99pEfimVpJlSIlMzNYx98wgarh1BfkF8rt5oKg00Bd52AjJn3eQniRn5FQB+qqo/BwAR+QaA6wAwkFMszoadbjAdJDE1U8NtDx5p6qkSxqcf+REUYj1DlAGZkpZEIK8CeN719QsA3uH9JhHZCWAnAAwNDSVwWyoy24adTnGaZW2e2Ldc1fK7V89GDuKAOf/uVKcwiFMndK38UFXvVdURVR0ZHBzs1m0pp/w27HTCGyrlphrvl083mtIpSehWioh6TxKBvAZglevri5ceI7JuLQ/S7Z2JjfmFSAuqpT5BpRzt10cA9h6njkgitfJDAG8VkTVYDOB/A+CDCVyXcsp2Qr2to6Fp232UdrJe/eW+0OWFDr8FTK+V/eXlRdHV43tCv04BpleoI2LPyFX1LIBPANgL4FkAD6rq0bjXpXxyb6MHWk+o9+5ktG2737JuMNJOSrdz23xdkEq5hHt2bMLM5967HIyjHsLMHijUCYnkyFX1u6r6Z6p6iap+IYlrUj6Fqfl2BzPbtvv9x2abtvCff0644CxYzG9HVSn3+X5wOKcKeWfTd1y7HuW+5uPhyn2ClZYWAOyBQp3AXiuUqDAzTncw8+sjMjpcxYHxrbh7xybruZlu7jROVGcXFDdcXl0+ss17cucfzppTNaPDVUzeuLGpr8rkjRux65r17IFCXcMt+pSooNy2N5iF2bYeZpZfEmmrVNDRmFfsPzaLA+NbjYde+JUP+tWGczcmdQMDOSXKtA3dmSlXDcEszLb1oFm+cyJOmIZWfguhtbm67+Jl1Pw2N/9QtzCQU6KibkN3Hnefd3mep6zPb5bv/XAI8yES9pg5L+a3KasYyClx7cxE3Tnol083msoUbbN27+Jj2A+RsW1rW/qnBGF+m7KMgZy6ylQz7ndghPtDIcwsP/SHiHc1MwAPM6YsYyCnrrGdPWlbyHTnpNuZ5dvO95zcexwNw4ETNlXXAQ5EWcRATl1jm3nbKk5MOemwhy+3c2CxCVMqlAesI6eusQXQedVQNddRDl9u58BiL9O5oURZxEBOXWMLoCWR5c04toOXgWiHL0c9sNhNADw3sR0HxrcyiFMuMLVCibOlP0zVJ8DijPzhQ7XA2a9fcPYKc2Cx7dCIAcv2eqKs4oycEuWX/hgdruKL129ASVpLRmwzazfbjN70uGnW7T2w+K6bNqJcah3L7149y3azlCsM5JSooPTH6HB1+TQer9pc3bd3eVBwdnM+NPzSNaPDVZx/TusfpY0FDfxQIcoSplYoUWHSH7a0h+C1U3RMvcvb2TUalON+pW7ulMh2s5QnDOQUmzsn3heilNC2s9LUu/y2B48AaA7m3kMpnHM222lMFaZpF1HWMbVCsXhz4qYgbkx/hNxZOa9qLTGMUo5oEyVdQ5RVnJFTKH67JE07M0siWFA1zpKj7qy0tZAN2tofZvNQ1HQNURYxkFOgdnZJLqjixMR243Pt5J9Nr/HLx/uN2RTMGbgpzxjIKVDQLkm/HHNSByubarv97h00WycqEubIKVDUXZJOjtnvYOWIzQeNtd1b1g0av3fLusFIm4eI8o6BnAL5bcTxq9f2O1j5Q1cORQrm3truqZkaHnjyeeP37j82G2nzEFHeMbVCgYKOY7PlmP1mxZ8f3YCRN1/QlHZZ/cYK/vtnL1kPUHau58z0bWd0vjhXx907NgUeIUdUFAzkFKjdyo6g/LnpA2BqpmbtgeK8LugwZnc/FVajUC9gIKdQ2qns2LJuEPcfPNUyw67N1fG2f/weziuXMHe60RRkbWdvumfTfnnuMH8pEBUNAzklbmqm1nSYskm9sYD60mn23tLAoNm0baZfEmH/cOpJopY8YyeNjIzo9PR01+9Lneet346iOlDBgfGtbd3DdBgzUdGIyCFVHfE+zhk5JSoof+0nbG05899EzWIFchG5EcAdAN4G4ApV5TS7gMKekwnEq9OWpXvZrh1lHES9JG4d+TMArgfwgwTGQhkUtTFVnDptBax9wNttkOV0R7T1OCcqglgzclV9FgDEcOILFUPUre6249zCqi31SQnbIOuW3Ycxufc4tqwbxP5js02zdQCh+60Q5VnXcuQishPATgAYGhrq1m0J8VISUbe6jw5XMX3yJdx38FTb4zUFW7+UTW2u3nQ/J2Cfu6KP/VaoJwSmVkTk+yLyjOHfdVFupKr3quqIqo4MDpp7ZFDy4vbsjrrVfWqmhocPxUtfmM7vjJqyqTfmreWP7LdCRRMYyFX1Pap6qeHft7sxQIon6AzNIKamWILFzT6m/HOUqhXTwccOb7A1jaNd7LdCRcOmWQUXtwvg6HAVN1xebWpwpQB2/+/zGHvoSMtM36+EsE+Alf3l5eZakx/YiKolqL6hUm76kACw3JwrrJX9ZZ7+Qz0hViAXkfeLyAsA/gLAHhHZm8ywKClJdAHcf2y2ZZt9Y0FbTvmpN+ZR8ln4Lolg1zXrcWJiOw6Mb8XocNU40y73CX5/5mzLhwQAHBjfint2bAqcnVfKJey6Zr21MyNRkcStWvkWgG8lNBbqgKDOhWFEySnbOhICr7WidQdS0+ae02fO4uXTzflt9yKl6TWmqhX3gc1ERcadnQWXxC7Idk70sTFdx9vcas34HuNr3R8obIhF9BoG8h4QN+iZZvXlPgEEkQ5RBoJ3bwLB7W+JqBkXOwsuiZ2NplOAJm/cuLxYGWU7mN/uTYff8XFE1Ioz8gKLcpJ8ENus3nls88S+0OmXoJy7c807v3N0OVd+7grOOYhs+NtRYHFryKOw1ZubhE2RvLrUrxwA5uqNSBuZiHoJA3mBdfMkeafe3Ck/LIngLy+5oO0USTc/hIjyjoG8wLp5kryzNd8pP5xXxVOnXsENl1fbquPu5ocQUd4xR15gSdSQh2WbQe8/Nhvq1B8vVq4QhccZeYGZqk06tbPRbwbdTuUMK1eIwuOZneQrqAWu87ytYqW/3AeFtHW+Jk8EImpmO7OTgZysgg45DnPQsghg+l8s7EHLRPQaHr5ccJ2Yvdry3rc9eAS37j6MPhHf3iqAOYgD4Q9aJqJgzJEXQNzDI2xsee95VSj8G2Q5bN0Qna36RBQfA3kBdKrmOm6FSKVcws3vWGXcGBRmqz4RhcNAXgCdqrlu51QeJ2g7FTKfH93Q0ss8qfER0SLmyAugUzXX3ha4tpx4SQQLqtbcfJU14UQdxRl5Adj6nNTm6m13PHSMDldxYHwrTkxsx103bTTWdt9100acmNiOsW1rMbn3eEu9OGvCiTqLM/ICcM+ca3N1CLCczojT8dDvPt7qmDCdFlkTTtQZrCMvGFs72U7Xbad1X6JeYqsjZ2qlYGwLiLW5eqzDJdq9Lxc0iTqPgbxg/BYQk6wxD3tfLmgSdR4DecGEKRmsN+Zx53eOxj4CLui+XNAk6g4udhaMd2HRtgLy8unG8jFqSSyIckGTKD1c7Cy4S27/bqit9AAXJomyjoudPSpsEAe4MEmUVwzkBVeNsNjIhUmifGIgLzjTImS5JCj3Nbey4sIkUX5xsbPgbIuQpse4MEmUT7EWO0VkEsA1AM4A+BmAv1PVuaDXcbEzWTwSjag3dGqx8wkAl6rqZQB+AuD2mNejiDp1qAQR5UesQK6qj6vq2aUvDwK4OP6QelvUE+c7dagEEeVHkjnyjwHYbXtSRHYC2AkAQ0NDCd62OMJ0EPRijxMiCpyRi8j3ReQZw7/rXN/zGQBnAdxvu46q3quqI6o6Mjg4mMzoC6ad2TV7nBBR4IxcVd/j97yIfBTA1QDerWlsEy2QdmbXY9vWNs3iAZYSEvWaWKkVEbkKwKcAvFNVTyczpN7VzpFt7HFCRHFz5F8BcC6AJ0QEAA6q6sdjj6pHtTu7Hh2uMnAT9bBYgVxV/zSpgRBn10TUHu7szBjOrokoKvZaISLKOQZyIqKcYyAnIso5BnIiopxjICciyjkGciKinGMgJyLKOQZyIqKc44agguKpQUS9g4G8gNrpa05E+cXUSgHx1CCi3sJAXkA8NYiotzCQFxBPDSLqLQzkBTS2bS0q5VLTYzw1iKi4uNhZQOxrTtRbGMgLin3NiXoHUytERDnXkzNybpYhoiLpuUDOzTJEVDQ9l1rhZhkiKpqeC+TcLENERdNzgZybZYioaHoukHOzDBEVTc8tdnKzDBEVTc8FcoCbZYioWHoutUJEVDSxArmI/LOI/EhEDovI4yJyUVIDIyKicOLOyCdV9TJV3QTgMQCfS2BMREQUQaxArqq/cX15PgCNNxwiIooq9mKniHwBwN8CeAXAFp/v2wlgJwAMDQ3FvS0RES0RVf9JtIh8H8CfGJ76jKp+2/V9twM4T1V3Bd5UZBbAyYhjdbsQwK9ivL7o+P4E43vkj+9PsDTeozer6qD3wcBAHpaIDAH4rqpemsgF/e81raojnb5PXvH9Ccb3yB/fn2BZeo/iVq281fXldQCOxRsOERFFFTdHPiEiawEsYDFV8vH4QyIioihiBXJVvSGpgUR0b0r3zQu+P8H4Hvnj+xMsM+9RYjlyIiJKB7foExHlHAM5EVHO5TqQi8htIqIicmHaY8kaEZkUkWNLvXC+JSIDaY8pC0TkKhE5LiI/FZHxtMeTNSKySkT2i8iPReSoiHwy7TFlkYiURGRGRB5LeyxAjgO5iKwC8F4Ap9IeS0Y9AeBSVb0MwE8A3J7yeFInIiUAXwXw1wDeDuBmEXl7uqPKnLMAblPVtwO4EsDf8z0y+iSAZ9MehCO3gRzA3QA+BfZ3MVLVx1X17NKXBwFcnOZ4MuIKAD9V1Z+r6hkA38Di/gdaoqq/UNWnlv77t1gMVmze7yIiFwPYDuBraY/FkctALiLXAaip6pG0x5ITHwPwvbQHkQFVAM+7vn4BDFJWIrIawDCAJ9MdSebcg8VJ5ELaA3Fk9oQgvx4vAD6NxbRKTwvTB0dEPoPFP5fv7+bYKN9E5HUAHgZwi6fLaU8TkasB/FJVD4nIu9IejyOzgVxV32N6XEQ2AFgD4IiIAIspg6dE5ApV/b8uDjF1tvfIISIfBXA1gHcrNwwAQA3AKtfXFy89Ri4iUsZiEL9fVR9JezwZsxnAtSLyPgDnAfgjEblPVT+c5qByvyFIRJ4DMKKq7NTmIiJXAfgSgHeq6mza48kCEVmBxYXfd2MxgP8QwAdV9WiqA8sQWZwd/QeAl1T1lrTHk2VLM/J/UNWr0x5LLnPkFMpXALwewBNLR/H9S9oDStvS4u8nAOzF4iLegwziLTYD+AiArUv/3xxemn1ShuV+Rk5E1Os4IyciyjkGciKinGMgJyLKOQZyIqKcYyAnIso5BnIiopxjICciyrn/B7xd6ZijvR16AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9p323TGOSDSd"
      },
      "source": [
        "By visually inspecting the plot presented above, you should notice that there exists a positive correlation between the two variables: greater values of one of the variables correspond to greater values of the other variable, and vice-versa. We can confirm this by inspecting the empirical covariance matrix. See the code cell below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2eapih76SDjU",
        "outputId": "857870d6-8ca5-4395-a667-7638dfa8661c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "from sklearn.covariance import EmpiricalCovariance\n",
        "cov = EmpiricalCovariance().fit(X)\n",
        "print(cov.covariance_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.67876672 0.22978007]\n",
            " [0.22978007 0.09833763]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VwUy_BHuTHHD"
      },
      "source": [
        "The following code instantiates the PCA class of Scikit-Learn and invokes the `fit` method to compute the principal components for $X$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fQ82roEwUzQa",
        "outputId": "922630ee-ad41-4a06-ca4d-462f713f9af6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "pca = PCA(n_components=2)\n",
        "pca.fit(X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
              "    svd_solver='auto', tol=0.0, whiten=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fp-amk_OU48j",
        "outputId": "b0ad8078-fbe0-4365-b2df-5fa07d36c142",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "print(pca.components_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.94446029 -0.32862557]\n",
            " [-0.32862557  0.94446029]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R-A8K4pQU5hM",
        "outputId": "75b21215-5d4e-4e12-8a1a-9f64b5789c0d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(pca.explained_variance_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.7625315 0.0184779]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HNPofhp_TZRI"
      },
      "source": [
        "We can have a greater intuition about the meaning of the principal components through the following visualization."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mtxWpKFZVKIH",
        "outputId": "cf8033a7-eb54-44d7-d47f-eaa346652d63",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "# fonte: https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html\n",
        "import matplotlib.pyplot as plt\n",
        "def draw_vector(v0, v1, ax=None):\n",
        "    ax = ax or plt.gca()\n",
        "    arrowprops=dict(arrowstyle='->',\n",
        "                    linewidth=2,\n",
        "                    shrinkA=0, shrinkB=0)\n",
        "    ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
        "\n",
        "# plot data\n",
        "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
        "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
        "    v = vector * 3 * np.sqrt(length)\n",
        "    draw_vector(pca.mean_, pca.mean_ + v)\n",
        "plt.axis('equal');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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vvrqDfPv0KGGfm7pgufpmXdBHxi7y3XfOc8uOhkoHeno4TUvEz/bGcKUNmYJzye/UGLhu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\nGvX/A7y8SRLJIz1yAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AebQxMIrWfJl"
      },
      "source": [
        "In the visualization presented above, the vectors represent the main axes of the data in the new coordinate system determined by PCA. In addition, the length of each vector is an indication of how \"important\" the corresponding axis is in the description of the data distribution. More precisely, it is a measure of the variance of the data when projected for that axis."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "du3gKhXjj7jP"
      },
      "source": [
        "### PCA applications\n",
        "\n",
        "* Reduction of memory required for data storage.\n",
        "\n",
