LDA实例/LDA实例.ipynb · longlong/ML_Cases

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LDA实例.ipynb 19.37 KB

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. 目标：求解投影向量$ \\mathbf{w}$ ，二维情况下$\\mathbf{w}=\\begin{bmatrix}w_1\\\\w_2\\end{bmatrix}$，$\\mathbf{x}=\\begin{bmatrix}x_1\\\\x_2\\end{bmatrix}$\n",
    "\n",
    "   图中的y可计算，对于样本在投影向量上的投影结果的值为：$y=\\mathbf{w}^T\\mathbf{x}=|\\mathbf{w}|*|\\mathbf{x}|*cos(\\theta)=|\\mathbf{x}|*cos(\\theta)$，\n",
    "   $\\mathbf{w}$可以理解为这条过原点直线的单位方向向量，$\\theta$为$\\mathbf{w、x}的夹角$x_1,x_2为每个样本在两个维度上的取值。\n",
    "\n",
    "   给定两个类别：\n",
    "\n",
    "   X1 :\tshape：（m，2）表示m个样本，2两个维度，图中每个点表示\n",
    "\n",
    "   X2 :    描述同X1\n",
    "\n",
    "   均值向量$\\mu_i$：\tshape：（2，1）\t将m个样本取每个维度的均值，按列排列，得到均值均值向量$\\mu_i$  \n",
    "\n",
    "   协方差矩阵$\\sum_i$:\tshape：（2，2） （维度x维度）\n",
    "\n",
    "   样本中心在直线上的投影$\\mathbf{w}^T\\mu_i$ ：shape：（1，2）x（2，1）= (1,1)常量\n",
    "\n",
    "   样本的协方差：$\\mathbf{w}^T\\sum_i\\mathbf{w}$：shape：（1，2）x（2，2）x(2,1) = (1,1)常量 ???\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "类别1：\n",
      "[[3 5]\n",
      " [4 6]\n",
      " [3 3]\n",
      " [4 4]\n",
      " [4 4]\n",
      " [2 0]\n",
      " [1 0]\n",
      " [1 3]\n",
      " [4 3]\n",
      " [4 5]\n",
      " [0 2]\n",
      " [3 3]\n",
      " [0 6]\n",
      " [3 5]\n",
      " [5 2]\n",
      " [1 3]\n",
      " [0 0]\n",
      " [5 1]\n",
      " [1 0]\n",
      " [4 0]\n",
      " [1 5]\n",
      " [0 0]\n",
      " [1 2]\n",
      " [2 1]\n",
      " [1 0]\n",
      " [4 0]\n",
      " [4 1]\n",
      " [1 2]\n",
      " [3 0]\n",
      " [2 4]\n",
      " [6 1]\n",
      " [2 5]\n",
      " [0 5]\n",
      " [2 3]\n",
      " [4 6]\n",
      " [5 4]\n",
      " [0 5]\n",
      " [4 1]\n",
      " [0 6]\n",
      " [1 0]\n",
      " [2 1]\n",
      " [6 1]\n",
      " [3 3]\n",
      " [5 1]\n",
      " [0 6]\n",
      " [3 1]\n",
      " [3 4]\n",
      " [6 0]\n",
      " [3 6]\n",
      " [5 5]],\n",
      "大小：(50, 2)\n",
      "类别2：\n",
      "[[10  5]\n",
      " [10  7]\n",
      " [ 7  6]\n",
      " [ 9  8]\n",
      " [ 8  9]\n",
      " [ 5 10]\n",
      " [ 8  7]\n",
      " [ 9  5]\n",
      " [ 8  6]\n",
      " [ 9  5]\n",
      " [ 7  5]\n",
      " [ 8  8]\n",
      " [ 9 10]\n",
      " [ 5  6]\n",
      " [ 6  7]\n",
      " [ 6  5]\n",
      " [ 8  5]\n",
      " [ 9  6]\n",
      " [10  6]\n",
      " [ 9  5]\n",
      " [10 10]\n",
      " [ 6  7]\n",
      " [ 5  7]\n",
      " [10  9]\n",
      " [ 5  8]\n",
      " [ 9 11]\n",
      " [11  8]\n",
      " [13 11]\n",
      " [ 9  9]\n",
      " [10  8]\n",
      " [ 8  8]\n",
      " [13 13]\n",
      " [ 8 10]\n",
      " [ 7  9]\n",
      " [ 9  9]\n",
      " [ 9 10]\n",
      " [11 11]\n",
      " [10 13]\n",
      " [ 7  9]\n",
      " [10 10]\n",
      " [10 10]\n",
      " [11 13]\n",
      " [ 8 11]\n",
      " [10 11]\n",
      " [ 9 13]\n",
      " [12 11]\n",
      " [11 11]\n",
      " [11 12]\n",
