6 - Support Vector Machine/SVMs - Part 1 - Gradient Descent.ipynb

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    "# Support Vector Machines - Part 1\n",
    "\n",
    "## Overview\n",
    "- [1. What is SVMs?](#1)\n",
    "- [2. Primal Support Vector Machine](#2)\n",
    "    - [2.1 Distance between Two Parallel Lines](#2.1)\n",
    "    - [2.2 Optimal Hyperplane](#2.2)\n",
    "- [3. Hard Margin](#3)\n",
    "- [4. Soft Margin](#4)\n",
    "- [5. Solve SVMs by Gradient Descent](#5)\n",
    "    - [5.1 Hard Margin by Gradient Descent](#5.1)\n",
    "    - [5.2 Soft Margin by Gradient Descent](#5.2)\n",
    "- [6. References](#6)"
   ]
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    "<a name='1' ></a>\n",
    "## 1. What is SVMs?\n",
    "A *Support Vector Machine (SVM)* is a very powerful and versatile Machine Learning model, capable of performing linear or nonlinear classification, regression, and even outlier detection. It is one of the most popular models in Machine Learning, and anyone interested in Machine Learning should have it in their toolbox. SVMs are particularly well suited for classification of complex but small- or medium-sized datasets.\n",
    "\n",
    "SVMs can be also used for multinomial classification, but we almost focus on binary classification.\n",
    "\n",
    "<a name='2' ></a>\n",
    "## 2. Primal Support Vector Machine\n",
    "\n",
    "Assume we have a dataset that is linearly seperable with each pair of point, $(x^{(1)}, y_1), (x^{(2)}, y_2), (x^{(3)}, y_3), ..., (x^{(n)}, y_n)$, where $n$ is the number of observations, $x^{(i)} = (x_1, x_2, ..., x_d)$ and $d$ is the number of features of $i-th$ observation. \n",
    "\n",
    "We have infinitely many candidate hyperplanes (below images), and therefore classifiers,\n",
    "that solve our classification problem without any (training) errors. To find\n",
    "a unique solution, one idea is to choose the separating hyperplane that\n",
    "maximizes the margin between the positive and negative examples. In\n",
    "other words, we want the positive and negative examples to be separated\n",
    "by the **largest margin**.\n",
    "\n",
    "<div style=\"width:image width px; font-size:80%; text-align:center;\"><img src='images/margin.png' alt=\"alternate text\" width=\"width\" height=\"height\" style=\"width:600px;height:300px;\" />  </div>\n",
    "\n",
    "*The concept of the margin is intuitively simple: It is the distance of the\n",
    "separating hyperplane to the closest examples in the dataset, assuming\n",
    "that the dataset is linearly separable.*\n",
    "\n",
    "<a name='2.1' ></a>\n",
    "### 2.1 Distance between Two Parallel Lines\n",
    "When the lines are given by\n",
    "\n",
    "$$\n",
    "(l_1): w_{01} + w_1 x_1 + ... + w_n x_n = 0 \\\\\n",
    "(l_2): w_{02} + w_1 x_1 + ... + w_n x_n = 0\n",
    "$$\n",
    "\n",
    "It's easy to see that $l_1$ and $l_2$ is two parellel lines. From [formular](https://en.wikipedia.org/wiki/Distance_between_two_parallel_lines), the distance of two parellel lines is:\n",
    "\n",
    "$$d(l_1, l_2) = \\frac{|w_{01} - w_{02}|}{\\sqrt{w_1^2 + w_2^2 + ... + w_n^2}} = \\frac{|w_{01} - w_{02}|}{\\Vert w \\Vert_2}$$\n",
    "\n",
