notes/ml/Support-Vector-Machine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "09c89b26",
   "metadata": {},
   "source": [
    "### Support Vector Machine"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be219e60",
   "metadata": {},
   "source": [
    "#### Hyperplanes\n",
    "\n",
    "\\begin{align}\n",
    "\\mathcal{H_0}: wx_i+b &= 0 \\\\\n",
    "\\mathcal{H_1}: wx_i+b & \\geq 1 \\qquad\\text{if  } y_i=1 \\\\\n",
    "\\mathcal{H_2}: wx_i+b & < 1 \\qquad\\text{if  } y_i=-1\\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a1844e76",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "03f570cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11abc0f10>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1s = np.linspace(-5,5,100)\n",
    "# x2s = np.linspace(-5,5,100)\n",
    "w1,w2,b = 5,4,2\n",
    "x2s0 = (-b-w1*x1s)/w2\n",
    "x2s1 = (1-b-w1*x1s)/w2\n",
    "x2s3 = (2-b-w1*x1s)/w2\n",
    "x2s2 = (-1-b-w1*x1s)/w2\n",
    "x2s4 = (-2-b-w1*x1s)/w2\n",
    "plt.plot(x1s,x2s0)\n",
    "plt.plot(x1s,x2s1)\n",
    "plt.plot(x1s,x2s2)\n",
    "plt.plot(x1s,x2s3)\n",
    "plt.plot(x1s,x2s4)\n",
    "plt.legend(['$H_0 (0)$','$H_1 (1)$',\n",
    "            '$H_2 (-1)$', '$H_3 (2)$', '$H_4 (-2)$'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "39ce2481",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2)\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[1, 1], [1, 2],[2,1],[2,2],[-1,1],[-1,2],[-2,1],[-2,2],\n",
    "              [1, -1], [1, -2],[2,-1],[2,-2],[-1,-1],[-1,-2],[-2,-1],[-2,-2]])\n",
    "y = np.array([1,1,1,1,-1,-1,-1,-1,\n",
    "              1,1,1,1,-1,-1,-1,-1])\n",
    "w = np.array([[-1, -0.75]])\n",
    "b = 1\n",
    "print(w.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8f5d2518",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_decision_boundary(X, y, w):\n",
    "    \"\"\"\n",
    "    X --> Inputs\n",
    "    y --> Outputs\n",
    "    w --> weight parameters: ndarray with size(1,2)\n",
    "    \"\"\"\n",
    "   \n",
    "    # Plotting\n",
    "    plt.figure(figsize=(10, 8))\n",
    "    # if y == -1, red point\n",
    "    # if y == 1, blue point\n",
    "    plt.plot(X[:, 0][y == -1], X[:, 1][y == -1], \"r^\")\n",
    "    plt.plot(X[:, 0][y == 1], X[:, 1][y == 1], \"bs\")\n",
    "    plt.xlabel(\"feature 1\")\n",
    "    plt.ylabel(\"feature 2\")\n",
    "    if(w[0,1]==0):\n",
    "        plt.axvline(color=\"black\")\n",
    "    else:\n",
    "        plt.axline((0, 0), slope=-w[0,0] /w[0,1], color=\"black\")\n",
    "    plt.xlim(-3, 3)\n",
    "    plt.ylim(-3, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54617518",
   "metadata": {},
   "source": [
    "### Hard Margin\n",
    "\n",
    "\\begin{align*}\n",
    "&\\text{minimize}_{\\mathbf{w},b} & \\frac{1}{2}\\mathbf{w}^\\top \\mathbf{w} \\\\\n",
    "&\\text{subject to } \\quad & y_i(\\mathbf{w}^\\top x_i+b) \\geq 1\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9d579a2",
   "metadata": {},
   "source": [
    "where $y_i$ is the ground truth, $x_i$ the input, if $y_i$ and the prediction from $\\mathbf{w}^\\top x_i+b$ matches should be greater than 1. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cb76e12",
   "metadata": {},
   "source": [
    "$$\\mathcal{J}(\\mathbf{w},b) = \\frac{\\lambda}{2}\\mathbf{w}^\\top\\mathbf{w}+\\frac{1}{n}\\sum^n_{i=1}\\big(1-y_i(\\mathbf{w}^\\top \\mathbf{x}_i+b)\\big)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d43d0af5",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\nabla_\\mathbf{w}\\mathbf{J} &= \\lambda\\mathbf{w}-y_i\\mathbf{x}_i \\\\\n",
    "\\nabla_b\\mathbf{J} &= -y_i \\\\\n",
    "\\mathbf{w} &\\leftarrow \\mathbf{w} - \\alpha\\nabla_\\mathbf{w}\\mathbf{J} \\\\\n",
    "b &\\leftarrow b - \\alpha\\nabla_b\\mathbf{J} \\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0f63b00a",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SVM:\n",
    "    X, y = None, None\n",
    "    w, b = None, None\n",
    "    lr, lamb = 0.01, 1\n",
    "    epochs = 100\n",
    "    def __init__(self):\n",
    "        pass\n",