      " [ 7 10]\n",
      " [12  8]],\n",
      "大小：(50, 2)\n"
     ]
    }
   ],
   "source": [
    "M = 2 #属性个数\n",
    "N = 50#二分类。每类样本N个 #随机生成两个属性的N个第一类样本\n",
    "# 类别大小 两类都为 （50，2）\n",
    "feature11 = np.random.randint(0, 7, size = N)\n",
    "feature12 = np.random.randint(0, 7, size= N)\n",
    "temp_X1 = np.row_stack((feature11, feature12))\n",
    "#随机生成两个属性的N个第二类样本\n",
    "X1 = np.mat(temp_X1).reshape(50,2) \n",
    "feature21 = np.random.randint(5,11, size= N)\n",
    "feature22 = np.random.randint(7, 14, size= N)\n",
    "temp_X2 = np.row_stack((feature21, feature22))\n",
    "X2 = np.mat(temp_X2).reshape(50,2) \n",
    "print('类别1：\\n{},\\n大小：{}'.format(X1,X1.shape))\n",
    "print('类别2：\\n{},\\n大小：{}'.format(X2,X2.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "类别1的均值向量:\n",
      "[[ 2.62]\n",
      " [ 2.68]],\n",
      "类别二的均值向量:\n",
      "[[ 8.82]\n",
      " [ 8.62]]\n"
     ]
    }
   ],
   "source": [
    "#target: 求投影向量omega\n",
    "\n",
    "mu1 = np.mat(np.zeros((2,1)))\n",
    "mu2 = np.mat(np.zeros((2,1)))\n",
    "X_1t = np.array(X1) \n",
    "X_2t = np.array(X2)\n",
    "# 求两个类别的均值向量 （2，1）\n",
    "for i in range(M):\n",
    "    mu1[i, 0] = sum([j for j in X_1t[:,i]])/N\n",
    "for i in range(M):\n",
    "    mu2[i, 0] = sum([j for j in X_2t[:,i]])/N\n",
    "print('类别1的均值向量:\\n{},\\n类别二的均值向量:\\n{}'.format(mu1, mu2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "类内散度矩阵Sw:\n",
      "[[ 361.16   85.5 ]\n",
      " [  85.5   510.66]]\n"
     ]
    }
   ],
   "source": [
    "# 求解类内散度矩阵Sw\n",
    "s_w1 = np.mat(np.zeros(M))\n",
    "s_w2 = np.mat(np.zeros(M))\n",
    "for i in range(N):\n",
    "    s_w1 = s_w1 + (X1[i, :].reshape(2,1) - mu1)*(X1[i,:].reshape(2,1) - mu1).T\n",
    "for i in range(N):\n",
    "    s_w2 = s_w2 + (X2[i, :].reshape(2,1) - mu2)*(X2[i,:].reshape(2,1) - mu2).T\n",
    "s_w = s_w1 + s_w2\n",
    "print('类内散度矩阵Sw:\\n%s'%s_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "参数向量W:\n",
      "[[-0.01500805]\n",
      " [-0.0091192 ]]\n",
      "shape:\n",
      "(2, 1)\n"
     ]
    }
   ],
   "source": [
    "Omega = np.linalg.pinv(s_w)*(mu1 - mu2)\n",
    "print('参数向量W:\\n%s\\nshape:\\n%s'%(Omega,Omega.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
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lVDvZUOPmYgvbXLxmSU1s7XOz2vjxfinip5/CNdfA44/DUUeFjkpEpFQyukIv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\nT5vfNZZaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#画出散点图、投影面\n",
    "fig = plt.figure(1)\n",
    "plt.scatter(feature11, feature12, marker='+')\n",
    "plt.scatter(feature21, feature22, marker='*')\n",
    "xx_1 = np.linspace(0,10,num=50)\n",
    "yy_1 = Omega[1,0]/Omega[0,0]*xx_1\n",
    "plt.plot(xx_1,yy_1,color='r')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}

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提交于 2020-09-09 10:12 +08:00 . restruct

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