        "* Acceleration of learning algorithms: PCA can be applied to reduce the dimensionality of a data matrix before applying some learning algorithm. The resulting projected data matrix will usually be processed faster due to the lower number of features.\n",
        "\n",
        "* Preview: PCA can be used as an exploratory data analysis tool. In such context, we can apply PCA to reduce a dataset to 2 or 3 dimensions, in order to visually inspect its points and get some insight."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I0-V6jURPXLc"
      },
      "source": [
        "### Finding the intrinsic dimension\n",
        "\n",
        "An important procedure when using PCA is to estimate how many components are needed to adequately describe the data. This quantity is called [intrinsic dimension](https://en.wikipedia.org/wiki/Intrinsic_dimension) of the data set.\n",
        "\n",
        "The intrinsic dimension can be determined by looking at the accumulated explained variance rate as a function of the number of components.\n",
        "\n",
        "The following example uses the data set [digits](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_digits.html) to illustrate this process ([source](https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html))."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NWO37P2YOlqW",
        "outputId": "4b0158ee-24a7-44d2-bdb9-bb4d49b61580",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        }
      },
      "source": [
        "from sklearn.datasets import load_digits\n",
        "import matplotlib.pyplot as plt\n",
        "digits = load_digits()\n",
        "digits.data.shape\n",
        "\n",
        "pca = PCA(2)  # project from 64 to 2 dimensions\n",
        "projected = pca.fit_transform(digits.data)\n",
        "print(digits.data.shape)\n",
        "print(projected.shape)\n",
        "\n",
        "plt.scatter(projected[:, 0], projected[:, 1],\n",
        "            c=digits.target, edgecolor='none', alpha=0.5,\n",
        "            cmap=plt.cm.get_cmap('Blues', 10))\n",
        "plt.xlabel('component 1')\n",
        "plt.ylabel('component 2')\n",
        "plt.colorbar();"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1797, 64)\n",
            "(1797, 2)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Vi0rb56OnivzXv/CTVKpNCtkUqeT+lnA+m+T5p07w7Zcvd7dNjOaYnxnlC19+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\nDfH/rzXj5I8Zw7sAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sfg765yoPH2k",
        "outputId": "bef0f19e-3ea3-4a49-ff94-91b07c838b1d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "pca = PCA().fit(digits.data)\n",
        "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
        "plt.xlabel('number of components')\n",
        "plt.ylabel('cumulative explained variance')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gpKOIiCQqUn+Ddh54EviHmPIkYvmWetzVk1lEJMrpow+nLeYBU4DG2BIlYJnG\nPBIRAaL1aL447XErsIbgFFKX8dbmOkoL8xnat1vSUUREEhWlTeGaoxEkScs213HcgDLy8izpKCIi\niYpy+mgE8CVgePr27p6Rg9odjmWb6/jACQOSjiEikrgop4+eBH4D/AlIxRvn6GufWEeNzCIi0YpC\no7v/d+xJEqKJdURE9ohSFH5uZt8G/gI0ta9093mxpTqKNLGOiMgeUYrCeILhs89hz+kjD5eznibW\nERHZI0pR+Cgw0t2b4w6TBE2sIyKyR5QezYuB3nEHSYIm1hER2VuUI4XewFtmNpu92xSy/pJUTawj\nIrK3KEXh27GnSIgm1hER2VuUHs0vHo0gSdDEOiIie8vp+RRWbKljmCbWERHpkNPzKVRWNzCqonvS\nMUREMkbOzqfQlnJWb2tgZIVOHYmItMvZ+RTe3rmb5tYUI8t1pCAi0i5n51NYVV0PoCMFEZE0OTuf\nwqrqBgBGqk1BRKRDp20KZna/mfVOW+5jZvfEGyt+ldX19CwpoF/3oqSjiIhkjCgNzSe5+872BXff\nAUyKL9LRUVkdNDIHF1SJiAhEKwp5ZtanfcHM+hKtLSKjVW6t16kjEZF9RPlx/wnwmpk9Fi5/FPh+\nfJHiV9/UypbaJkapkVlEZC9RGpofMLM57Jk/4cPuviTeWPFaHTYyq+OaiMjeIp0GCotAVheCdJVb\ndTmqiMj+HFKP5q5iVXUDeQbD+nVLOoqISEbJyaJQWV3P4D7dKC7QQHgiIulytCg06MojEZH9yLmi\nkEp5cDlqudoTRET2FWtRMLMLzGyZma00s5v38/zXzGyJmS00s7+a2bA48wBsqm2ksSWlIwURkf2I\nrSiYWT5wB3AhMA64yszG7bPZfGCKu58EPA78MK487So7BsJTURAR2VecRwpTgZXuXunuzcAj7DO6\nqrvPcPdd4eJMYHCMeYCgPQFQxzURkf2IsygMAtanLW8I1x3ItcCzMeYBgiOF7kX59O9RHPdHiYhk\nnYwYw8jMPkkwec/7D/D8dcB1AEOHDn1Xn1W5VQPhiYgcSJxHChuBIWnLg8N1ezGzDwDfBC5x96b9\nvZG73+XuU9x9SkVFxbsKpXmZRUQOLM6iMBsYY2YjzKwIuBKYnr6BmU0CfkVQEKpizALA7uY2Nu7c\nreEtREQOILai4O6twI3Ac8BS4FF3f9PMbjWzS8LNfgSUAY+Z2RtmNv0Ab3dErN6q2dZERA4m1jYF\nd38GeGafdbekPf5AnJ+/r46B8NRxTURkv3KqR/OqquBIYUS5jhRERPYnp4pC5dZ6BvUupbRIA+GJ\niOxPbhUFDYQnInJQOVMU3J1vw+bqAAAIs0lEQVTK6npG6tSRiMgB5UxRqKproqG5TZejiogcRM4U\nhVUaCE9EpFM5UxTaB8LTkYKIyIHlTFHo36OY88cNYGDPkqSjiIhkrIwYEO9oOP89x3D+e45JOoaI\nSEbLmSMFERHpnIqCiIh0UFEQEZEOKgoiItJBRUFERDqoKIiISAcVBRER6aCiICIiHczdk85wSMys\nGlh7mC8vB7YewThJyPZ9UP7kZfs+KP/hGebuFZ1tlHVF4d0wsznuPiXpHO9Gtu+D8icv2/dB+eOl\n00ciItJBRUFERDrkWlG4K+kAR0C274PyJy/b90H5Y5RTbQoiInJwuXakICIiB5EzRcHMLjCzZWa2\n0sxuTjpPZ8zsHjOrMrPFaev6mtnzZrYivO+TZMaDMbMhZjbDzJaY2Ztm9s/h+mzahxIze93MFoT7\n8N1w/QgzmxV+l35vZkVJZz0YM8s3s/lm9lS4nDX5zWyNmS0yszfMbE64Lmu+QwBm1tvMHjezt8xs\nqZm9L5P3ISeKgpnlA3cAFwLjgKvMbFyyqTp1H3DBPutuBv7q7mOAv4bLmaoVuMndxwHTgBvCf/Ns\n2ocm4Bx3nwBMBC4ws2nAfwI/dffRwA7g2gQzRvHPwNK05WzLf7a7T0y7jDObvkMAPwf+7O5jgQkE\n/y0ydx/cvcvfgPcBz6UtfwP4RtK5IuQeDixOW14GDAwfDwSWJZ3xEPblf4DzsnUfgG7APOAUgo5H\nBeH6vb5bmXYDBhP86JwDPAVYluVfA5Tvsy5rvkNAL2A1YfttNuxDThwpAIOA9WnLG8J12WaAu28K\nH28GBiQZJiozGw5MAmaRZfsQnnp5A6gCngdWATvdvTXcJNO/Sz8D/hVIhcv9yK78DvzFzOaa2XXh\numz6Do0AqoF7w1N4vzaz7mTwPuRKUehyPPgTI+MvHTOzMuAPwFfcvTb9uWzYB3dvc/eJBH9xTwXG\nJhwpMjO7CKhy97lJZ3kXTnf3yQSnfm8wszPTn8yC71ABMBn4pbtPAhrY51RRpu1DrhSFjcCQtOXB\n4bpss8XMBgKE91UJ5zkoMyskKAgPufsfw9VZtQ/t3H0nMIPgdEtvMysIn8rk79JpwCVmtgZ4hOAU\n0s/Jnvy4+8bwvgp4gqAwZ9N3aAOwwd1nhcuPExSJjN2HXCkKs4Ex4VUXRcCVwPSEMx2O6cBnwsef\nIThPn5HMzIDfAEvd/b/Snsqmfagws97h41KCNpGlBMXhI+FmGbsP7v4Ndx/s7sMJvvN/c/dPkCX5\nzay7mfVofwycDywmi75D7r4ZWG9mx4erzgWWkMn7kHSjxlFs8PkgsJzgnPA3k84TIe/DwCagheCv\njWsJzgf/FVgB/C/QN+mcB8l/OsEh8ULgjfD2wSzbh5OA+eE+LAZuCdePBF4HVgKPAcVJZ42wL2cB\nT2VT/jDngvD2Zvv/t9n0HQrzTgTmhN+jJ4E+mbwP6tEsIiIdcuX0kYiIRKCiICIiHVQURESkg4qC\niIh0UFEQEZEOKgqS1czsBTOLfb5bM/tyOMLlQ3F/VpLCET2/mHQOSY6KguSstF69UXwROM+Dzl9d\nWW+CfZUcpaIgsTOz4eFf2XeH8xL8JewhvNdf+mZWHg7JgJl91syeDMeaX2NmN5rZ18JBxWaaWd+0\nj/hUON7+YjObGr6+ezgnxevhay5Ne9/pZvY3gs5D+2b9Wvg+i83sK+G6Owk6Uj1rZl/dZ/t8M/tx\nuP1CM/tSuP7c8HMXhTmKw/VrzOzf2+cHMLPJZvacma0ys+vDbc4ys5fM7GkL5gC508zywueuCt9z\nsZn9Z1qOejP7vgVzP8w0swHh+goz+4OZzQ5vp4XrvxPmesHMKs3sy+Fb/QcwKsz3IzMbGGZp//c9\n47C/CJIdku49p1vXvxEMAd4KTAyXHwU+GT5+AZgSPi4H1oSPP0vQ47YHUAHUANeHz/2UYIC99tff\nHT4+k3CoceAHaZ/Rm6A3e/fwfTewnx6kwHuBReF2ZQS9aCeFz61hnyGcw/VfIBjPpn0o6r5ACcGo\nvMeF6x5Iy7sG+ELafixM28ct4fqzgEaCQpRPMDrrR4BjgXXhtgXA34DLwtc4cHH4+IfAv4WPf0cw\nqBzAUIJhRwC+A7wKFIf/7tuAQt45XPtN7OlJnA/0SPr7pFu8t0M5fBZ5N1a7+xvh47kEPz6dmeHu\ndUCdmdUAfwrXLyIYgqLdwwDu/pKZ9QzHKzqfYDC4r4fblBD8KAI87+7b9/N5pwNPuHsDgJn9ETiD\nYKiLA/kAcKeHQ1G7+3YzmxDu7/Jwm/uBGwiGsYY9424tAsrS9rGpfawl4HV3rwxzPBxmawFecPfq\ncP1DBIXwSaCZYL4ECP59z0vLNy4YigqAnhaMXAvwtLs3AU1mVsX+h2+eDdxjweCGT6b9N5QuSkVB\njpamtMdtQGn4uJU9pzFLDvKaVNpyir2/u/uO1eIEk8lc4e7L0p8ws1MIhi9OUvp+7LuP7fu1v306\nmBZ3b9+mLe198oBp7t6YvnFYJPb9b/KO34Ow0J4JfAi4z8z+y90f6CSLZDG1KUjS1hCctoE9I3ce\nqo8DmNnpQI271wDPAV8KR2vFzCZFeJ+/A5eZWbdwVM7Lw3UH8zzw+fZG67CtYxkw3MxGh9t8Cnjx\nEPdpqgWj+uYR7N/LBIPYvT9se8kHrorwvn8BvtS+YGYTO9m+juB0Vvv2wwhOa90N/Jpg2GfpwlQU\nJGk/Br5gZvMJzm0fjsbw9XeyZ77h2wjOkS80szfD5YNy93kEc2O/TjBL3K/d/WCnjiD4oVwXfs4C\n4Orwr/JrgMfMbBHBEcCdh7hPs4HbCYbqXk1wWmsTwQQtMwhGDp3r7p0NufxlYErYCL4EuP5gG7v7\nNuCVsFH5RwTtGwvCf9+PE8zHIF2YRkkVyTBmdhbwdXe/KOksknt0pCAiIh10pCAiIh10pCAiIh1U\nFEREpIOKgoiIdFBREBGRDioKIiLSQUVBREQ6/H+Tyau6S0LvzAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d7WoniLnOlVc"
      },
      "source": [
        "Through the graph above, we see that the two-dimensional projection loses a lot of information (measured by the explained variance) and that we need about 20 components to retain around 90% of the variance. Looking at this graph for a large data set can help you understand the level of redundancy present in the data set."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "57wHtb9RkLgX"
      },
      "source": [
        "### PCA - practical considerations\n",
        "\n",
        "* At first, we could erroneously consider adding PCA unconditionally to the usual ML task implementation workflow. A more appropriate approach is, before applying PCA, to try the ML algorithm (s) on the original data set. If the results are unsatisfactory, consider applying PCA.\n",
        "\n",
        "* The projection must be constructed using only the training set. After building this mapping, it can be applied to the validation and test sets.\n",
        "\n",
        "* A weakness of the PCA is that it tends to be heavily affected by * outliers *. Therefore, it is worth an exploratory analysis to identify whether there are extreme values ​​in the data set.\n",
        "\n",
        "* The resizing of attributes is important for the correct functioning of the PCA, as shown in the following figure. (See also [Importance of Feature Scaling](https://scikit-learn.org/stable/auto_examples/preprocessing/plot_scaling_importance.html#sphx-glr-auto-examples-preprocessing-plot-scaling-importance-py))\n",
        "\n",
        "![alt text](https://scikit-learn.org/stable/_images/sphx_glr_plot_scaling_importance_001.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B9bffGsU_bjs"
      },
      "source": [
        "### Case study\n",
        "\n",
        "In this section, we investigate a PCA application case study on the Iris data set (4D) to project it on the plane (2D space) defined by the first two principal components, preserving a large part of the data set variance."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YSpK7USuxuCF"
