PCA/PCA_fromScratch (4).ipynb

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      "metadata": {
        "id": "zPJ9l1TqfY67"
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      "source": [
        "import pandas as pd\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def mean(x):\n",
        "  return sum(x)/len(x)"
      ],
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        "id": "MPAb3MRPgQrP"
      },
      "execution_count": 2,
      "outputs": []
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        "def std(x):\n",
        "  return (sum((i-mean(x))**2 for i in x)/len(x))**0.5"
      ],
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        "id": "ncFDqso5jj6I"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def standardize_data(x):\n",
        "  std_data=x-mean(x)/std(x)\n",
        "  return std_data\n"
      ],
      "metadata": {
        "id": "lKM4pZO-kPhI"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def covariance(x):\n",
        " cov_mat=(standardize_data(x).T @ standardize_data(x))/(standardize_data(x).shape[0]-1)\n",
        " return cov_mat"
      ],
      "metadata": {
        "id": "NbN1h88mktGM"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def eigen_val_vector(x,k):\n",
        "  eig_vals,eig_vecs = np.linalg.eig(covariance(x))\n",
        "  sort_idx=np.argsort(eig_vals)[::-1]\n",
        "  eig_vals=eig_vals[sort_idx]\n",
        "  eig_vecs=eig_vecs[:,sort_idx]\n",
        "  components=eig_vecs[:k]\n",
        "  explained_variance=np.sum(eig_vals[:k])/np.sum(eig_vals)\n",
        "  return explained_variance"
      ],
      "metadata": {
        "id": "epeHVK5nmeqo"
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      "execution_count": 10,
      "outputs": []
    },
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      "cell_type": "code",
      "source": [
        "def transform(x,k):\n",
        "  x-=mean(x)\n",
        "  return np.dot(x,eigen_val_vector.components(x,k).T)\n"
      ],
      "metadata": {
        "id": "QFsCX_aMqWXg"
      },
      "execution_count": 11,
      "outputs": []
    },
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      "cell_type": "code",
      "source": [
        "class PCA:\n",
        "  def __init__(self,num_components):\n",
        "    self.num_components=num_components\n",
        "\n",
        "\n",
        "  def standardize_data(self,x):\n",
        "    self.mean= np.sum(x)/len(x)\n",
        "    self.std= (sum((i-mean(x))**2 for i in x)/len(x))**0.5\n",
        "    std_data=x-mean(x)/std(x)\n",
        "    return std_data\n",
        "  def covariance(self,x):\n",
        "    cov_mat=(self.standardize_data(x).T @ self.standardize_data(x))/(self.standardize_data(x).shape[0]-1)\n",
        "    return cov_mat\n",
        "  def fit_n_transform(self,x):\n",
        "    eig_vals,eig_vecs = np.linalg.eig(self.covariance(x))\n",
        "    sort_idx=np.argsort(eig_vals)[::-1]\n",
        "    eig_vals=eig_vals[sort_idx]\n",
        "    eig_vecs=eig_vecs[:,sort_idx]\n",
        "    self.components=eig_vecs[:self.num_components]\n",
        "    explained_variance=np.sum(eig_vals[:self.num_components])/np.sum(eig_vals)\n",
        "    print(\"component variance:\\n\",explained_variance)\n",
        "    comp=self.components.T\n",
        "    print(\"PCA:\\n\",np.dot(standardize_data(x),comp))"
      ],
      "metadata": {
        "id": "Il1Pvoh1XkcM"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data=pd.read_csv(\"/content/sample_data/california_housing_train.csv\")\n",
        "data"
      ],
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        "outputId": "6c5eaba2-0c78-4a40-9f93-c3569f54b0c3"
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      "execution_count": 29,
      "outputs": [
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              "       longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
              "0        -114.31     34.19                15.0       5612.0          1283.0   \n",
              "1        -114.47     34.40                19.0       7650.0          1901.0   \n",
              "2        -114.56     33.69                17.0        720.0           174.0   \n",
              "3        -114.57     33.64                14.0       1501.0           337.0   \n",
              "4        -114.57     33.57                20.0       1454.0           326.0   \n",
              "...          ...       ...                 ...          ...             ...   \n",
              "16995    -124.26     40.58                52.0       2217.0           394.0   \n",
              "16996    -124.27     40.69                36.0       2349.0           528.0   \n",
              "16997    -124.30     41.84                17.0       2677.0           531.0   \n",
              "16998    -124.30     41.80                19.0       2672.0           552.0   \n",
              "16999    -124.35     40.54                52.0       1820.0           300.0   \n",
              "\n",
              "       population  households  median_income  median_house_value  \n",
              "0          1015.0       472.0         1.4936             66900.0  \n",
              "1          1129.0       463.0         1.8200             80100.0  \n",
              "2           333.0       117.0         1.6509             85700.0  \n",
              "3           515.0       226.0         3.1917             73400.0  \n",
              "4           624.0       262.0         1.9250             65500.0  \n",
              "...           ...         ...            ...                 ...  \n",
              "16995       907.0       369.0         2.3571            111400.0  \n",
              "16996      1194.0       465.0         2.5179             79000.0  \n",
              "16997      1244.0       456.0         3.0313            103600.0  \n",
              "16998      1298.0       478.0         1.9797             85800.0  \n",
              "16999       806.0       270.0         3.0147             94600.0  \n",
              "\n",
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              "      <th></th>\n",
              "      <th>longitude</th>\n",
              "      <th>latitude</th>\n",
              "      <th>housing_median_age</th>\n",
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              "      <th>0</th>\n",
              "      <td>-114.31</td>\n",
              "      <td>34.19</td>\n",
              "      <td>15.0</td>\n",