    "We mention the above because they are closely related when it comes to maximize margin. If we maximize the margin, it also means that we maximize the distance between two parallel lines passing through the points on the margin.\n",
    "\n",
    "<a name='2.2' ></a>\n",
    "### 2.2 Optimal Hyperplane\n",
    "\n",
    "As mentioned, we need to find the optimal hyperplane with largest margin. Let example $\\mathbf{x} \\in \\mathbb{R}^d$ be an\n",
    "element of the data space. Consider a function\n",
    "\n",
    "$$\n",
    "f: \\mathbb{R}^d \\rightarrow \\mathbb{R} \\\\\n",
    "\\mathbf{x} \\mapsto f(\\mathbf{x}) := \\mathbf{w^T x} + b = \\langle \\mathbf{w, x} \\rangle + b\n",
    "$$\n",
    "\n",
    "parametrized by $\\mathbf{w} \\in \\mathbb{R}^d$ and $b \\in \\mathbb{R}$. Recall that hyperplanes are affine subspaces. Therefore, we define the hyperplane that separates the two classes in our binary classification problem as\n",
    "\n",
    "$$\\{ \\mathbf{x} \\in \\mathbb{R}^d: f(\\mathbf{x}) = 0 \\}$$\n",
    "\n",
    "When training the classifier, we want to ensure that the examples with\n",
    "positive labels are on the positive side of the hyperplane, i.e.,\n",
    "\n",
    "$$\\mathbf{w^T x} + b  \\geq 0 \\text{ when $y = +1$} $$\n",
    "\n",
    "and the examples with negative labels are on the negative side, i.e.,\n",
    "\n",
    "$$\\mathbf{w^T x} + b  < 0 \\text{ when $y = -1$}$$"
   ]
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    "<a name='3' ></a>\n",
    "## 3. Hard Margin\n",
    "Another approach that does not change the properties of the optimal hyperplane is\n",
    "\n",
    "$$\\mathbf{w^T x} + b  = 1 \\text{ (anything on or above this boundary is of one class, with label $1$)} $$\n",
    "$$\\mathbf{w^T x} + b  = -1 \\text{ (anything on or above this boundary is of one class, with label $-1$)} $$\n",
    "\n",
    "<div style=\"width:image width px; font-size:80%; text-align:center;\"><img src='images/hard-margin.ppm' alt=\"alternate text\" width=\"width\" height=\"height\" style=\"width:300px;height:300px;\" />  </div>\n",
    "\n",
    "We want the positive and negative examples to be at least 1 away from the hyperplane, which yields the condition\n",
    "\n",
    "$$y_i (\\mathbf{w^T x^{(i)}} + b) \\geq 1$$\n",
    "\n",
    "Combining the margin maximization with the fact that examples need to be on the correct side of the hyperplane (based on their labels) gives us\n",
    "\n",
    "$$\\max_{w, b} \\frac{1}{\\mathbf{\\Vert w \\Vert}}$$\n",
    "\n",
    "subject to $y_i (\\mathbf{w^T x^{(i)}} + b) \\geq 1$ for all $i=1, 2, ..., n$. Instead of maximizing the reciprocal of the norm as the above, we often minimize the squared norm. We also often include a constant $\\frac12$ that does\n",
    "not affect the optimal $\\mathbf{w}, b$ but yields a tidier form when we compute the gradient. Then, our objective becomes\n",
    "\n",
    "$$\\min_{w, b} \\frac{1}{2} \\Vert \\mathbf{w} \\Vert^2$$\n",
    "\n",
    "subject to $y_i (\\mathbf{w^T x^{(i)}} + b) \\geq 1$ for all $i=1, 2, ..., n$\n",
    "\n",
    "This equation is known as the *hard margin SVM*. The reason for the expression “hard” is because the formulation does not allow for any violations of the margin condition."