      },
      "source": [
        "Load the data set into a Pandas DataFrame"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vQtl9TNq_fod"
      },
      "source": [
        "import pandas as pd\n",
        "url = \"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\"\n",
        "df = pd.read_csv(url, names=['sepal length','sepal width','petal length','petal width','target'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VJolHjig_nL4"
      },
      "source": [
        "Resize the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FSF2VoDv_myo"
      },
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "features = ['sepal length', 'sepal width', 'petal length', 'petal width']\n",
        "\n",
        "# data matrix (only features)\n",
        "X = df.loc[:, features].values\n",
        "\n",
        "# target vector\n",
        "y = df.loc[:,['target']].values\n",
        "\n",
        "# Rescaling the features\n",
        "X = StandardScaler().fit_transform(X)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5n37QgSp_03v"
      },
      "source": [
        "Invokes PCA to project the dataset to two dimensions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PXS0XaqH_3nk"
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "pca = PCA(n_components=2)\n",
        "principalComponents = pca.fit_transform(X)\n",
        "principalDf = pd.DataFrame(data = principalComponents\n",
        "             , columns = ['principal component 1', 'principal component 2'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MUx7YZW00N2H"
      },
      "source": [
        "Determines the intrinsic dimension of the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CF6MR4Wb0OHn",
        "outputId": "1af5e0bd-e04e-4cba-b7a3-5c928d616eac",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "pca = PCA().fit(X)\n",
        "print(pca.explained_variance_)\n",
        "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
        "plt.xlabel('number of components')\n",
        "plt.ylabel('cumulative explained variance');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2.93035378 0.92740362 0.14834223 0.02074601]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6TZBS5WqAFMr"
      },
      "source": [
        "finalDf = pd.concat([principalDf, df[['target']]], axis = 1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_AvhS-axA8Gh"
      },
      "source": [
        "The next code cell plots the resulting two-dimensional data. Notice in the graph below that the classes appear well separated from each other."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n1J0bE4kA8-v",
        "outputId": "4a613404-1792-47bf-e5cb-2d191c8b10d2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 523
        }
      },
      "source": [
        "fig = plt.figure(figsize = (8,8))\n",
        "ax = fig.add_subplot(1,1,1) \n",
        "ax.set_xlabel('Principal Component 1', fontsize = 15)\n",
        "ax.set_ylabel('Principal Component 2', fontsize = 15)\n",
        "ax.set_title('2 component PCA', fontsize = 20)\n",
        "targets = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']\n",
        "colors = ['r', 'g', 'b']\n",
        "for target, color in zip(targets,colors):\n",
        "    indicesToKeep = finalDf['target'] == target\n",
        "    ax.scatter(finalDf.loc[indicesToKeep, 'principal component 1']\n",
        "               , finalDf.loc[indicesToKeep, 'principal component 2']\n",
        "               , c = color\n",
        "               , s = 50)\n",
        "ax.legend(targets)\n",
        "ax.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CF7c5c2DzZp9kt3Gj76Lv7VWAFxGR2CnI10JHB5x3Xr1bISIiTUbd9SIiIimlIC8iIpJS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\n3Ww3Nmc2kxnO0Dm5QW9rywizRESjBsb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Rd7cfgw8K9O3tMGNG7dskIsmXP9SXk/se6emB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\nJZQneeeccy6h/h+6VlhgJXMAHgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f18H10Z9BNZq"
      },
      "source": [
        "The `explained_variance_ratio_` field of the PCA object tells you how much information (variance) can be attributed to each of the main components. When inspecting the `explained_variance_ratio_` vector, we can see that the first main component contains 72.77% of the variance, and the second main component contains 23.03% of the variance. Together, the two components contain 95.80% of the information."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uM328auqBUje",
        "outputId": "df1a2ad5-55d5-4083-acea-73fcf0df99b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "pca.explained_variance_ratio_"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.72770452, 0.23030523])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SrUIFtJwC3Vy"
      },
      "source": [
        "You can find out how many components PCA chooses after adjusting the model using the `pca.n_components_` field."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rHRWfqN3DEfd",
        "outputId": "f0eee45e-c72a-4dac-bd93-7b14dc8cbe25",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "pca.n_components_"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2q-e_0I5SWQ1"
      },
      "source": [
        "### Variants of PCA\n",
        "\n",
        "Some variants of PCA have been developed. Scikit-Learn contains some implementations of these variants, including the following:\n",
        "\n",
        "* `IncrementalPCA`. One problem with the classic PCA implementation is that it requires the entire training set to fit in memory for the SVD algorithm to run. The IncrementalPCA implementation can divide the training set into mini-batches and feed the decomposition procedure one mini-batch at a time. This is useful for large training sets.\n",
        "\n",
        "* `RandomizedPCA`. This implementation uses a non-deterministic method to quickly approximate the first few major components in very large data. `RandomizedPCA` implements a stochastic algorithm that quickly finds an approximation of the first $k$ main components. Its computational complexity is $O(m \\times k^2) + O(k^3)$. In comparison to the $O(m \\times n^2) + O(n^3)$ complexity of the original version, this stochastic version is significantly faster when $k$ is much less than $n$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6dzkyoh0YdtM"
      },
      "source": [
        "The following code divides the MNIST data set into 100 mini-batches (using NumPy's `array_split()` function) and supplies them to the IncrementalPCA class to reduce the dimensionality of the MNIST data set to 154 dimensions. Note that you must call the `partial_fit()` method with each mini-batch instead of the `fit()` method with the entire training set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xxU5Ty6zYdVA",
        "outputId": "f778a64e-04c4-4457-cafc-47c1f6c9a02a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "from sklearn.decomposition import IncrementalPCA\n",
        "from sklearn.datasets import fetch_openml\n",
        "\n",
        "# Load data from https://www.openml.org/d/554\n",
        "X_mnist, y_mnist = fetch_openml('mnist_784', version=1, return_X_y=True)\n",
        "\n",
        "print(X_mnist.data.shape)\n",
        "\n",
        "n_batches = 100\n",
        "inc_pca = IncrementalPCA(n_components=154)\n",
        "for X_batch in np.array_split(X_mnist, n_batches):\n",
        "        inc_pca.partial_fit(X_batch)\n",
        "X_mnist_reduced = inc_pca.transform(X_mnist)\n",
        "\n",
        "print(X_mnist_reduced.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(70000, 784)\n",
            "(70000, 154)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ILsJh5CEexPi"
      },
      "source": [
        "The following example illustrates the use of the class `RandomizedPCA`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZnWewI_Vewn9"
      },
      "source": [
        "rnd_pca = PCA(n_components=154, svd_solver=\"randomized\")\n",
        "X_reduced = rnd_pca.fit_transform(X_mnist)\n",
        "print(X_mnist_reduced.shape)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FhQWEli1cR9G"
      },
      "source": [
        "# Seleção de Atributos"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "shtyhtQycbMs"
      },
      "source": [
        "## Seleção baseada em variância\n",
        "\n",
        "No Scikit-Learn, a classe [`VarianceThreshold`](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.VarianceThreshold.html) implementa um procedimento simples para a seleção de atributos. Essa estratégia remove todos os atributos cuja variância não atinge algum limite fornecido. Por padrão, esse procedimento remove todos os atributos cuja variância é zero."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NVbSswAccNiK"
      },
      "source": [
        "A célula a seguir (adaptada deste [exemplo](https://)) ilustra um dataset com três atributos binários. O código descarta os atributos que possuem mais de 80% de zeros (ou de uns). Repare que o primeiro atributo é descartado, visto que há uma probabilidade igual a $5/6$ (maior do que $0.8$) de encontrar um zero.\n",
        "\n",
        "N.B.: a variância de uma variável aleatória de Bernoulli $X$ cuja probabilidade de sucesso é $p$ é dada por $\\operatorname {Var} [X]=p(1-p)$.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IwUzaRNRcVj9",
