3-NeuralNetwok/NeuralNetwork.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里显示 使用神经网络 对数字识别进行预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import io as spio\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import optimize\n",
    "from matplotlib.font_manager import FontProperties\n",
    "import time\n",
    "font = FontProperties(fname=r\"c:\\windows\\fonts\\simsun.ttc\", size=14)    # 解决windows环境下画图汉字乱码问题\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 显示100个数字\n",
    "def display_data(imgData):\n",
    "    sum = 0\n",
    "    '''\n",
    "    显示100个数（若是一个一个绘制将会非常慢，可以将要画的数字整理好，放到一个矩阵中，显示这个矩阵即可）\n",
    "    - 初始化一个二维数组\n",
    "    - 将每行的数据调整成图像的矩阵，放进二维数组\n",
    "    - 显示即可\n",
    "    '''\n",
    "    m,n = imgData.shape\n",
    "    width = np.int32(np.round(np.sqrt(n)))\n",
    "    height = np.int32(n/width)\n",
    "    rows_count = np.int32(np.floor(np.sqrt(m)))\n",
    "    cols_count = np.int32(np.ceil(m/rows_count))\n",
    "    pad = 1\n",
    "    display_array = -np.ones((pad+rows_count*(height+pad),pad+cols_count*(width+pad)))\n",
    "    for i in range(rows_count):\n",
    "        for j in range(cols_count):\n",
    "            if sum >= m: # 超过了行数，退出当前循环\n",
    "                break\n",
    "            display_array[pad+i*(height+pad):pad+i*(height+pad)+height,pad+j*(width+pad):pad+j*(width+pad)+width] = imgData[sum,:].reshape(height,width,order=\"F\")    # order=F指定以列优先，在matlab中是这样的，python中需要指定，默认以行\n",
    "            sum += 1\n",
    "        if sum >= m:  # 超过了行数，退出当前循环\n",
    "            break\n",
    "            \n",
    "    plt.imshow(display_array,cmap='gray')   # 显示灰度图像\n",
    "    plt.axis('off')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 代价函数\n",
    "def nnCostFunction(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda):\n",
    "    length = nn_params.shape[0] # theta的中长度\n",
    "    # 还原theta1和theta2\n",
    "    Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1)\n",
    "    Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1)\n",
    "    \n",
    "    # np.savetxt(\"Theta1.csv\",Theta1,delimiter=',')\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    class_y = np.zeros((m,num_labels))      # 数据的y对应0-9，需要映射为0/1的关系\n",
    "    # 映射y\n",
    "    for i in range(num_labels):\n",
    "        class_y[:,i] = np.int32(y==i).reshape(1,-1) # 注意reshape(1,-1)才可以赋值\n",
    "     \n",
    "    '''去掉theta1和theta2的第一列，因为正则化时从1开始'''    \n",
    "    Theta1_colCount = Theta1.shape[1]    \n",
    "    Theta1_x = Theta1[:,1:Theta1_colCount]\n",