              "      <td>5612.0</td>\n",
              "      <td>1283.0</td>\n",
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              "      <td>472.0</td>\n",
              "      <td>1.4936</td>\n",
              "      <td>66900.0</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-114.47</td>\n",
              "      <td>34.40</td>\n",
              "      <td>19.0</td>\n",
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              "      <td>1901.0</td>\n",
              "      <td>1129.0</td>\n",
              "      <td>463.0</td>\n",
              "      <td>1.8200</td>\n",
              "      <td>80100.0</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-114.56</td>\n",
              "      <td>33.69</td>\n",
              "      <td>17.0</td>\n",
              "      <td>720.0</td>\n",
              "      <td>174.0</td>\n",
              "      <td>333.0</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-114.57</td>\n",
              "      <td>33.64</td>\n",
              "      <td>14.0</td>\n",
              "      <td>1501.0</td>\n",
              "      <td>337.0</td>\n",
              "      <td>515.0</td>\n",
              "      <td>226.0</td>\n",
              "      <td>3.1917</td>\n",
              "      <td>73400.0</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-114.57</td>\n",
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              "      <td>20.0</td>\n",
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              "      <td>2217.0</td>\n",
              "      <td>394.0</td>\n",
              "      <td>907.0</td>\n",
              "      <td>369.0</td>\n",
              "      <td>2.3571</td>\n",
              "      <td>111400.0</td>\n",
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              "    <tr>\n",
              "      <th>16996</th>\n",
              "      <td>-124.27</td>\n",
              "      <td>40.69</td>\n",
              "      <td>36.0</td>\n",
              "      <td>2349.0</td>\n",
              "      <td>528.0</td>\n",
              "      <td>1194.0</td>\n",
              "      <td>465.0</td>\n",
              "      <td>2.5179</td>\n",
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              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
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              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
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              "\n",
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              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
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              "\n",
              "      .colab-df-generate:hover {\n",
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            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x=data.drop('median_house_value',axis=1)\n",
        "x=np.asarray(x)"
      ],
      "metadata": {
        "id": "vKBSEy0D1ldj"
      },
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3j0iJZPw2Skx",
        "outputId": "99c6f4d3-a130-4283-cc40-f890e56a129c"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-114.31  ,   34.19  ,   15.    , ..., 1015.    ,  472.    ,\n",
              "           1.4936],\n",
              "       [-114.47  ,   34.4   ,   19.    , ..., 1129.    ,  463.    ,\n",
              "           1.82  ],\n",
              "       [-114.56  ,   33.69  ,   17.    , ...,  333.    ,  117.    ,\n",
              "           1.6509],\n",
              "       ...,\n",
              "       [-124.3   ,   41.84  ,   17.    , ..., 1244.    ,  456.    ,\n",
              "           3.0313],\n",
              "       [-124.3   ,   41.8   ,   19.    , ..., 1298.    ,  478.    ,\n",
              "           1.9797],\n",
              "       [-124.35  ,   40.54  ,   52.    , ...,  806.    ,  270.    ,\n",
              "           3.0147]])"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SvijLKUo4tYx",
        "outputId": "848414d7-55bd-42d9-b360-7a62d41b01ba"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(17000, 8)"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "xnew=standardize_data(x)"
      ],
      "metadata": {
        "id": "WzabF1hy2EOi"
      },
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "xnew.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bfjsqYQ_4wWI",
        "outputId": "33d6dab3-be31-40c2-f46d-28b3531c7090"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(17000, 8)"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "xnew"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B99W8FlA21Lp",
        "outputId": "26a0b306-9bce-4f39-d324-2a50560e3937"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-5.46812209e+01,  1.75214887e+01,  1.27285821e+01, ...,\n",
              "         1.01375453e+03,  4.70696464e+02, -5.41711197e-01],\n",
              "       [-5.48412209e+01,  1.77314887e+01,  1.67285821e+01, ...,\n",
              "         1.12775453e+03,  4.61696464e+02, -2.15311197e-01],\n",
              "       [-5.49312209e+01,  1.70214887e+01,  1.47285821e+01, ...,\n",
              "         3.31754530e+02,  1.15696464e+02, -3.84411197e-01],\n",
              "       ...,\n",
              "       [-6.46712209e+01,  2.51714887e+01,  1.47285821e+01, ...,\n",
              "         1.24275453e+03,  4.54696464e+02,  9.95988803e-01],\n",
              "       [-6.46712209e+01,  2.51314887e+01,  1.67285821e+01, ...,\n",
              "         1.29675453e+03,  4.76696464e+02, -5.56111972e-02],\n",
              "       [-6.47212209e+01,  2.38714887e+01,  4.97285821e+01, ...,\n",
              "         8.04754530e+02,  2.68696464e+02,  9.79388803e-01]])"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "PCA(num_components=2).fit_n_transform(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mzfY7ehX4j-G",
        "outputId": "1e4f9506-6bf0-4c21-c81a-8ab5a39e9fce"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "component variance:\n",
            " 0.9977592804937393\n",
            "PCA:\n",
            " [[ 673.97779405 -540.00589271]\n",
            " [ 962.51922422 -630.29468679]\n",
            " [ 172.55623587 -136.07609091]\n",
            " ...\n",
            " [ 550.91077689 -494.70940483]\n",
            " [ 589.42397248 -521.3590202 ]\n",
            " [ 311.01020754 -289.49490706]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "nPSmjVFI46dA"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}