        "outputId": "83455805-e5af-467f-822e-597a1569446b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 235
        }
      },
      "source": [
        "from sklearn.feature_selection import VarianceThreshold\n",
        "import numpy as np\n",
        "\n",
        "X = [[0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 1, 1], [0, 1, 0], [0, 1, 1]]\n",
        "\n",
        "print(np.asarray(X))\n",
        "\n",
        "sel = VarianceThreshold(threshold=(.8 * (1 - .8)))\n",
        "sel.fit_transform(X)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0 0 1]\n",
            " [0 1 0]\n",
            " [1 0 0]\n",
            " [0 1 1]\n",
            " [0 1 0]\n",
            " [0 1 1]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 1],\n",
              "       [1, 0],\n",
              "       [0, 0],\n",
              "       [1, 1],\n",
              "       [1, 0],\n",
              "       [1, 1]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5MTdmHG9eFwh"
      },
      "source": [
        "## Seleção de atributos univariada\n",
        "\n",
        "A seleção de atributos univariada é útil para seleção de atributos no contexto da tarefa de **classificação**. Essa estratégia seleciona os melhores atributos com base em algum teste estatístico capaz de medir a dependência entre duas variáveis. \n",
        "\n",
        "O Scikit-learn expõe rotinas de seleção de atributos como classes que implementam o método de transformação `fit_transform`. Esse método recebe como argumentos a matrix de dados $X$ e a matriz alvo $y$.\n",
        "\n",
        "Uma dessas rotinas é fornecida pela classe `SelectKBest`. Essa classe pode ser configurada com um dentre um conjunto de testes estatísticos diferentes para selecionar um número específico de atributos. Um dos parâmetros a ser passado é uma função de pontuação, que deve ser aplicável a um par (𝑋, 𝑦). O resultado é uma matriz de pontuações, com uma pontuação para cada atributo de 𝑋. O objeto `SelectKBest` então simplesmente mantém os primeiros $k$ atributos de 𝑋 com as pontuações mais altas.\n",
        "\n",
        "Se, por exemplo, for passada `chi2` como função de pontuação, `SelectKBest` irá calcular a estatística `chi2` entre cada atributo de 𝑋 e o atributo alvo 𝑦 (presumindo que este último contém os rótulos da classe). Um valor pequeno significará que o atributo é independente de 𝑦. Um valor grande significará que o atributo não está relacionado aleatoriamente a 𝑦 e, portanto, provavelmente fornecerá informações importantes para o estimador. Apenas os 𝑘 atributos de maior pontuação são mantidos.\n",
        "\n",
        "O exemplo abaixo ilustra o uso de `SelectKBest` com o teste estatístico qui quadrado ($\\chi^2$) para selecionar os melhores 4 atributos do conjunto de dados de original."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bY8uWUhsnMye",
        "outputId": "a99af585-9cc5-4954-d042-23920a71eb54",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "from sklearn.datasets import load_iris\n",
        "from sklearn.feature_selection import SelectKBest\n",
        "from sklearn.feature_selection import chi2\n",
        "iris = load_iris()\n",
        "X, y = iris.data, iris.target\n",
        "print(X.shape)\n",
        "\n",
        "X_new = SelectKBest(chi2, k=2).fit_transform(X, y)\n",
        "print(X_new.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(150, 4)\n",
            "(150, 2)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qQvR-wHf3fol"
      },
      "source": [
        "### Seleção por informação mútua\n",
        "\n",
        "A [informação mútua](https://en.wikipedia.org/wiki/Mutual_information) (mutual information, MI) entre duas variáveis aleatórias é um valor não negativo, que mede a dependência entre as variáveis. É igual a zero se e somente se duas variáveis aleatórias forem independentes. Quanto maior o valor de MI, maior a dependência estatística entre as variáveis. \n",
        "\n",
        "Formalmente,  dadas duas variáveis aleatórias $X$ e $Y$, a MI mede o quão diferente a distribuição conjunta do par ${\\displaystyle (X, Y)}$ é do produto de distribuições marginais de ${\\displaystyle X}$ e ${\\displaystyle Y}$.\n",
        "\n",
        "Intuitivamente, MI mede o quanto o conhecimento de uma dessas variáveis reduz a incerteza sobre a outra. Por exemplo, se ${\\displaystyle X}$ e ${\\displaystyle Y}$ forem independentes, saber ${\\displaystyle X}$ não fornecerá informações sobre ${\\displaystyle Y}$ e vice-versa. Portanto, a informação mútua neste caso é zero. No outro extremo, se ${\\displaystyle X}$ é uma função determinística de ${\\displaystyle Y}$ e ${\\displaystyle Y}$ é uma função determinística de ${\\displaystyle X}$, então toda a informação transmitida por ${\\displaystyle X }$ é compartilhada com ${\\displaystyle Y}$: conhecer ${\\displaystyle X}$ determina o valor de ${\\displaystyle Y}$ e vice-versa.\n",
        "\n",
        "A MI não está limitada a variáveis aleatórias de valor real e nem a dependências lineares (como acontece no caso do coeficiente de correlação).\n",
        "\n",
        "No Scikit-Learn, a função [sklearn.feature_selection.mutual_info_classif](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.mutual_info_classif.html) permite estimar a *informação mútua* entre cada atributo previsor e um atributo alvo discreto.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AjKOPFEcnz2n",
        "outputId": "cd085057-dffd-43e4-ed9b-1d63864b0732",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "import numpy as np\n",
        "from sklearn.feature_selection import mutual_info_classif\n",
        "X = np.array([[0, 0, 0, 1],\n",
        "              [1, 1, 0, 2],\n",
        "              [2, 0, 1, 3],\n",
        "              [2, 0, 1, 3],\n",
        "              [1, 0, 1, 2]])\n",
        "y = np.array([0, 1, 2, 2, 1])\n",
        "mutual_info_classif(X, y, discrete_features=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.05492017, 0.22314355, 0.39575279, 1.05492017])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H_8APMn7MO8A",
        "outputId": "9c17fd4b-cd6d-4594-86d4-9981431e65d4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "print(X[:,0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0 1 2 2 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "URCWiPDaV245"
      },
      "source": [
        "As duas células a seguir ilustram de que forma a computação da MI pode ser implementada. Para entendimento deste código, vale a leitura do link a seguir: https://en.wikipedia.org/wiki/G-test#Relation_to_mutual_information."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PCZJMZ0wNY_8",
        "outputId": "8d0753a2-20af-4a14-d1c0-d4f1534d2529",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "source": [
        "import numpy as np\n",
        "x = np.array([1, 2, 0, 0, 2])\n",
        "y = np.array([0, 1, 2, 2, 1])\n",
        "bins = 3\n",
        "c_xy = np.histogram2d(x, y, bins)[0]\n",
        "print(c_xy)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0. 0. 2.]\n",
            " [1. 0. 0.]\n",
            " [0. 2. 0.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wYOVhIRYMGPF",
        "outputId": "2470e081-acee-478c-d0ea-aad0b6885074",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "from scipy.stats import chi2_contingency\n",
        "\n",
        "def calc_MI(x, y, bins):\n",
        "    c_xy = np.histogram2d(x, y, bins)[0]\n",
        "    g, p, dof, expected = chi2_contingency(c_xy, lambda_=\"log-likelihood\")\n",
        "    mi = 0.5 * g / c_xy.sum()\n",
        "    return mi\n",
        "calc_MI(X[:,0], y, 3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0549201679861442"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EDa23lhhK7Wt"
      },
      "source": [
        "A classe `SelectPercentile` funciona de forma similar. Essa classe também deve ser configurada com uma função de pontuação. Entretanto, em vez de passar a *quantidade* de atributos que devem permanecer, passamos a *porcentagem* de atributos que devem permanecer (relativamente à quantidade total de atributos em $X$).\n",
        "\n",
        "No exemplo a seguir, $X$ contém 64 atributos. Após a seleção (repare o uso do parâmetro `percentile` para definir que 10% dos atributos devem ser retidos), o conjunto de dados contém apenas 7 atributos."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5gYDonlDntbW",
        "outputId": "2f30746d-e2da-4fed-95ec-aa58892e5768",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "from sklearn.datasets import load_digits\n",
        "from sklearn.feature_selection import SelectPercentile, chi2\n",
        "X, y = load_digits(return_X_y=True)\n",
        "print('Antes da seleção:', X.shape)\n",
        "\n",
        "X_new = SelectPercentile(chi2, percentile=10).fit_transform(X, y)\n",
        "print('Depois da seleção:', X_new.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Antes da seleção: (1797, 64)\n",
            "Depois da seleção: (1797, 7)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fNbo0k_U-PhC"
      },
      "source": [
        "## Recursive Feature Elimination"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "siUCyJmRMxOt"
      },
      "source": [