    "    Theta2_colCount = Theta2.shape[1]    \n",
    "    Theta2_x = Theta2[:,1:Theta2_colCount]\n",
    "    # 正则化向theta^2\n",
    "    term = np.dot(np.transpose(np.vstack((Theta1_x.reshape(-1,1),Theta2_x.reshape(-1,1)))),np.vstack((Theta1_x.reshape(-1,1),Theta2_x.reshape(-1,1))))\n",
    "    \n",
    "    '''正向传播,每次需要补上一列1的偏置bias'''\n",
    "    a1 = np.hstack((np.ones((m,1)),X))      \n",
    "    z2 = np.dot(a1,np.transpose(Theta1))    \n",
    "    a2 = sigmoid(z2)\n",
    "    a2 = np.hstack((np.ones((m,1)),a2))\n",
    "    z3 = np.dot(a2,np.transpose(Theta2))\n",
    "    h = sigmoid(z3)\n",
    "    '''代价'''    \n",
    "    J = -(np.dot(np.transpose(class_y.reshape(-1,1)),np.log(h.reshape(-1,1)))+np.dot(np.transpose(1-class_y.reshape(-1,1)),np.log(1-h.reshape(-1,1)))-Lambda*term/2)/m   \n",
    "    \n",
    "    return np.ravel(J)\n",
    "\n",
    "# 梯度\n",
    "def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda):\n",
    "    length = nn_params.shape[0]\n",
    "    Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1)\n",
    "    Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1)\n",
    "    m = X.shape[0]\n",
    "    class_y = np.zeros((m,num_labels))      # 数据的y对应0-9，需要映射为0/1的关系    \n",
    "    # 映射y\n",
    "    for i in range(num_labels):\n",
    "        class_y[:,i] = np.int32(y==i).reshape(1,-1) # 注意reshape(1,-1)才可以赋值\n",
    "     \n",
    "    '''去掉theta1和theta2的第一列，因为正则化时从1开始'''\n",
    "    Theta1_colCount = Theta1.shape[1]    \n",
    "    Theta1_x = Theta1[:,1:Theta1_colCount]\n",
    "    Theta2_colCount = Theta2.shape[1]    \n",
    "    Theta2_x = Theta2[:,1:Theta2_colCount]\n",
    "    \n",
    "    Theta1_grad = np.zeros((Theta1.shape))  #第一层到第二层的权重\n",
    "    Theta2_grad = np.zeros((Theta2.shape))  #第二层到第三层的权重\n",
    "    \n",
    "    Theta1[:,0] = 0\n",
    "    Theta2[:,0] = 0\n",
    "    '''正向传播，每次需要补上一列1的偏置bias'''\n",
    "    a1 = np.hstack((np.ones((m,1)),X))\n",
    "    z2 = np.dot(a1,np.transpose(Theta1))\n",
    "    a2 = sigmoid(z2)\n",
    "    a2 = np.hstack((np.ones((m,1)),a2))\n",
    "    z3 = np.dot(a2,np.transpose(Theta2))\n",
    "    h = sigmoid(z3)\n",
    "    \n",
    "    '''反向传播，delta为误差，'''\n",
    "    delta3 = np.zeros((m,num_labels))\n",
    "    delta2 = np.zeros((m,hidden_layer_size))\n",
    "    for i in range(m):\n",
    "        delta3[i,:] = h[i,:]-class_y[i,:]\n",
    "        Theta2_grad = Theta2_grad+np.dot(np.transpose(delta3[i,:].reshape(1,-1)),a2[i,:].reshape(1,-1))\n",