   ]
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    "<a name='4' ></a>\n",
    "## 4. Soft Margin \n",
    "\n",
    "In the case where data is not linearly separable, we may wish to allow\n",
    "some examples to fall within the margin region, or even to be on the\n",
    "wrong side of the hyperplane as illustrated in the below.\n",
    "\n",
    "<div style=\"width:image width px; font-size:80%; text-align:center;\"><img src='images/soft-margin.png' alt=\"alternate text\" width=\"width\" height=\"height\" style=\"width:600px;height:300px;\" />  </div>\n",
    "\n",
    "The model that allows for some classification errors is called the *soft margin SVM*.\n",
    "\n",
    "<div style=\"width:image width px; font-size:80%; text-align:center;\"><img src='images/error-soft-margin.png' alt=\"alternate text\" width=\"width\" height=\"height\" style=\"width:500px;height:300px;\" />  </div>\n",
    "\n",
    "The key geometric idea is to introduce a slack variable $\\xi_i$ corresponding\n",
    "to each example–label pair $(x^{(i)} , y_i)$ that allows a particular example to be\n",
    "within the margin or even on the wrong side of the hyperplane.\n",
    "The *slack variable $\\xi$* measures the distance of a positive example $x_+$ to the positive\n",
    "margin hyperplane $h_\\mathbf{w^Tx} + b = 1$ when $x_+$ is on the wrong side. The new objective function\n",
    "\n",
    "$$\\min_{\\mathbf{w}, b, \\mathbf{\\xi}} \\frac{1}{2} \\Vert \\mathbf{w} \\Vert^2 + C\\sum_{i=1}^n \\xi_i$$\n",
    "\n",
    "subject to \n",
    "- $y_i (\\mathbf{w^T x^{(i)}} + b) \\geq 1 - \\xi_i$\n",
    "- $\\xi_i \\geq 0$\n",
    "\n",
    "for all $i=1, 2, ..., n$\n",
    "\n",
    "### Hinge Loss Function \n",
    "\n",
    "<div style=\"width:image width px; font-size:80%; text-align:center;\"><img src='images/hinge-loss.png' alt=\"alternate text\" width=\"width\" height=\"height\" style=\"width:500px;height:300px;\" /> The hinge loss is a convex upper bound of zero-one loss. </div>\n",
    "\n",
    "In SVMs, we use **hinge-loss** to represent error $\\xi$\n",
    "\n",
    "$$l(t) = \\max\\{ 0, 1-t \\}$$ \n",
    "\n",
    "where $t = yf(\\mathbf{x}) = y(\\mathbf{w^T x} + b)$. We can equivalently replace minimization of the hinge loss over t with a minimization of a slack variable ξ with two constraints. In equation form,\n",
    "\n",
    "$$\\min_t max\\{ 0, 1-t \\}$$\n",
    "\n",
    "is equivalent to \n",
    "\n",
    "$$\\min_{\\xi, t} \\xi$$\n",
    "\n",
    "subject to $\\xi \\geq 0$, $\\xi \\geq 1 - t$. Therefore, the objective function can be written\n",
    "\n",
    "$$\\min_{\\mathbf{w}, b} \\frac{1}{2} \\Vert \\mathbf{w} \\Vert^2 + C\\sum_{i=1}^n \\max\\{ 0, 1 - y_i(\\mathbf{w^T x^{(i)}} + b) \\}$$\n",
    "\n",
    "or\n",
    "\n",
    "$$\\min_{\\mathbf{w}, b} \\underbrace{\\frac{1}{2} \\lambda \\Vert \\mathbf{w} \\Vert^2}_\\text{regularizer} + \\underbrace{\\sum_{i=1}^n \\max\\{ 0, 1 - y_i(\\mathbf{w^T x^{(i)}} + b) \\}}_\\text{error term} $$\n",
    "\n",
    "where $\\lambda = \\frac{1}{C}$"
   ]
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    "def loss(w, b, X, y, lamda):\n",
    "    \"\"\"\n",
    "    Calculate value of loss function.\n",
    "    \n",
    "    Args:\n",
    "        w: weight\n",
    "        b: bias\n",
    "        X: training example\n",
    "        y: labels\n",
    "        lamda: parameter for regularizer\n",
    "    Return:\n",
    "        l: the value of loss\n",
    "    \"\"\"\n",
    "    hinge = 1 - np.dot(X @ w.T + b, y)\n",
    "    l = 1/2 * lamda * np.dot(w.T, w) + np.sum(np.maximum(0, hinge))\n",