    "        \n",
    "    def set_data(self, X, y):\n",
    "        self.X = X\n",
    "        self.y = y\n",
    "        \n",
    "    def set_params(self, w, b):\n",
    "        self.w = w\n",
    "        self.b = b\n",
    "        \n",
    "    def set_hyperparams(self, lr, epochs, lamb):\n",
    "        self.lr = lr\n",
    "        self.epochs = epochs\n",
    "        self.lamb = lamb\n",
    "        \n",
    "    def activation(self, value):\n",
    "        return 1 if value>=0 else -1\n",
    "    \n",
    "    def eval_err_rate(self):\n",
    "        n, D = self.X.shape\n",
    "        n_miss = 0\n",
    "        for j in range(n):\n",
    "            wx = np.dot(self.w,self.X[j])\n",
    "            y_pred = self.activation(wx)\n",
    "            if y_pred!=self.y[j]:\n",
    "                n_miss+=1\n",
    "        return n_miss/n\n",
    "        \n",
    "    def compute_cost(self):\n",
    "        loss = np.mean(1-(np.dot(self.X,\n",
    "                    self.w.T)+self.b).squeeze()*self.y)\n",
    "        loss += self.lamb/2*np.sum(self.w**2)\n",
    "        return loss\n",
    "        \n",
    "    def fit(self):\n",
    "        n, D = self.X.shape\n",
    "        plot_decision_boundary(\n",
    "            self.X, self.y, self.w)\n",
    "        print(self.w, self.b)\n",
    "        costs, errs = [], []\n",
    "        for epoch in range(self.epochs):\n",
    "            costs.append(self.compute_cost())\n",
    "            errs.append(self.eval_err_rate())\n",
    "            for j in random.sample(list(range(n)),n):\n",
    "                gradw = self.lamb*self.w-self.y[j]*self.X[j]\n",
    "                gradb = -self.y[j]\n",
    "                self.w -= self.lr*gradw\n",
    "                self.b -= self.lr*gradb\n",
    "            \n",
    "        plot_decision_boundary(\n",
    "            self.X, self.y, self.w)\n",
    "        print(self.w, self.b)\n",
    "        costs.append(self.compute_cost())\n",
    "        errs.append(self.eval_err_rate())\n",
    "        return costs, errs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d16e26b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = SVM()\n",
    "model.set_data(X.copy(), y.copy())\n",
    "model.set_params(w.copy(), b)\n",
    "model.set_hyperparams(5e-3, 100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "33eb00eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.   -0.75]] 1\n",
      "[[ 1.49900598e+00 -9.49058926e-04]] 0.9999999999999999\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "costs, errs = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "100d0ada",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'cost')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(costs)\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('cost')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8a897646",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'error rate')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(errs)\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('error rate')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3281ac28",
   "metadata": {},
   "source": [
    "### Soft Margin\n",
    "$$\\mathcal{J}(\\mathbf{w},b) = \\frac{\\lambda}{2}\\mathbf{w}^\\top\\mathbf{w} + \\frac{1}{b}\\sum^n_{i=1}\\max\\big(0, 1-y_i(\\mathbf{w}_i^\\top\\mathbf{x_i}+b)\\big)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "860f6d03",
   "metadata": {},
   "source": [
    "#### References\n",
    "1. https://towardsdatascience.com/implementing-svm-from-scratch-784e4ad0bc6a\n",
    "2. https://en.wikipedia.org/wiki/Sign_function\n",
    "3. https://towardsdatascience.com/algorithms-from-scratch-support-vector-machine-6f5eb72fce10\n",
    "4. https://jonathan-hui.medium.com/rl-dual-gradient-descent-fac524c1f049\n",
    "5. https://www.baeldung.com/cs/svm-hard-margin-vs-soft-margin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "03e80765",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "258e995d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}