Support-Vector-Machine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Support Vector Machine\n",
    "\n",
    "* Objective: classify vectors into positive and negative samples based on labled training data\n",
    "* Collection of input vectors $\\mathbf x_i$ for $i=1,\\dots,N$ and $\\mathbf x_i \\in {\\rm I\\!R}^m$\n",
    "* For every $\\mathbf x_i$ in the training data set we have a label $y_i$ (+1 or -1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* `x[i,:]` corresponds to $\\vec x_i$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dots are the input vectors $\\vec x_i$ and the color represent the labels $y_i$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Ubuntu/Debian install also the package `libnlopt-dev`:\n",
    "\n",
    "```bash\n",
    "sudo apt install libnlopt-dev\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot\n",
    "using NLopt\n",
    "using LinearAlgebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-2.4, 6.4, 0.75, 6.25)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [-2 4;\n",
    "     4  1;\n",
    "     1  6;\n",
    "     2  4;\n",
    "     6  3;\n",
    "     -1  3]\n",
    "\n",
    "y = [-1,-1,1,1,1,-1]\n",
    "\n",
    "function plotdata(x,y)\n",
    "  ind = findall(y .== -1)\n",
    "  plot(x[ind,1],x[ind,2],\"ro\")\n",
    "  ind = findall(y .== 1)\n",
    "  plot(x[ind,1],x[ind,2],\"bo\")\n",
    "  axis(\"equal\")\n",
    "end\n",
    "\n",
    "plotdata(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(-5, 15, 'w')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function plotline(w,b;kwargs...)\n",
    "  t = -2:6\n",
    "  plot(t,-(b .+ w[1]*t)/w[2]; kwargs...)\n",
    "end\n",
    "\n",
    "plotdata(x,y)\n",
    "plotline([0.5, 1], -4; color = \"g\")\n",
    "plotline([0.5, 1], -5; color = \"k\", linestyle=\":\")\n",
    "plotline([0.5, 1], -3; color = \"k\", linestyle=\":\")\n",
    "arrow(0,0,0.5, 1; head_width=0.1, head_length=0.2, length_includes_head = true )\n",
    "annotate(\"w\",[0,0]; xytext=(-5, 15), textcoords = \"offset points\", fontweight = \"bold\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that all lines are perpendicular to the vector $\\vec w$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any positive samples:\n",
    "\n",
    "$$\n",
    " \\mathbf w^T \\mathbf x_+ + b \\ge 1 \n",
    "$$\n",
    "\n",
    "For any negative samples:\n",
    "\n",
    "$$\n",
    " \\mathbf w^T \\mathbf x_- + b \\le -1 \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For two samples at the limit of this \"road\" ($\\mathbf x_+$ and $\\mathbf x_-$) we have:\n",
    " \n",
    "$$\n",
    " \\mathbf w^T \\mathbf x_+ + b = 1 \\\\\n",
    " \\mathbf w^T \\mathbf x_- + b = -1 \n",
    "$$\n",
    "\n",
    "\n",
    "The width of the \"road\" is computed by projecting the vector $(\\mathbf x_+ - \\mathbf x_-)$\n",
    "to a normal vector perpendicular to the central line (vector $\\frac{\\mathbf w}{\\| \\mathbf w \\|}$):\n",
    "\n",
    "$$\n",
    "\\left|(\\mathbf x_+ - \\mathbf x_-)^T  \\frac{\\mathbf w}{\\| \\mathbf w \\|} \\right| =\n",
    "\\left|\\mathbf x_+^T \\mathbf w - \\mathbf x_-^T \\mathbf w \\right| \\frac{1}{\\| \\mathbf w \\|}  =\n",
    "\\left|1-b - (-1 -b) \\right|  \\frac{1}{\\| \\mathbf w \\|}  =\n",
    "\\frac{2}{\\|\\mathbf w\\|}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "Maximize $ \\frac{2}{\\|\\mathbf w\\|}$ under the inequality constrain:\n",
    "\n",
    "$$\n",
    " y_i (\\mathbf w^T \\mathbf x_i + b) \\ge 1 \n",
    "$$\n",
    "\n",
    "\n",
    "Maximizing $ \\frac{2}{\\|\\mathbf w\\|}$ is the same as minimizing $\\frac{1}{2} \\| \\mathbf w \\|^2$.\n",
    "\n",
    "The contraint is introduced using the Lagrange multipliers $\\alpha_i$ ([Karush–Kuhn–Tucker conditions](https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions))\n",
    "\n",
    "$$\n",
    "L(\\mathbf w,b,\\alpha_1,\\alpha_2,...) = \\frac{1}{2} \\| \\mathbf w \\|^2 - \\sum_i \\alpha_i ( y_i (\\mathbf w^T \\mathbf x_i + b) -1 )\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial L}{\\partial \\mathbf w} = \\mathbf w - \\sum_i \\alpha_i y_i \\mathbf x_i = 0\n",
    "$$\n",
    "\n",
    "Thus $\\mathbf w$ is a linear sum of the samples $\\mathbf x_i$: \n",
    "\n",
    "$$\n",
    "\\mathbf w = \\sum_i \\alpha_i y_i \\mathbf x_i\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\frac{\\partial L}{\\partial b} = -\\sum_i \\alpha_i y_i = 0 \\rightarrow \\sum_i \\alpha_i y_i = 0\n",
    "$$\n",
    "\n",
    "$$\n",