        "A estratégia *Recursive Feature Elimination*, implementada na classe [sklearn.feature_selection.RFE](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.RFE.html) utiliza algum algoritmo de ML que gere modelos preditivos (classificador ou regressor) para selecionar atributos. Essa estratégia é útil em tarefas de classificação ou de regressão, nas quais há um conjunto de atributos previsores e um atributo alvo. A RFE permite selecionar os atributos previsores mais relevantes para predizer o atributo alvo.\n",
        "\n",
        "O RFE ajusta um modelo preditivo (classificador ou regressor) a diferentes combinações de atributos. Para cada combinação, ele usa a acurácia do modelo ajustado para identificar quais atributos contribuem mais para prever o atributo alvo. Sendo assim, uma pressuposição para aplicar o RFE é que o algoritmo usado para ajuste do modelo a um conjunto de dados $X$ produz um peso (i.e., um indicador numérido de importância) para cada atributo em $X$. \n",
        "\n",
        "Inicialmente, o algoritmo de ML é aplicado ao conjunto de dados original $X$. Em seguida, o atributo menos relevante (de acordo com os coeficientes retornados pelo modelo ajustado) é removido de $X$, o que resulta em um novo conjunto de dados $X^\\prime$. Um novo modelo é então ajustado sobre novo conjunto de dados $X^\\prime$, para gerar uma nova lista de coeficientes de importância. Esse procedimento é realizado recursivamente, até que a quantidade de atributos desejada seja alcançada.\n",
        "\n",
        "A classe `RFE` possui dois atributos, `support_` e `ranking_`, vetores (do tipo *numpy array*) que podem ser consultados para analisar o resultado da seleção de atributos."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0NdiBH9lu9q5"
      },
      "source": [
        "No código de exemplo abaixo, o conjunto de dados Iris é usado para ilustrar o uso de RFE. O conjunto de dados Iris tem 4 atributos previsores, todos medidos em cm:\n",
        "* comprimento da sépala, \n",
        "* largura da sépala, \n",
        "* comprimento da pétala, \n",
        "* largura da pétala. \n",
        "\n",
        "No exemplo  abaixo, o vetor `ranking_` resultante é `[2 1 1 1]`, o que significa que a largura da sépala, o comprimento da pétala e a largura da pétala são todos mais importantes do que o comprimento da sépala."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IMvpWDdKu9Sq",
        "outputId": "15f6dbcf-1444-4131-e76f-e2f158ebac98",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        }
      },
      "source": [
        "from sklearn.svm import LinearSVC\n",
        "from sklearn.feature_selection import RFE\n",
        "from sklearn import datasets\n",
        "\n",
        "dataset = datasets.load_iris()\n",
        "\n",
        "svm = LinearSVC()\n",
        "\n",
        "# create the RFE model for the svm classifier \n",
        "# and select attributes\n",
        "rfe = RFE(svm, n_features_to_select=3)\n",
        "rfe = rfe.fit(dataset.data, dataset.target)\n",
        "\n",
        "#\n",
        "# imprime sumários relativos aos atributos selecionados\n",
        "#\n",
        "\n",
        "# um array com valores booleanos para indicar os atributos selecionados\n",
        "print(rfe.support_)\n",
        "\n",
        "# um array de inteiros positivos para indicar o ranking de atributos\n",
        "# (pontuação mais baixa indica um ranking mais alto) \n",
        "print(rfe.ranking_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[False  True  True  True]\n",
            "[2 1 1 1]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LOWAL7edWppm",
        "outputId": "76c568fb-23ec-47c6-9c22-494e866f888e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "from sklearn.datasets import make_friedman1\n",
        "from sklearn.feature_selection import RFE\n",
        "from sklearn.svm import SVR\n",
        "X, y = make_friedman1(n_samples=50, n_features=10, random_state=0)\n",
        "estimator = SVR(kernel=\"linear\")\n",
        "selector = RFE(estimator, n_features_to_select=5, step=1)\n",
        "selector = selector.fit(X, y)\n",
        "\n",
        "print(selector.support_)\n",
        "\n",
        "\n",
        "print(selector.ranking_)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ True  True  True  True  True False False False False False]\n",
            "[1 1 1 1 1 6 4 3 2 5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "02P-FOvo8cXn"
      },
      "source": [
        "Outra classe do scikit-learn fornecida para seleção de atributos é [`RFECV`](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.RFECV.html).  Essa é uma sublcasse de RFE.\n",
        "\n",
        "Uma desvantagem da classe RFE é que a quantidade de atributos a selecionar deve ser fornecida por meio do parâmetro `n_features_to_select`. A classe RFECV ajuda a ajustar (i.e., determinar) o valor desse parâmetro usando validação cruzada. Para cada etapa em que o número de atributos definido em `steps` é eliminado, a RFECV calcula a acurácia em um conjunto de dados de validação. A combinação de atributos que fornece a acurácia máxima nos dados de validação é retornada."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dOeW9i6AMw5S",
        "outputId": "08840ff4-421b-4967-c718-f27fa5d5d1bd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "from sklearn.feature_selection import RFECV\n",
        "regression = SVR(kernel=\"linear\")\n",
        "selector = RFECV(estimator=regression, cv=10)\n",
        "selector.fit(X, y)\n",
        "print(\"Quantidade ótima de atributos: %d\" % selector.n_features_)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Quantidade ótima de atributos: 5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ic-3i1S_N6wU",
        "outputId": "eb301f5b-b131-4853-d778-5b4a0bf754ca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "from sklearn.datasets import make_friedman1\n",
        "from sklearn.feature_selection import RFECV\n",
        "from sklearn.svm import SVR\n",
        "X, y = make_friedman1(n_samples=50, n_features=10, random_state=0)\n",
        "estimator = SVR(kernel=\"linear\")\n",
        "selector = RFECV(estimator, step=1, cv=5)\n",
        "selector = selector.fit(X, y)\n",
        "selector.support_ \n",
        "\n",
        "\n",
        "selector.ranking_"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 1, 1, 1, 1, 6, 4, 3, 2, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WEs52zrzTKi4",
        "outputId": "7d55f893-41d6-418e-daef-113f033f319a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        }
      },
      "source": [
        "# https://scikit-learn.org/stable/auto_examples/feature_selection/plot_rfe_with_cross_validation.html#sphx-glr-auto-examples-feature-selection-plot-rfe-with-cross-validation-py\n",
        "\n",
        "print(__doc__)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.svm import SVC\n",
        "from sklearn.model_selection import StratifiedKFold\n",
        "from sklearn.feature_selection import RFECV\n",
        "from sklearn.datasets import make_classification\n",
        "\n",
        "# Build a classification task using 3 informative features\n",
        "X, y = make_classification(n_samples=1000, n_features=25, n_informative=3,\n",
        "                           n_redundant=2, n_repeated=0, n_classes=8,\n",
        "                           n_clusters_per_class=1, random_state=0)\n",
        "\n",
        "# Create the RFE object and compute a cross-validated score.\n",
        "svc = SVC(kernel=\"linear\")\n",
        "# The \"accuracy\" scoring is proportional to the number of correct\n",
        "# classifications\n",
        "rfecv = RFECV(estimator=svc, step=1, cv=StratifiedKFold(2),\n",
        "              scoring='accuracy')\n",
        "rfecv.fit(X, y)\n",
        "\n",
        "print(\"Optimal number of features : %d\" % rfecv.n_features_)\n",
        "\n",
        "# Plot number of features VS. cross-validation scores\n",
        "plt.figure()\n",
        "plt.xlabel(\"Number of features selected\")\n",
        "plt.ylabel(\"Cross validation score (nb of correct classifications)\")\n",
        "plt.plot(range(1, len(rfecv.grid_scores_) + 1), rfecv.grid_scores_)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Automatically created module for IPython interactive environment\n",
            "Optimal number of features : 3\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qskJ1XSOjhpQwYnBJpkMREUmbqAXxjKCxeYa732xmU4Hx7r7ycPu4e7uZXQM8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\nTPCl+DN3T3SJz4vPv6djT8d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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IYn9kA_lm0Km"
      },
      "source": [
        "import pandas as pd\n",
        "data = pd.read_csv('./breast-cancer.csv')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ttwhAX4enezj",
        "outputId": "33e070cb-c5f4-422a-f037-1e587abcc2fe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        }
      },
      "source": [
        "data.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>diagnosis</th>\n",
              "      <th>radius_mean</th>\n",
              "      <th>texture_mean</th>\n",
              "      <th>perimeter_mean</th>\n",
              "      <th>area_mean</th>\n",
              "      <th>smoothness_mean</th>\n",
              "      <th>compactness_mean</th>\n",