    "        delta2[i,:] = np.dot(delta3[i,:].reshape(1,-1),Theta2_x)*sigmoidGradient(z2[i,:])\n",
    "        Theta1_grad = Theta1_grad+np.dot(np.transpose(delta2[i,:].reshape(1,-1)),a1[i,:].reshape(1,-1))\n",
    "    \n",
    "    '''梯度'''\n",
    "    grad = (np.vstack((Theta1_grad.reshape(-1,1),Theta2_grad.reshape(-1,1)))+Lambda*np.vstack((Theta1.reshape(-1,1),Theta2.reshape(-1,1))))/m\n",
    "    return np.ravel(grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# S型函数    \n",
    "def sigmoid(Z):\n",
    "    A = 1.0/(1.0+np.exp(-Z))\n",
    "    return A\n",
    "\n",
    "# S型函数导数\n",
    "def sigmoidGradient(z):\n",
    "    g = sigmoid(z)*(1-sigmoid(z))\n",
    "    return g\n",
    "\n",
    "# 随机初始化权重theta\n",
    "def randInitializeWeights(L_in,L_out):\n",
    "    W = np.zeros((L_out,1+L_in))    # 对应theta的权重\n",
    "    epsilon_init = (6.0/(L_out+L_in))**0.5\n",
    "    W = np.random.rand(L_out,1+L_in)*2*epsilon_init-epsilon_init # np.random.rand(L_out,1+L_in)产生L_out*(1+L_in)大小的随机矩阵\n",
    "    return W\n",
    "\n",
    "\n",
    "# 检验梯度是否计算正确\n",
    "def checkGradient(Lambda = 0):\n",
    "    '''构造一个小型的神经网络验证，因为数值法计算梯度很浪费时间，而且验证正确后之后就不再需要验证了'''\n",
    "    input_layer_size = 3\n",
    "    hidden_layer_size = 5\n",
    "    num_labels = 3\n",
    "    m = 5\n",
    "    initial_Theta1 = debugInitializeWeights(input_layer_size,hidden_layer_size)\n",
    "    initial_Theta2 = debugInitializeWeights(hidden_layer_size,num_labels)\n",
    "    X = debugInitializeWeights(input_layer_size-1,m)\n",
    "    y = 1+np.transpose(np.mod(np.arange(1,m+1), num_labels))  # 初始化y\n",
    "    \n",
    "    y = y.reshape(-1,1)\n",
    "    nn_params = np.vstack((initial_Theta1.reshape(-1,1),initial_Theta2.reshape(-1,1)))  #展开theta \n",
    "    '''BP求出梯度'''\n",
    "    grad = nnGradient(nn_params, input_layer_size, hidden_layer_size, \n",
    "                     num_labels, X, y, Lambda)  \n",
    "    '''使用数值法计算梯度'''\n",
    "    num_grad = np.zeros((nn_params.shape[0]))\n",
    "    step = np.zeros((nn_params.shape[0]))\n",
    "    e = 1e-4\n",
    "    for i in range(nn_params.shape[0]):\n",
    "        step[i] = e\n",
    "        loss1 = nnCostFunction(nn_params-step.reshape(-1,1), input_layer_size, hidden_layer_size, \n",
    "                              num_labels, X, y, \n",
    "                              Lambda)\n",
    "        loss2 = nnCostFunction(nn_params+step.reshape(-1,1), input_layer_size, hidden_layer_size, \n",
    "                              num_labels, X, y, \n",
    "                              Lambda)\n",
