Linear SVM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create features for items from two artificial classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "X_C1 = rand(100,2);\n",
    "X_C2 = bsxfun(@plus,rand(100,2),[0.2 1.2]);\n",
    "\n",
    "X = [X_C1;X_C2];\n",
    "\n",
    "Y = ones(200,1);\n",
    "Y(1:100) = -1;\n",
    "%Y = diag(Y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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LJ0+ePHDgwP3792dlZbEICQB0p2IgCSGGDh26c+fO855sPEFg2rRptlmE5MCF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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure,\n",
    "plot(X_C1(:,1),X_C1(:,2),'k.'), xlabel('x1'), ylabel('x2')\n",
    "hold on\n",
    "plot(X_C2(:,1),X_C2(:,2),'r.')\n",
    "hold off\n",
    "legend('Class1','Class2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formulate the necessary matrices for optimization function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "H = zeros(3);\n",
    "H(1:2,1:2) = eye(2);\n",
    "f = zeros(3,1);\n",
    "A = -diag(Y)*[X ones(200,1)];\n",
    "b = -ones(200,1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the optimization function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "opt = optimoptions('quadprog','Display','off');\n",
    "wb = quadprog(H,f,A,b,[],[],[],[],[],opt);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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A7MDQHhTsmNL+7ZCBceXf+v090agIBsXlWiEej4tEQvj9wavvtyj4hoLAgCfV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\nAgkAIAUCCQAgBQIJACCF/w/kthJlWRYK8gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure,\n",
    "plot(X_C1(:,1),X_C1(:,2),'k.'), xlabel('x1'), ylabel('x2')\n",
    "hold on\n",
    "plot(X_C2(:,1),X_C2(:,2),'r.')\n",
    "legend('Class1','Class2')\n",
    "\n",
    "% svm separating hyperplane\n",
    "x1 = 0:0.1:2.5;\n",
    "x2 = (-wb(1)*x1-repmat(wb(3),size(x1,1),size(x1,2)))./wb(2);\n",
    "plot(x1,x2)\n",
    "\n",
    "% margin\n",
    "marg_up =  (1-wb(1)*x1-repmat(wb(3),size(x1,1),size(x1,2)))./wb(2);\n",
    "marg_down =  (-1-wb(1)*x1-repmat(wb(3),size(x1,1),size(x1,2)))./wb(2);\n",
    "plot(x1,marg_up,'k-.')\n",
    "plot(x1,marg_down,'k-.')\n",
    "\n",
    "% find the support vectors\n",
    "D = abs([X ones(200,1)]*wb);\n",
    "sv = find(abs(D-1)<0.0001);\n",
    "for s=1:length(sv)\n",
    "    plot(X(sv(s),1),X(sv(s),2),'ro')\n",
    "end\n",
    "hold off"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Matlab",
   "language": "matlab",
   "name": "matlab"
  },
  "language_info": {
   "codemirror_mode": "octave",
   "file_extension": ".m",
   "help_links": [
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "matlab",
   "version": "0.15.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}