核函數羅吉斯回歸(Kernel Logistic Regression).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# L2正則化核函數羅吉斯回歸(Kernel Logistic Regression with L2 Regularization)"
   ]
  },
  {
   "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 math\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d.axes3d import Axes3D"
   ]
  },
  {
   "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=-0.05\n",
    "    if(i<30):\n",
    "        y[i]=1\n",
    "        x[i,0]=random.random()\n",
    "        x[i,1]=random.uniform(x[i,0],1)+f\n",
    "    else:\n",
    "        y[i]=0\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": [
    "# Sigmoid Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(s):\n",
    "    return(1/(1+np.exp(-s)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Polynomial_kernel(x,xx,power,gamma,zeta):\n",
    "    # 最後出來要為N*N的矩陣\n",
    "    # 這裡可以對照文章公式\n",
    "    return (zeta+gamma*np.dot(x,xx.T))**power"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# L2 Regularized Logistic Regression with Polynomial Kernal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.8485553214193686e-05\n"
     ]
    },
    {
     "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": [
    "N=60\n",
    "# c為次方數\n",
    "c=5\n",
    "gamma=1\n",
    "zeta=1\n",
    "lambda_2=1\n",
    "# r: learning Rate\n",
    "r=0.0002\n",
    "a=np.ones(N)\n",
    "K=Polynomial_kernel(x,x,c,gamma,zeta)\n",
    "for i in range(0,900000):\n",
    "    # 執行梯度下降演算法，可以對照文章中公式\n",
    "    A=(2*lambda_2/N)*np.dot(K,a)\n",
    "    B=np.dot(K/np.outer(np.ones(N)+np.exp(-np.dot(K,a)),np.ones(N)).T,np.ones(N)-y)/N\n",
    "    C=np.dot(K/np.outer(np.ones(N)+np.exp(np.dot(K,a)),np.ones(N)).T,-y)/N\n",
    "    a=a-r*(A+B+C)\n",
    "# 輸出我們最後的梯度，確保a收斂\n",
    "print(sum(A+B+C))\n",
    "# 視覺化\n",
    "plt.rcParams[\"figure.figsize\"] = (18,18)\n",
    "\n",
    "# 畫出所有的數據點\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",
    "#標記圖片邊界\n",
    "x1_low_limit=min(x[:,0])\n",
    "x1_high_limit=max(x[:,0])\n",
    "x2_low_limit=min(x[:,1])\n",
    "x2_high_limit=max(x[:,1])\n",
    "# 畫出分割線\n",
    "# 這裡的做法是\n",
    "# 從x1最小值到x1最大值中間取200個點\n",
    "# 從x2最小值到x2最大值中間取500個點\n",
    "# 總共執行10000次，每次計算其套入分割線的方程式，並存入SUM\n",
    "# 如果SUM從正變負或負變正，代表中間點為分割線\n",
    "\n",
    "x1=np.linspace(x1_low_limit,x1_high_limit,200)\n",
    "x2=np.linspace(x2_low_limit,x2_high_limit,500)\n",
    "\n",
    "for i in x1:\n",
    "    SUM_TEMP=0\n",
    "    count=0\n",
    "    for j in x2:\n",
    "        SUM=np.dot(a,Polynomial_kernel(x,np.array([i,j]),c,gamma,zeta))\n",
    "        if(np.sign(SUM)!=np.sign(SUM_TEMP)):\n",
    "            if(count>0):\n",
    "                plt.plot(i,(x2[count]+x2[count-1])/2,\"ko\")\n",
    "        count+=1\n",
    "        SUM_TEMP=SUM\n",
    "x1=np.linspace(x1_low_limit,x1_high_limit,500)\n",
    "x2=np.linspace(x2_low_limit,x2_high_limit,200)\n",
    "for j in x2:\n",
    "    SUM_TEMP=0\n",
    "    count=0\n",
    "    for i in x1:\n",
    "        SUM=np.dot(a,Polynomial_kernel(x,np.array([i,j]),c,gamma,zeta))\n",
    "        if(np.sign(SUM)!=np.sign(SUM_TEMP)):\n",
    "            if(count>0):\n",
    "                plt.plot((x1[count]+x1[count-1])/2,j,\"ko\")\n",
    "        count+=1\n",
    "        SUM_TEMP=SUM    \n",
    "\n",
    "plt.xticks(fontsize=30)\n",
    "plt.yticks(fontsize=30)\n",
    "#plt.xlim([x1_low_limit,x1_high_limit])\n",
    "#plt.ylim([x2_low_limit,x2_high_limit])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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