              "      <th>concavity_mean</th>\n",
              "      <th>concave points_mean</th>\n",
              "      <th>symmetry_mean</th>\n",
              "      <th>fractal_dimension_mean</th>\n",
              "      <th>radius_se</th>\n",
              "      <th>texture_se</th>\n",
              "      <th>perimeter_se</th>\n",
              "      <th>area_se</th>\n",
              "      <th>smoothness_se</th>\n",
              "      <th>compactness_se</th>\n",
              "      <th>concavity_se</th>\n",
              "      <th>concave points_se</th>\n",
              "      <th>symmetry_se</th>\n",
              "      <th>fractal_dimension_se</th>\n",
              "      <th>radius_worst</th>\n",
              "      <th>texture_worst</th>\n",
              "      <th>perimeter_worst</th>\n",
              "      <th>area_worst</th>\n",
              "      <th>smoothness_worst</th>\n",
              "      <th>compactness_worst</th>\n",
              "      <th>concavity_worst</th>\n",
              "      <th>concave points_worst</th>\n",
              "      <th>symmetry_worst</th>\n",
              "      <th>fractal_dimension_worst</th>\n",
              "      <th>Unnamed: 32</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>842302</td>\n",
              "      <td>M</td>\n",
              "      <td>17.99</td>\n",
              "      <td>10.38</td>\n",
              "      <td>122.80</td>\n",
              "      <td>1001.0</td>\n",
              "      <td>0.11840</td>\n",
              "      <td>0.27760</td>\n",
              "      <td>0.3001</td>\n",
              "      <td>0.14710</td>\n",
              "      <td>0.2419</td>\n",
              "      <td>0.07871</td>\n",
              "      <td>1.0950</td>\n",
              "      <td>0.9053</td>\n",
              "      <td>8.589</td>\n",
              "      <td>153.40</td>\n",
              "      <td>0.006399</td>\n",
              "      <td>0.04904</td>\n",
              "      <td>0.05373</td>\n",
              "      <td>0.01587</td>\n",
              "      <td>0.03003</td>\n",
              "      <td>0.006193</td>\n",
              "      <td>25.38</td>\n",
              "      <td>17.33</td>\n",
              "      <td>184.60</td>\n",
              "      <td>2019.0</td>\n",
              "      <td>0.1622</td>\n",
              "      <td>0.6656</td>\n",
              "      <td>0.7119</td>\n",
              "      <td>0.2654</td>\n",
              "      <td>0.4601</td>\n",
              "      <td>0.11890</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>842517</td>\n",
              "      <td>M</td>\n",
              "      <td>20.57</td>\n",
              "      <td>17.77</td>\n",
              "      <td>132.90</td>\n",
              "      <td>1326.0</td>\n",
              "      <td>0.08474</td>\n",
              "      <td>0.07864</td>\n",
              "      <td>0.0869</td>\n",
              "      <td>0.07017</td>\n",
              "      <td>0.1812</td>\n",
              "      <td>0.05667</td>\n",
              "      <td>0.5435</td>\n",
              "      <td>0.7339</td>\n",
              "      <td>3.398</td>\n",
              "      <td>74.08</td>\n",
              "      <td>0.005225</td>\n",
              "      <td>0.01308</td>\n",
              "      <td>0.01860</td>\n",
              "      <td>0.01340</td>\n",
              "      <td>0.01389</td>\n",
              "      <td>0.003532</td>\n",
              "      <td>24.99</td>\n",
              "      <td>23.41</td>\n",
              "      <td>158.80</td>\n",
              "      <td>1956.0</td>\n",
              "      <td>0.1238</td>\n",
              "      <td>0.1866</td>\n",
              "      <td>0.2416</td>\n",
              "      <td>0.1860</td>\n",
              "      <td>0.2750</td>\n",
              "      <td>0.08902</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>84300903</td>\n",
              "      <td>M</td>\n",
              "      <td>19.69</td>\n",
              "      <td>21.25</td>\n",
              "      <td>130.00</td>\n",
              "      <td>1203.0</td>\n",
              "      <td>0.10960</td>\n",
              "      <td>0.15990</td>\n",
              "      <td>0.1974</td>\n",
              "      <td>0.12790</td>\n",
              "      <td>0.2069</td>\n",
              "      <td>0.05999</td>\n",
              "      <td>0.7456</td>\n",
              "      <td>0.7869</td>\n",
              "      <td>4.585</td>\n",
              "      <td>94.03</td>\n",
              "      <td>0.006150</td>\n",
              "      <td>0.04006</td>\n",
              "      <td>0.03832</td>\n",
              "      <td>0.02058</td>\n",
              "      <td>0.02250</td>\n",
              "      <td>0.004571</td>\n",
              "      <td>23.57</td>\n",
              "      <td>25.53</td>\n",
              "      <td>152.50</td>\n",
              "      <td>1709.0</td>\n",
              "      <td>0.1444</td>\n",
              "      <td>0.4245</td>\n",
              "      <td>0.4504</td>\n",
              "      <td>0.2430</td>\n",
              "      <td>0.3613</td>\n",
              "      <td>0.08758</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>84348301</td>\n",
              "      <td>M</td>\n",
              "      <td>11.42</td>\n",
              "      <td>20.38</td>\n",
              "      <td>77.58</td>\n",
              "      <td>386.1</td>\n",
              "      <td>0.14250</td>\n",
              "      <td>0.28390</td>\n",
              "      <td>0.2414</td>\n",
              "      <td>0.10520</td>\n",
              "      <td>0.2597</td>\n",
              "      <td>0.09744</td>\n",
              "      <td>0.4956</td>\n",
              "      <td>1.1560</td>\n",
              "      <td>3.445</td>\n",
              "      <td>27.23</td>\n",
              "      <td>0.009110</td>\n",
              "      <td>0.07458</td>\n",
              "      <td>0.05661</td>\n",
              "      <td>0.01867</td>\n",
              "      <td>0.05963</td>\n",
              "      <td>0.009208</td>\n",
              "      <td>14.91</td>\n",
              "      <td>26.50</td>\n",
              "      <td>98.87</td>\n",
              "      <td>567.7</td>\n",
              "      <td>0.2098</td>\n",
              "      <td>0.8663</td>\n",
              "      <td>0.6869</td>\n",
              "      <td>0.2575</td>\n",
              "      <td>0.6638</td>\n",
              "      <td>0.17300</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>84358402</td>\n",
              "      <td>M</td>\n",
              "      <td>20.29</td>\n",
              "      <td>14.34</td>\n",
              "      <td>135.10</td>\n",
              "      <td>1297.0</td>\n",
              "      <td>0.10030</td>\n",
              "      <td>0.13280</td>\n",
              "      <td>0.1980</td>\n",
              "      <td>0.10430</td>\n",
              "      <td>0.1809</td>\n",
              "      <td>0.05883</td>\n",
              "      <td>0.7572</td>\n",
              "      <td>0.7813</td>\n",
              "      <td>5.438</td>\n",
              "      <td>94.44</td>\n",
              "      <td>0.011490</td>\n",
              "      <td>0.02461</td>\n",
              "      <td>0.05688</td>\n",
              "      <td>0.01885</td>\n",
              "      <td>0.01756</td>\n",
              "      <td>0.005115</td>\n",
              "      <td>22.54</td>\n",
              "      <td>16.67</td>\n",
              "      <td>152.20</td>\n",
              "      <td>1575.0</td>\n",
              "      <td>0.1374</td>\n",
              "      <td>0.2050</td>\n",
              "      <td>0.4000</td>\n",
              "      <td>0.1625</td>\n",
              "      <td>0.2364</td>\n",
              "      <td>0.07678</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         id diagnosis  ...  fractal_dimension_worst  Unnamed: 32\n",
              "0    842302         M  ...                  0.11890          NaN\n",
              "1    842517         M  ...                  0.08902          NaN\n",
              "2  84300903         M  ...                  0.08758          NaN\n",
              "3  84348301         M  ...                  0.17300          NaN\n",
              "4  84358402         M  ...                  0.07678          NaN\n",
              "\n",
              "[5 rows x 33 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CwuCqczsnoCk",
        "outputId": "d4a9c247-5715-462c-bbc6-fad3648dca7a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        }
      },
      "source": [
        "# feature names as a list\n",
        "col = data.columns       # .columns gives columns names in data \n",
        "print(col)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Index(['id', 'diagnosis', 'radius_mean', 'texture_mean', 'perimeter_mean',\n",
            "       'area_mean', 'smoothness_mean', 'compactness_mean', 'concavity_mean',\n",
            "       'concave points_mean', 'symmetry_mean', 'fractal_dimension_mean',\n",
            "       'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se',\n",
            "       'compactness_se', 'concavity_se', 'concave points_se', 'symmetry_se',\n",
            "       'fractal_dimension_se', 'radius_worst', 'texture_worst',\n",