    "    return l"
   ]
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    "<a name='5' ></a>\n",
    "## 5. Solve SVMs by Gradient Descent\n",
    "Using the hinge loss gives us the unconstrained optimization problem, so we can use *Gradient Descent* to approximate the optimal value. \n",
    "\n",
    "*Gradient Descent Formula*\n",
    "$$\\mathbf{w}^{(i+1)} = \\mathbf{w}^{(i)} - \\alpha \\nabla J(\\mathbf{w}^{(i)})$$\n",
    "\n",
    "where\n",
    "- $\\mathbf{w}^{(i)}$ is weight at $i^{th}$ iteration\n",
    "- $\\alpha$ is *learning rate*\n",
    "- $\\nabla J(\\mathbf{w}^{(i)})$ is gradient of $J$ at $\\mathbf{w}^{(i)}$\n",
    "and \n",
    "$$J(\\mathbf{w}) = \\frac{1}{2} \\lambda \\Vert \\mathbf{w} \\Vert^2 + \\sum_{i=1}^n \\max\\{ 0, 1 - y_i(\\mathbf{w^T x^{(i)}} + b) \\}$$"
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    "**Case 1:** $y_i(\\mathbf{w^T x^{(i)}} + b) < 1$ \n",
    "\n",
    "$$\\Rightarrow 1 - y_i(\\mathbf{w^T x^{(i)}} + b) > 0 \\\\\n",
    "\\Rightarrow J(\\mathbf{w}) = \\frac{1}{2} \\lambda \\Vert \\mathbf{w} \\Vert^2 + \\sum_{i} \\left(1 - y_i(\\mathbf{w^T x^{(i)}} + b) \\right) \\\\\n",
    "$$\n",
    "\n",
    "- $\\nabla \\frac{\\partial J}{\\partial \\mathbf{w}} = \\lambda \\mathbf{w} - \\sum_{i} y_i\\mathbf{x^{(i)}}$ \n",
    "- $\\nabla \\frac{\\partial J}{\\partial b} = \\sum_{i} y_i$ \n",
    "\n",
    "where \n",
    "$\\mathbf{X} = \\begin{bmatrix} \\mathbf{x^{(1)}} \\\\ \\mathbf{x^{(2)}} \\\\ \\vdots\\\\ \\mathbf{x^{(n)}} \\end{bmatrix}$,\n",
    "$\\mathbf{y} = \\begin{bmatrix} y_1 \\\\ y_2 \\\\ \\vdots\\\\ y_n \\end{bmatrix}$\n",
    "and $\\mathbf{x^{(i)}}$ is a vector $(1, d)$,\n",
    "\n",
    "\n",
    "**Case 2:** $y_i(\\mathbf{w^T x^{(i)}} + b) \\geq 1$ \n",
    "\n",
    "$$\\Rightarrow 1 - y_i(\\mathbf{w^T x^{(i)}} + b) \\leq 0 \\\\\n",
    "\\Rightarrow J(\\mathbf{w}) = \\frac{1}{2} \\lambda \\Vert \\mathbf{w} \\Vert^2 \\\\\n",
    "$$\n",
    "\n",
    "- $\\nabla \\frac{\\partial J}{\\partial \\mathbf{w}} = \\lambda \\mathbf{w}$\n",
    "- $\\nabla \\frac{\\partial J}{\\partial b} = 0$ "
   ]
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   "cell_type": "code",
   "execution_count": 43,
   "id": "09f116d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Package\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn import datasets\n",
    "from utils import visualize_svm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "f9ca9d50",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SVM:\n",
    "    def __init__(self, learning_rate=0.001, lamda=0.001, n_iters=300):\n",
    "        self.lr = learning_rate\n",
    "        self.lamda = lamda\n",
    "        self.n_iters = n_iters\n",
    "        self.w = None\n",
    "        self.b = None\n",
    "\n",
    "    def fit(self, X, y, verbose=0):\n",
    "        n_samples, n_features = X.shape\n",
    "        y_ = np.where(y <= 0, -1, 1)\n",
    "\n",
    "        self.w = np.zeros(n_features)\n",
    "        self.b = 0\n",
    "\n",
    "        for i in range(self.n_iters):\n",
    "            for idx, x_i in enumerate(X):\n",
    "                condition = y_[idx] * (np.dot(x_i, self.w) + self.b) >= 1\n",
    "                if condition:\n",
    "                    self.w -= self.lr * (self.lamda * self.w)\n",
    "                else:\n",
    "                    self.w -= self.lr * (self.lamda * self.w - np.dot(x_i, y_[idx]))\n",
    "                    self.b -= self.lr * y_[idx]\n",
    "                    \n",
    "            if verbose and i % 50 == 0:\n",
    "                l = loss(self.w, self.b, X, y, self.lamda)\n",