    "L = \\frac{1}{2} \\left( \\sum_i \\alpha_i y_i \\mathbf x_i^T \\right)  \\left( \\sum_j \\alpha_j y_j \\mathbf x_j \\right) \n",
    "- \n",
    "\\sum_i \\alpha_i  y_i  \\mathbf x_i^T \\left(\\sum_j \\alpha_j y_j \\mathbf x_j \\right) \n",
    "- b \\sum_i \\alpha_i y_i\n",
    "+ \\sum_i \\alpha_i \n",
    "$$\n",
    "\n",
    "Maximum of \n",
    "\n",
    "$$\n",
    "L = \\sum_i \\alpha_i \n",
    "- \\frac{1}{2} \n",
    "\\sum_i \\sum_j \n",
    "\\alpha_i \\alpha_j y_i y_j \\mathbf x_i^T \\mathbf x_j\n",
    "$$\n",
    "\n",
    "with the contraints $\\alpha_i \\ge 0$ and $\\sum_i \\alpha_i y_i = 0$.\n",
    "* It depends only on the dot product of pairs of samples $\\mathbf x_i^T \\mathbf x_j$\n",
    "* maximization of $L$ is a convex problem -> there is only one maximum (no local maximum)\n",
    "\n",
    "Decision rule\n",
    "\n",
    "$$\n",
    "\\mbox{if}\\;\\;\n",
    "\\sum_i \\alpha_i  y_i  \\mathbf x_i^T \\mathbf u > 0 \\;\\;\\mbox{then $\\mathbf u$ is a positive sample}\n",
    "$$\n",
    "\n",
    "Or a negative sample otherwise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute $b$, we can use any $i$ (for which $\\alpha_i > 0$):\n",
    "\n",
    "$$\n",
    "y_i (\\vec w^T \\vec x_i + b) - 1 = 0\n",
    "$$\n",
    "\n",
    "or\n",
    "$$\n",
    "b = y_i - \\vec w^T \\vec x_i\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6249999999932578, [0.2916677599437004, 0.33333386811399474, 3.4711640783697557e-23, 0.6250016280576951, 1.82641479164194e-21, 2.74520565571948e-22], :XTOL_REACHED)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function L(α,x,y)\n",
    "    N = length(y)\n",
    "    Lval = sum(α)\n",
    "    for j = 1:N\n",
    "       for i = 1:N\n",
    "           Lval -= 0.5 * α[i] * α[j] * y[i] * y[j] * (x[i,:] ⋅ x[j,:]) \n",
    "        end\n",
    "    end\n",
    "    #@show α,Lval\n",
    "    return Lval\n",
    "end\n",
    "\n",
    "using NLopt\n",
    "N = length(y)\n",
    "#opt = Opt(:GN_DIRECT, N)\n",
    "opt = Opt(:LN_COBYLA, N)\n",
    "#opt = Opt(:LD_MMA, N)\n",
    "\n",
    "max_objective!(opt, (α,grad) -> L(α,x,y))\n",
    "lower_bounds!(opt, zeros(N))\n",
    "equality_constraint!(opt, (α,grad) -> sum(y.*α))\n",
    "\n",
    "xtol_rel!(opt,1e-6)\n",
    "maxeval!(opt,10000)\n",
    "\n",
    "minL,α,ret = optimize(opt, ones(N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Points travers by the dottes black line are called support vectors.\n",
    "$\\vec x_i$ is a support vector if $\\alpha_i > 0$ (i.e. if $\\alpha_i$ is *different* from zero).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute $\\vec w$ and $b$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(w, b) = ([0.5000033035468121, 1.000001604341984], -3.9999998102743115)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([0.5000033035468121, 1.000001604341984], -3.9999998102743115)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = zeros(size(x,2))\n",
    "for i = 1:N\n",
    "   w += α[i] * y[i] * x[i,:]\n",
    "end\n",
    "\n",
    "# index of a support vector\n",
    "i = findfirst(α .> eps()) # for any i such that α[i] > 0\n",
    "b = y[i] - w' * x[i,:]\n",
    "\n",
    "@show w,b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Width of the \"road\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7888497222353612"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2/norm(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All support vectors are marked by a cross:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plotdata(x,y)\n",
    "plotline(w,b)\n",
    "plotline(w,b-1; color = \"k\", linestyle=\":\")\n",
    "plotline(w,b+1; color = \"k\", linestyle=\":\")\n",
    "\n",
    "isupport = findall(α .> eps())\n",
    "plot(x[isupport,1],x[isupport,2],\"x\",color=\"k\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If sample are not linearily separable, then one can introduce a transformation function $\\vec \\phi(\\vec x)$ such that the transformed samples are separable.\n",
    "\n",
    "Kernel $K$\n",
    "\n",
    "$$\n",
    "K(\\vec x_i,\\vec x_j) = \\phi(\\vec x_i)^T \\phi(\\vec x_j)\n",
    "$$\n",
    "\n",
    "Possible kernels:\n",
    "\n",
    "* $K(\\vec u,\\vec v) = (\\vec u^T \\vec v + 1)^n$\n",
    "* $K(\\vec u,\\vec v) = \\exp(- \\| \\vec u - \\vec v \\| / \\sigma ) $\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "kernelspec": {
   "display_name": "Julia 1.5.0",
   "language": "julia",
   "name": "julia-1.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}