            "       'perimeter_worst', 'area_worst', 'smoothness_worst',\n",
            "       'compactness_worst', 'concavity_worst', 'concave points_worst',\n",
            "       'symmetry_worst', 'fractal_dimension_worst', 'Unnamed: 32'],\n",
            "      dtype='object')\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6rCH0utZnseU",
        "outputId": "3c03efec-d447-4a5d-cbd2-a6d542f5081a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        }
      },
      "source": [
        "# y includes our labels and x includes our features\n",
        "y = data.diagnosis                          # M or B \n",
        "list = ['Unnamed: 32','id','diagnosis']\n",
        "x = data.drop(list,axis = 1 )\n",
        "x.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>radius_mean</th>\n",
              "      <th>texture_mean</th>\n",
              "      <th>perimeter_mean</th>\n",
              "      <th>area_mean</th>\n",
              "      <th>smoothness_mean</th>\n",
              "      <th>compactness_mean</th>\n",
              "      <th>concavity_mean</th>\n",
              "      <th>concave points_mean</th>\n",
              "      <th>symmetry_mean</th>\n",
              "      <th>fractal_dimension_mean</th>\n",
              "      <th>radius_se</th>\n",
              "      <th>texture_se</th>\n",
              "      <th>perimeter_se</th>\n",
              "      <th>area_se</th>\n",
              "      <th>smoothness_se</th>\n",
              "      <th>compactness_se</th>\n",
              "      <th>concavity_se</th>\n",
              "      <th>concave points_se</th>\n",
              "      <th>symmetry_se</th>\n",
              "      <th>fractal_dimension_se</th>\n",
              "      <th>radius_worst</th>\n",
              "      <th>texture_worst</th>\n",
              "      <th>perimeter_worst</th>\n",
              "      <th>area_worst</th>\n",
              "      <th>smoothness_worst</th>\n",
              "      <th>compactness_worst</th>\n",
              "      <th>concavity_worst</th>\n",
              "      <th>concave points_worst</th>\n",
              "      <th>symmetry_worst</th>\n",
              "      <th>fractal_dimension_worst</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>17.99</td>\n",
              "      <td>10.38</td>\n",
              "      <td>122.80</td>\n",
              "      <td>1001.0</td>\n",
              "      <td>0.11840</td>\n",
              "      <td>0.27760</td>\n",
              "      <td>0.3001</td>\n",
              "      <td>0.14710</td>\n",
              "      <td>0.2419</td>\n",
              "      <td>0.07871</td>\n",
              "      <td>1.0950</td>\n",
              "      <td>0.9053</td>\n",
              "      <td>8.589</td>\n",
              "      <td>153.40</td>\n",
              "      <td>0.006399</td>\n",
              "      <td>0.04904</td>\n",
              "      <td>0.05373</td>\n",
              "      <td>0.01587</td>\n",
              "      <td>0.03003</td>\n",
              "      <td>0.006193</td>\n",
              "      <td>25.38</td>\n",
              "      <td>17.33</td>\n",
              "      <td>184.60</td>\n",
              "      <td>2019.0</td>\n",
              "      <td>0.1622</td>\n",
              "      <td>0.6656</td>\n",
              "      <td>0.7119</td>\n",
              "      <td>0.2654</td>\n",
              "      <td>0.4601</td>\n",
              "      <td>0.11890</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>20.57</td>\n",
              "      <td>17.77</td>\n",
              "      <td>132.90</td>\n",
              "      <td>1326.0</td>\n",
              "      <td>0.08474</td>\n",
              "      <td>0.07864</td>\n",
              "      <td>0.0869</td>\n",
              "      <td>0.07017</td>\n",
              "      <td>0.1812</td>\n",
              "      <td>0.05667</td>\n",
              "      <td>0.5435</td>\n",
              "      <td>0.7339</td>\n",
              "      <td>3.398</td>\n",
              "      <td>74.08</td>\n",
              "      <td>0.005225</td>\n",
              "      <td>0.01308</td>\n",
              "      <td>0.01860</td>\n",
              "      <td>0.01340</td>\n",
              "      <td>0.01389</td>\n",
              "      <td>0.003532</td>\n",
              "      <td>24.99</td>\n",
              "      <td>23.41</td>\n",
              "      <td>158.80</td>\n",
              "      <td>1956.0</td>\n",
              "      <td>0.1238</td>\n",
              "      <td>0.1866</td>\n",
              "      <td>0.2416</td>\n",
              "      <td>0.1860</td>\n",
              "      <td>0.2750</td>\n",
              "      <td>0.08902</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>19.69</td>\n",
              "      <td>21.25</td>\n",
              "      <td>130.00</td>\n",
              "      <td>1203.0</td>\n",
              "      <td>0.10960</td>\n",
              "      <td>0.15990</td>\n",
              "      <td>0.1974</td>\n",
              "      <td>0.12790</td>\n",
              "      <td>0.2069</td>\n",
              "      <td>0.05999</td>\n",
              "      <td>0.7456</td>\n",
              "      <td>0.7869</td>\n",
              "      <td>4.585</td>\n",
              "      <td>94.03</td>\n",
              "      <td>0.006150</td>\n",
              "      <td>0.04006</td>\n",
              "      <td>0.03832</td>\n",
              "      <td>0.02058</td>\n",
              "      <td>0.02250</td>\n",
              "      <td>0.004571</td>\n",
              "      <td>23.57</td>\n",
              "      <td>25.53</td>\n",
              "      <td>152.50</td>\n",
              "      <td>1709.0</td>\n",
              "      <td>0.1444</td>\n",
              "      <td>0.4245</td>\n",
              "      <td>0.4504</td>\n",
              "      <td>0.2430</td>\n",
              "      <td>0.3613</td>\n",
              "      <td>0.08758</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>11.42</td>\n",
              "      <td>20.38</td>\n",
              "      <td>77.58</td>\n",
              "      <td>386.1</td>\n",
              "      <td>0.14250</td>\n",
              "      <td>0.28390</td>\n",
              "      <td>0.2414</td>\n",
              "      <td>0.10520</td>\n",
              "      <td>0.2597</td>\n",
              "      <td>0.09744</td>\n",
              "      <td>0.4956</td>\n",
              "      <td>1.1560</td>\n",
              "      <td>3.445</td>\n",
              "      <td>27.23</td>\n",
              "      <td>0.009110</td>\n",
              "      <td>0.07458</td>\n",
              "      <td>0.05661</td>\n",
              "      <td>0.01867</td>\n",
              "      <td>0.05963</td>\n",
              "      <td>0.009208</td>\n",
              "      <td>14.91</td>\n",
              "      <td>26.50</td>\n",
              "      <td>98.87</td>\n",
              "      <td>567.7</td>\n",
              "      <td>0.2098</td>\n",
              "      <td>0.8663</td>\n",
              "      <td>0.6869</td>\n",
              "      <td>0.2575</td>\n",
              "      <td>0.6638</td>\n",
              "      <td>0.17300</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>20.29</td>\n",
              "      <td>14.34</td>\n",
              "      <td>135.10</td>\n",
              "      <td>1297.0</td>\n",
              "      <td>0.10030</td>\n",
              "      <td>0.13280</td>\n",
              "      <td>0.1980</td>\n",
              "      <td>0.10430</td>\n",
              "      <td>0.1809</td>\n",
              "      <td>0.05883</td>\n",
              "      <td>0.7572</td>\n",
              "      <td>0.7813</td>\n",
              "      <td>5.438</td>\n",
              "      <td>94.44</td>\n",
              "      <td>0.011490</td>\n",
              "      <td>0.02461</td>\n",
              "      <td>0.05688</td>\n",
              "      <td>0.01885</td>\n",
              "      <td>0.01756</td>\n",
              "      <td>0.005115</td>\n",
              "      <td>22.54</td>\n",
              "      <td>16.67</td>\n",
              "      <td>152.20</td>\n",
              "      <td>1575.0</td>\n",
              "      <td>0.1374</td>\n",
              "      <td>0.2050</td>\n",
              "      <td>0.4000</td>\n",
              "      <td>0.1625</td>\n",
              "      <td>0.2364</td>\n",
              "      <td>0.07678</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   radius_mean  texture_mean  ...  symmetry_worst  fractal_dimension_worst\n",
              "0        17.99         10.38  ...          0.4601                  0.11890\n",
              "1        20.57         17.77  ...          0.2750                  0.08902\n",
              "2        19.69         21.25  ...          0.3613                  0.08758\n",
              "3        11.42         20.38  ...          0.6638                  0.17300\n",
              "4        20.29         14.34  ...          0.2364                  0.07678\n",
              "\n",
              "[5 rows x 30 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nA65Elxkn0I-",
        "outputId": "f69eccca-14cc-4d17-c2eb-74b72d696b65",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        }
      },
      "source": [
        "import seaborn as sns\n",