    "                print(f'Loss at iteration {i}: {l}')\n",
    "\n",
    "    def predict(self, X):\n",
    "        approx = np.dot(X, self.w) + self.b\n",
    "        return np.sign(approx)"
   ]
  },
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   "id": "c2ef5a96",
   "metadata": {},
   "source": [
    "<a name='5.1' ></a>\n",
    "### 5.1 Hard Margin by Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "c931690c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss at iteration 0: 3.320620155219481e-05\n",
      "Loss at iteration 50: 0.00012613298437035817\n",
      "Loss at iteration 100: 0.00012487793958176996\n",
      "Loss at iteration 150: 0.00012363538270369282\n",
      "Loss at iteration 200: 0.0001274891832005812\n",
      "Loss at iteration 250: 0.00012622064400144868\n",
      "[0.48082209 0.15117092] -0.03000000000000002\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = datasets.make_blobs(n_samples=100, n_features=2, centers=2, cluster_std=1.05, random_state=40)\n",
    "y = np.where(y == 0, -1, 1)\n",
    "\n",
    "clf = SVM()\n",
    "clf.fit(X, y, verbose=1)\n",
    "\n",
    "print(clf.w, clf.b)\n",
    "visualize_svm(X, y, clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cde397f1",
   "metadata": {},
   "source": [
    "<a name='5.2' ></a>\n",
    "### 5.2 Soft Margin by Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "779b8482",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss at iteration 0: 2.9873191362208774e-05\n",
      "Loss at iteration 50: 0.00036738620058293056\n",
      "Loss at iteration 100: 0.000505374126975878\n",
      "Loss at iteration 150: 0.0005803647647793129\n",
      "Loss at iteration 200: 0.0006601508949804827\n",
      "Loss at iteration 250: 0.0007446571435896224\n",
      "[1.25029846 0.31818442] -0.45600000000000035\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = datasets.make_blobs(n_samples=100, n_features=2, centers=2, cluster_std=2.05, random_state=40)\n",
    "y = np.where(y == 0, -1, 1)\n",
    "\n",
    "clf = SVM()\n",
    "clf.fit(X, y, verbose=1)\n",
    "\n",
    "print(clf.w, clf.b)\n",
    "visualize_svm(X, y, clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65b1fb76",
   "metadata": {},
   "source": [
    "So, in this section, we solved SVMs using gradient descent; in the following notebook, we will solve SVMs using the dual problem by Lagrange method.\n",
    "\n",
    "<a name='6' ></a>\n",
    "## 6. References\n",
    "\n",
    "- [https://en.wikipedia.org/wiki/Support_vector_machine](https://en.wikipedia.org/wiki/Support_vector_machine)\n",
    "- [https://machinelearningcoban.com/2017/04/09/smv/](https://machinelearningcoban.com/2017/04/09/smv/)\n",
    "- [https://machinelearningcoban.com/2017/04/13/softmarginsmv/](https://machinelearningcoban.com/2017/04/13/softmarginsmv/)\n",
    "- [Mathematics for Machine Learning](https://mml-book.github.io/book/mml-book.pdf)\n",
    "- [Hands-on Machine Learning with Scikit-Learn, Keras, and TensorFlow (Page 177-189)](https://www.knowledgeisle.com/wp-content/uploads/2019/12/2-Aur%C3%A9lien-G%C3%A9ron-Hands-On-Machine-Learning-with-Scikit-Learn-Keras-and-Tensorflow_-Concepts-Tools-and-Techniques-to-Build-Intelligent-Systems-O%E2%80%99Reilly-Media-2019.pdf)\n",
    "- [https://www.python-engineer.com/courses/mlfromscratch/07_svm/](https://www.python-engineer.com/courses/mlfromscratch/07_svm/)\n",
    "- [https://scikit-learn.org/stable/modules/svm.html](https://scikit-learn.org/stable/modules/svm.html)"
   ]
  }
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