對偶支撐向量機(Dual Support Vector Machine).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 對偶支撐向量機(Dual Support Vector Machine)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 先引入我們需要的packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os \n",
    "import numpy as np\n",
    "import random\n",
    "import cvxopt\n",
    "from cvxopt import matrix, solvers\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 設定我們有60個點，其中30個是圈圈，30個是叉叉"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 這裡我們建立一個60*2的矩陣x\n",
    "# 60代表我們有60個點，2代表為2維空間(平面)\n",
    "x=np.zeros((60,2))\n",
    "# 這裡我們建立一個長度60的向量y\n",
    "# 用來儲存我們的標記資料是圈圈(+1)還是叉叉(-1)\n",
    "y=np.zeros(60)\n",
    "# 因為有60筆資料，所以跑60個迴圈\n",
    "for i in range(0,60): \n",
    "    # 標記y前半段0~29為圈圈(+1)，後半段30~59為叉叉(-1)\n",
    "    # 也就是圈圈30個點，叉叉30個點\n",
    "    f=0\n",
    "    if(i<30):\n",
    "        y[i]=1\n",
    "        x[i,0]=random.random()\n",
    "        x[i,1]=random.uniform(x[i,0],1)\n",
    "    else:\n",
    "        y[i]=-1\n",
    "        x[i,0]=random.random()\n",
    "        x[i,1]=random.uniform(0,x[i,0])-f\n",
    "    # 這裡我們隨機給定我們資料的位置\n",
    "    # 而f可以決定我們圈圈和叉叉兩組數據分的越開或是越近\n",
    "    \n",
    "# 設定我們輸出圖片的大小\n",
    "plt.rcParams[\"figure.figsize\"] = (18,18)\n",
    "#畫出圈圈的點，bo：b代表藍色、o代表圈圈、marksize為大小\n",
    "plt.plot(x[:30,0],x[:30,1],\"bo\",markersize=20)\n",
    "#畫出叉叉的點，rX：r代表紅色、X代表叉叉、marksize為大小\n",
    "plt.plot(x[30:,0],x[30:,1],\"rX\",markersize=20)\n",
    "# 設定x和y軸座標的字體大小\n",
    "plt.xticks(fontsize=30)\n",
    "plt.yticks(fontsize=30)\n",
    "#畫出來\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 特徵轉換"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 我們總共有60個點\n",
    "N=60\n",
    "# c代表轉換的次方數\n",
    "c=3\n",
    "# D為每筆特徵的個數\n",
    "D=int((c+1)*(c+2)/2)\n",
    "# 創建z矩陣\n",
    "z=np.ones((60,D))\n",
    "z[:,1:3]=x\n",
    "k=3\n",
    "# 計算特徵\n",
    "for i in range(2,c+1):\n",
    "    for j in range(0,i+1):\n",
    "        z[:,k]=(x[:,1]**j)*(x[:,0]**(c-j))\n",
    "        k+=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 二次規劃"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 二次規劃\n",
    "Q = cvxopt.matrix((np.outer(y,y) * np.dot(z,z.T)))\n",
    "p = cvxopt.matrix(np.ones(N)*-1.,(N,1))\n",
    "G = cvxopt.matrix(np.diag(np.ones(N)* -1.)) \n",
    "h = cvxopt.matrix(np.zeros(N))\n",
    "A = cvxopt.matrix(y,(1,N))\n",
    "b = cvxopt.matrix(0.0)\n",
    "# 利用cvxopt套件求解\n",
    "cvxopt.solvers.options['show_progress'] = False\n",
    "cvxopt.solvers.options['abstol'] = 1e-10\n",
    "cvxopt.solvers.options['reltol'] = 1e-10\n",
    "cvxopt.solvers.options['feastol'] = 1e-10\n",
    "\n",
    "# 求出alpha值\n",
    "a=np.array(cvxopt.solvers.qp(Q, p, G, h, A, b)['x']).flatten()\n",
    "# 計算權重和截距\n",
    "w=np.zeros(D)\n",
    "w = np.dot(z.T,y*a)\n",
    "s=a>1e-6\n",
    "for i in range(0,N):\n",
    "    if(a[i]>1e-6):\n",
    "        index=i\n",
    "w[0]=y[index]-np.dot(w,z[index,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 視覺化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 繪圖\n",
    "plt.rcParams[\"figure.figsize\"] = (18,18)\n",
    "# 畫出所有的數據點和支撐向量\n",
    "for i in range(0,N):\n",
    "    if(a[i]>1e-6):\n",
    "        plt.plot(x[i,0],x[i,1],\"ko\",markersize=40)\n",
    "plt.plot(x[:30,0],x[:30,1],\"bo\",markersize=20)\n",
    "plt.plot(x[30:,0],x[30:,1],\"rX\",markersize=20)\n",
    "\n",
    "###### 這邊帶入x1求解 ######\n",
    "x1=np.linspace(0,1,500)\n",
    "for i in range(0,len(x1)):\n",
    "    plot1=np.zeros(c+1)\n",
    "    g=0\n",
    "    for j in range(0,c+2):\n",
    "        for k in range(0,j):\n",
    "            plot1[c-k]+=w[g]*(x1[i]**(j-k-1))\n",
    "            g+=1\n",
    "    temp=np.roots(plot1)\n",
    "    for tt in temp:\n",
    "        if isinstance(tt,complex):\n",
    "            if(tt.imag==0):\n",
    "                plt.plot(x1[i],tt.real,\"ko\")\n",
    "        else:\n",
    "            plt.plot(x1[i],tt,\"ko\")\n",
    "\n",
    "###### 這邊帶入x2求解 ######\n",
    "x2=np.linspace(0,1,500)\n",
    "for i in range(0,len(x2)):\n",
    "    plot2=np.zeros(c+1)\n",
    "    g=0\n",
    "    for j in range(0,c+2):\n",
    "        for k in range(0,j):\n",
    "            plot2[c-j+k+1]+=w[g]*(x2[i]**k)\n",
    "            g+=1\n",
    "    temp=np.roots(plot2)\n",
    "    for tt in temp:\n",
    "        if isinstance(tt,complex):\n",
    "            if(tt.imag==0):\n",
    "                plt.plot(tt.real,x2[i],\"ko\")\n",
    "        else:\n",
    "            plt.plot(tt,x2[i],\"ko\")\n",
    "            \n",
    "\n",
    "plt.xticks(fontsize=30)\n",
    "plt.yticks(fontsize=30)\n",
    "plt.xlim([-0,1])\n",
    "plt.ylim([-0.1-f,1.1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}