        "ax = sns.countplot(y,label=\"Count\")       # M = 212, B = 357\n",
        "B, M = y.value_counts()\n",
        "print('Number of Benign: ',B)\n",
        "print('Number of Malignant : ',M)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of Benign:  357\n",
            "Number of Malignant :  212\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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py4CQJHUZEJKkLgNCktRlQEiSugwISVKXASFJ6jIgJEldBoQkqcuAkCR1LbmASHJOkvuT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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-OKauXPHmBL"
      },
      "source": [
        "## SelectFromModel\n",
        "\n",
        "A classe [sklearn.feature_selection.SelectFromModel](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.SelectFromModel.html) pode ser usada com qualquer estimador que tenha campos `coef_` ou `feature_importances_`. Os atributos considerados sem importância são aqueles cujos correspondentes em `coef_` (ou em `feature_importances_`) estiverem abaixo do parâmetro de limite fornecido (`threshold`).\n",
        "\n",
        "<center>`threshold : string, float, optional default None`</center>\n",
        "\n",
        "> *The threshold value to use for feature selection. Features whose importance is greater or equal are kept while the others are discarded. If “median” (resp. “mean”), then the threshold value is the median (resp. the mean) of the feature importances. A scaling factor (e.g., “1.25*mean”) may also be used. If None and if the estimator has a parameter penalty set to l1, either explicitly or implicitly (e.g, Lasso), the threshold used is 1e-5. Otherwise, “mean” is used by default.*\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gl4aWBcJn0Ew",
        "outputId": "a7b30d8b-9382-426f-d935-c6ad81d0eea2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        }
      },
      "source": [
        "import pandas as pd\n",
        "from sklearn.ensemble import ExtraTreesClassifier\n",
        "from sklearn.feature_selection import SelectFromModel\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import numpy as np\n",
        "\n",
        "df_iris = sns.load_dataset('iris')\n",
        "\n",
        "y = df_iris['species'] # atributo alvo \n",
        "X = df_iris.drop('species', axis=1) # remove atributo alvo da matrix de dados \n",
        "clf = ExtraTreesClassifier(n_estimators=250)\n",
        "clf = clf.fit(X, y)\n",
        "\n",
        "print('Atributos previsores:', X.columns)\n",
        "print('Importâncias:', clf.feature_importances_)\n",
        "\n",
        "print('Média das importâncias:', np.mean(clf.feature_importances_))\n",
        "\n",
        "model = SelectFromModel(clf, prefit=True)\n",
        "X_new = model.transform(X)\n",
        "\n",
        "feature_idx = model.get_support().astype(int)\n",
        "\n",
        "feature_idx = np.argwhere(feature_idx==1)\n",
        "\n",
        "feature_name = df_iris.columns[feature_idx]\n",
        "\n",
        "print('Atributos selecionados:', feature_name)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Atributos previsores: Index(['sepal_length', 'sepal_width', 'petal_length', 'petal_width'], dtype='object')\n",
            "Importâncias: [0.10385294 0.05613477 0.36595459 0.4740577 ]\n",
            "Média das importâncias: 0.25\n",
            "Atributos selecionados: Index([['petal_length'], ['petal_width']], dtype='object')\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rEEex5-SiNla"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qCV6RXYImCz8"
      },
      "source": [
        "O próximo exemplo é retirado da própria documentação do scikit-learn ([Feature importances with forests of trees](https://scikit-learn.org/stable/auto_examples/ensemble/plot_forest_importances.html#sphx-glr-auto-examples-ensemble-plot-forest-importances-py))"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q_5ghS80nz_q",
        "outputId": "40e821a9-1349-426f-91e4-15d8f801b5c2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from sklearn.datasets import make_classification\n",
        "from sklearn.ensemble import ExtraTreesClassifier\n",
        "\n",
        "# Build a classification task using 3 informative features\n",
        "X, y = make_classification(n_samples=1000,\n",
        "                           n_features=10,\n",
        "                           n_informative=3,\n",
        "                           n_redundant=0,\n",
        "                           n_repeated=0,\n",
        "                           n_classes=2,\n",
        "                           random_state=0,\n",
        "                           shuffle=False)\n",
        "\n",
        "# Build a forest and compute the feature importances\n",
        "forest = ExtraTreesClassifier(n_estimators=250,\n",
        "                              random_state=0)\n",
        "\n",
        "forest.fit(X, y)\n",
        "importances = forest.feature_importances_\n",
        "std = np.std([tree.feature_importances_ for tree in forest.estimators_],\n",
        "             axis=0)\n",
        "indices = np.argsort(importances)[::-1]\n",
        "\n",
        "# Print the feature ranking\n",
        "print(\"Feature ranking:\")\n",
        "\n",
        "for f in range(X.shape[1]):\n",
        "    print(\"%d. feature %d (%f)\" % (f + 1, indices[f], importances[indices[f]]))\n",
        "\n",
        "# Plot the feature importances of the forest\n",
        "plt.figure()\n",
        "plt.title(\"Feature importances\")\n",
        "plt.bar(range(X.shape[1]), importances[indices],\n",
        "       color=\"r\", yerr=std[indices], align=\"center\")\n",
        "plt.xticks(range(X.shape[1]), indices)\n",
        "plt.xlim([-1, X.shape[1]])\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Feature ranking:\n",
            "1. feature 1 (0.295902)\n",
            "2. feature 2 (0.208351)\n",
            "3. feature 0 (0.177632)\n",
            "4. feature 3 (0.047121)\n",
            "5. feature 6 (0.046303)\n",
            "6. feature 8 (0.046013)\n",
            "7. feature 7 (0.045575)\n",
            "8. feature 4 (0.044614)\n",
            "9. feature 9 (0.044577)\n",
            "10. feature 5 (0.043912)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j2mFDOPUq01W"
      },
      "source": [
        "## RFE vs SelectFromModel \n",
        "\n",
        "As estratégias de seleção de atributos implementadas em RFE e SelectFromModel têm o mesmo propósito, a saber, selecionar um conjunto de atributos relevantes para uma tarefa de predição, mas a metodologia usada em cada técnica varia, conforme descrito a seguir.\n",
        "\n",
        "* `RFE` remove atributos menos relevantes de forma iterativa: primeiro remove alguns atributos que não são importantes e, em seguida, ajusta novo modelo e remove novamente outros atributos e ajusta novo modelo. Essa estratégia repete essa iteração até atingir um número pré-estabelecido de atributos.\n",
        "\n",
        "* `SelectFromModel` apenas remove atributos menos importantes com base em um limite fornecido como um parâmetro. Não há iteração envolvida."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vnT7_yIFkIQd"
      },
      "source": [
        "# Exercícios\n",
        "\n",
        "**1** - Considere que a matrix de dados abaixo corresponde a notas de 5 estudantes, nas disciplinas Matemática, Português e Artes. Construa a matriz de covariâncias correspondente à matriz de dados fornecida. Qual o teste que possui maior variância? Qual par de disciplinas está mais correlacionado?\n",
        "$$\n",
        "\\begin{matrix} \n",
        "90 & 60 & 90 \\\\ \n",
        "90 & 90 & 30 \\\\ \n",
        "60 & 60 & 60  \\\\\n",
        "60 & 60 & 90 \\\\ \n",
        "30 & 30 & 30 \\\\ \n",
        "\\end{matrix}\n",
        "$$\n",
        "\n",
        "**2** - Neste exercício, considere a implementação em PCA em numpy e scipy fornecida. O que você espera que os conjuntos de dados projetados sejam para a matriz de dados $X1$ fornecida abaixo? Explique os resultados para $k = 3$ e $k = 1$.\n",
        "\n",
        "```\n",
        "X1 = np.array([\n",
        "        [1,   2, -.05],\n",
        "        [2,   4, -.05],\n",
        "        [4,   8, -.05],\n",
        "        [8,  16, -.05],\n",
        "    ])\n",
        "pca(X=X1, k=3)\n",
        "pca(X=X1, k=1)\n",
        "```\n",
        "\n",
        "\n",
        "**3** - Considere o conjunto de dados [MNIST](https://en.wikipedia.org/wiki/MNIST_database), composto de imagens de dígitos de 28x28 pixels. A dimensão original deste conjunto de dados é 784. Utilizando a abordagem de plotar a soma acumulada das variâncias explicadas, determine a dimensão intrínseca desse conjunto de dados. Abaixo, é fornecido o código para carregar o conjunto de dados. \n",
        "\n",
        "```\n",
        "# Load data from https://www.openml.org/d/554\n",
        "X_mnist, y_mnist = fetch_openml('mnist_784', version=1, return_X_y=True)\n",
        "\n",
        "print(X_mnist.data.shape)\n",
        "```\n",
        "\n",
        "**4** - Considere o conjunto de dados PIMA Indians (fornecido como arquivo em formato CSV). Use as abordagens de seleção de atributos univariada e RFE para determinar quais os atributos mais relevantes relativamente ao atributo alvo.\n",
        "\n",
        "\n"
      ]
    }
  ]
}