    "        num_grad[i] = (loss2-loss1)/(2*e)\n",
    "        step[i]=0\n",
    "    # 显示两列比较\n",
    "    res = np.hstack((num_grad.reshape(-1,1),grad.reshape(-1,1)))\n",
    "    print(res)\n",
    "\n",
    "# 初始化调试的theta权重\n",
    "def debugInitializeWeights(fan_in,fan_out):\n",
    "    W = np.zeros((fan_out,fan_in+1))\n",
    "    x = np.arange(1,fan_out*(fan_in+1)+1)\n",
    "    W = np.sin(x).reshape(W.shape)/10\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 预测\n",
    "def predict(Theta1,Theta2,X):\n",
    "    m = X.shape[0]\n",
    "    #num_labels = Theta2.shape[0]\n",
    "    #p = np.zeros((m,1))\n",
    "    '''正向传播，预测结果'''\n",
    "    X = np.hstack((np.ones((m,1)),X))\n",
    "    h1 = sigmoid(np.dot(X,np.transpose(Theta1)))\n",
    "    h1 = np.hstack((np.ones((m,1)),h1))\n",
    "    h2 = sigmoid(np.dot(h1,np.transpose(Theta2)))\n",
    "    \n",
    "    '''\n",
    "    返回h中每一行最大值所在的列号\n",
    "    - np.max(h, axis=1)返回h中每一行的最大值（是某个数字的最大概率）\n",
    "    - 最后where找到的最大概率所在的列号（列号即是对应的数字）\n",
    "    '''\n",
    "    #np.savetxt(\"h2.csv\",h2,delimiter=',')\n",
    "    p = np.array(np.where(h2[0,:] == np.max(h2, axis=1)[0]))  \n",
    "    for i in np.arange(1, m):\n",
    "        t = np.array(np.where(h2[i,:] == np.max(h2, axis=1)[i]))\n",
    "        p = np.vstack((p,t))\n",
    "    return p    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GKxhUVWVgYICDBw9iNptZWVkhKSmJI0eOoCgK8fHxZGZmkpSUxOPHjwOKnBV/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x40e3f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 1.059037\n",
      "         Iterations: 18\n",
      "         Function evaluations: 182\n",
      "         Gradient evaluations: 170\n",
      "(u'\\u6267\\u884c\\u65f6\\u95f4\\uff1a', 50.123000144958496)\n",
      "[-0.42109302 -0.03209883 -0.0867308  ..., -0.4111507   1.69801146\n",
      "  0.23224257]\n"
     ]
    },
    {
     "data": {
      "image/png": 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73BVbU9jY2DjgpjSFa6zeePlms71kVcfkmN619rRWZqtvIzNrbS5DdP/quc2g\nM3MeQdlMx92v1u6BrcjSSln1XyjIttpFsIlxaW7J5j/w1xxgstoDyOj+lqD33DXqtBGozUBVL9S+\nH9C6lfptXMjeOa4Na31mYzxamr55EqHPqv+CcWgUKU2KjWe1c7T/PWVqhvGtKWxsbLwkeKgr3MuB\ne/fuvfxCbGx8ieP+/fuXg2OCrSlsbGwccFM2hXe84x0zc569uOfTPY1Y98r27df2kfav3ae2KpP7\n/G4P+Ju/+ZsHWe1DW4ti9WhsVB55WfjJrI2eDNRSzQ6iD/aOjXl43/veNzMzb33rW2fmWAfA3tiz\n/PUsspDZvSz8+l2P0OafrH/IpSre5vfXf/3XZ2bmne9858yce27WluBZ5tozzZln9/p1n77iUpSp\nseXBqv/vf//7Z2bm3e9+98yc5r02F+8omerPUm9Vc1s/kJnT+6AfbArsZt65Vob6nd/5nYv9vYat\nKWxsbBxwU5pCI8dYj3tujc3LJDPnWXRa/bfZluvPYIVv/r9rdR6cYmDOS/kUmucRu2KFeuhhvPoI\n0CzIrk/aI2MjHnvmvl6LZeoT4Fpame95T2LhVojCmGTSJ+1pZ2Uz89zPzc3QnAWYsuxsPFnwjZs5\nbv1P7aw5My5poeu9QAMyx8bhWq7FeqO6vppBT5xW1AO29SqhGbgeFFtT2NjYOGAvChsbGwfc1PaB\n+tc0bEAdaqDQatSjdlH/JAilYtaJRht1erItcN81FZd6XFVudSyxbagMLf9e92Vh30KotU1lNQ7U\nXirrNTfnNZS2iVbrQGUcqLPGQ7/q8NNQ6iYnacr3S1sZaNl3QVrGqQFmLWar7Y6Ddo0T46GxWLc0\nTR7rfao6z1DItbqp/6n0nnXNKNh3vcV0Z87DAPSfrHVm2qXoNzY2XhLclKbQ5JiMXFipzGA1/djH\nPvaFNspUGIr7sZBU9zagx/XSql8LLmlpuyYCWd1hsQutpOHJmA0DXAvDBdc39VnT2AM2W7WdugjX\nndfvgo6aVNd12Kgshs2rYRnvVVNokhXXYEAMz8CKbRtc1GCrhmArflvtznu2GmhrYO4cQjWmlrDX\nN9/XkFu35hbbkapv5tzNucF82jJ3HfsHxdYUNjY2DrgpTaGJTaDs4nd77TWpqhUbs1lp6/DhHkyo\nrSZnaSk3aMKT7vdX9/Eeifnsmh69kqVBMrQW/cekDcLqXrpazSqDZ7qnjkJ1Zupx8Oc+97mZOU93\npyw8W0ST2azFYJoURtsNCTfWPe7DqmwKNCOsXruQv3X+WbWXzmOD88D3DaAyNz3yrTbsr77qQ21f\n6zPqDGfee3Tbwr0Piq0pbGxAuWfoAAAgAElEQVRsHHBTmkL3b7XkNp02i679/8yJoX74h394ZmZe\n85rXzMxp//ipT31qZmY++MEPHp7tWVj60UcfnZkTo9URhKwtQ4cJVptCmYgWwrZgZcdwda6pUxPt\nBbASe0mD3MokM+e2Fs9uuTJjXceranPuu+Ys1iLBq3a3ag0z58ljr6U0p6VAU6CTqXPS9+vS+FQr\nvVaKrQ5QxrMu6DSohnfXDlBX9UtFZvoutiCPOVvd2u+CrSlsbGwccFOaQlmoJd3ssVlqrc7rXlmx\nWSt23VA947HHHpuZ88AgqzBmxDK1kFvRW1atJyQz52fO9sAYUr8Uzv3whz88MydmpI3cu3dvZk5M\n1+QqmKF7dOO47oe5K+uHsaSF+L5uu2w0UsSRTb/ZHppmXPtOAPR15pwNm2QGm5aFe+rQ1Hk93Wnx\n4Pp7rMVT6tthHKoh0dJoROYC82tbO96npr/zvDe+8Y0zc3p/1gRC2q7vRP+fNHjrrtiawsbGxgE3\npSm03LtVFDM22SqNYT2Xt6+W9rtJObEP1sG+b37zm2fmVKC2+9fu9TyzAVY0h7X0W9OFe/Yjjzwy\nMye2UZzECq9IrpWfRvHwww/PzLnFG1P2pKTMud7bMmb2yLQb4+Czoq5N/V4Ni52npcsupY6rjaTB\nQ02BhkW1de30hdZirmpraMi6U471GnLWexTIdunUaebcVtDyeS15R6Py+5qqzrOdmNWbtP3cNoWN\njY2XBDelKbQgRpNh9Lz64x//+OH6mdN+HLDAa1/72pk5j6/4wR/8wZk5L6iBday+9QCEhnlj/TVt\nOU2Hf3xlscd99tlnZ+ak7WBpMimHRkPCsNik3pWgb6tXJvma5LT7UG2T1ekNdN/eoq39C2waM+de\ngmQz9p7dEwHj0FT5+ut642F8mmyXzGtcg36bz2sxCtWYgGbR98gzWlbOO11/j/WEpeHn3mEag3Gk\nOXVcHxRbU9jY2DjgpjQFDFF2sapaTa26Vm978ZmZD33oQzNzWkWdRrAxsJ7b39uf+b7n9t23g++b\n7s2+3unGzGm/SdPBPtiEdtM9MRlY6p966qmZOdkUmratpw5wqaBNU7TXz4L20tMV/eQP4vze9/qm\nvXrZYfE1gq9xJfW2bBGUxnI0dkEsDBnIWk9Ic2jOV1uM/jgt8bkMX+0DazdRjOuMqz73ZM3fz3zm\nM4cxWH9rijsaaAvlbo/GjY2NlwQ3pSm07Ldz/GtJQH1v9Z05WeyxgTZaprs+DzQBzGC1bfJUYO9o\nnDzr8brHtI8si37iE5+YmZkXXnhhZk4M2eIovCtpCNomG9Ztijnw3FXbaZl3Y6nN5qXARuwY1Qxq\neylr9ZRilbHRfNrEsmTC6J5tXOtTQhaysl84EWqkItlWmcy396hl9MCzteH98h60L41gpL017V1T\nE86c5qpjD42V2cVgNjY2XhLclKZgj2fFw77YpSxslV73Ts7HraZW+nqSOX+mQXz2s589/O5ZZOpJ\nCGZtqTcstZ5597y9pw1d2T3bOGA6+9UWksUq2i/zGos1mSzWaVQoNGksn4onn3xyZs6zIzUPQFPn\n19NvtW+U8Wg+jXjF7I28rNck20tPLYxzvRWbS2PtRyNZO04ts+edNce1STV3RuNe6gex4lJ6/FVG\n/Wtmr7tiawobGxsH3JSmgBG638Icvud3b8/46U9/+gttvOUtb5mZ89LfrLmegYVaONVnK3jbgUb7\n1TaxMqGTCD4AtUewFegHDcjJCb8GWlCjLpsnoHEaWHz1aKz3Y63h+uuenuVjumaywow0g2oItBnj\nNXPu9XjNJ0R/mw+zXqWNDehJStPRX/IEbd4IbTdHY/Mkmndza1yakclceTfK9s2JscrZd7F5My+d\nNt0FW1PY2Ng44KY0BasuFrdaWuGtuva59rWPP/74F9poVp1avzFeS603f5/9pVW37GVfhzn6eWVC\nrFqbwA/90A/NzImN/I4JsIj4DH1xEtATEr7u14qmrDYFzMZPo2XiaAy0sY4f9nUfWeorYa4af7HK\nUos++RufYW5934jLznltLPUpqUfpKlNzM1yD/jVKtqcNnkljaO7Gxq/AasPwbpnv5qw0p40Ruiu2\nprCxsXHATWkK2NtKVx8BJwRWdntuNob1OyusfXwZnQWbNuIZ9dCzP72WcaexA1gOm8+ctA+aQIvg\nehavSyzlmc3dqE+1XPvcqMKe96/jU58PcmurEZraJnM9P/2undoiyLBqM6tWtbZJizNe5qo1OcQH\nkKEnBe7XrnHXnr6t/iE9rWp+RKh/hme2CHDjL4xfM5U3/8d6gtDyibUH+fz/OsF4EGxNYWNj44Cb\n0hS6mlrZrdpW/LLzei5vf4VN7KuwQaMoW3WoHnpd8YEM9obN0ssqvz7bit6z7vq5+0wDwrqeYZ+P\nVWg39Y4DbLP2wVhiKvdixsYsNLLwWt0Lf8lQD0Z2j9W6fi2bMy2lHoj1tqwG0IKzxolG0XmoPWjt\n17UCvKAfrTBGk9RmtRbt9KSErP6uOREa/cqeo03elD2FuSu2prCxsXHATWkKVnis0qpDLS9/KW+e\neAKsgVUxXXPmWWVbxr174HoJYjH2DXvK7jlnZj7ykY8cZGrE3LVoUOyi/83ajAmagacW89YqWJ9Z\nb1Ft1WrejMrGpxqU+zGh39kWaD3rOHXM3NO6DY3TENdCNtfTEs2ZCNh6ofb3VXvxb3Ibh44lLcz4\nsQ14r6oV6kvzdppL89HxWn+rvafZnMhyKRP0g2BrChsbGwfclKZg1bVq9vTByUKz+K7n3FZYK7Xf\nrKos3Vi3zFVGcF3j6JtpCOtc8jd3nt4qwD2jbq5Bf+0rjUdjIjAoZqim0H3wzInRsC12Ncb63zPx\n2jPMVbWUVr1qZe2VQeu9h/FpK63T0AxE3ddj/mssXVbv/TPnpyrXoiTr8eh9qN2iGaX1ke3FyYdx\nYieiec2cVwr3PlXLaz7Su2JrChsbGwfclKaARbBTV9HW1+Pxt1pZsacVvuxZ5u8JR9m7laCgGkGt\n8usq7Rn+YlmsQiZttlqTvmAjMmEb9+tD971kWz3cmrXHM6t1mIPmi2jkIY3DXPnb/W3tA2v/gGaE\nyevPYY6brZlno/uaX4L22JOBeq+u/asmWI0RaiuA1qrwfpgzz24uiGocM6f/F96tatR995qX40Gx\nNYWNjY0D9qKwsbFxwE1tH6hs1MM63bSghlDj1fjjmI+qWENRA3Ja+LMqPhWsxztUTeqh3y8lEYGq\nr3UyattkaEIORtMGDvUYFXy/quwN8KrRrclFqO4MYE2MUjfvyky11c6lNGNQI6c5MW7Gp8WD9Ona\nVsdzWni2yVjW/jSoqoZG80zmblVsfTr37jOOjKNkdPS7Oi/ZDrnGGDZ03O/XQtC/GLamsLGxccBD\nXaVfDty7d+/lF2Jj40sc9+/fPz+bvoCtKWxsbBxwUzaFd7zjHTNz7nxhz2yP2PRsa4k2xzTsEd1n\nOVLS9jVNyX3asQd8+umnD7K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vH5K7YmsKGxsbB9yUpgBlnSZIgSYPXf9tRbZ6WqmlBbcH\ntJKLQ7D6Wm2two0nqG96tZe1IAsZrqV2q29FU5S3mEvZ3Phgq8qqnXXPXI2KvI3LMOYt3SdOoAle\nPIOW09gTfVllLPt2XDpu3ec34rNp6NuHFgGuprGOh2v1s1qYMdfvel1Ww6jmoN1Gq0rqu45TtV6p\n4jzjWnTsXbE1hY2NjQNuSlNoks9GkPm9/uJr7ENZtpGI2vI7jaEFZe0zpfJqPEH3wWWC1YMNC7AG\n+605Gapt0JjkTyADBsXaGJDmVHtHPQbX8cB89Y5rsVascy2eQL/NReMPyGRO1z11S6a7pyx8rdhv\nU76bG+XcezJ07969Q3vm/lKBGnNRrQy8Rz0xqufmtdICfY9c571d5/Kpp56amfN4i0bytqjvXbE1\nhY2NjQNuSlOwKjeKsKsx5qMVYPWZE1tYYf21al7TOgBbWHX5qJdtu4fuKr1e3/P1ntVrSwxETwaw\nBnZpoRsWcuxe0CTW5Kr638SjLTjSsa+mVd+KnqD47OTA59WHoFmZWibPX+NBI/K9vTUGlaGop1ag\nJB5N7FJ2qCZY9Vu1mpZ9cyqz+qnMnNu2tNPMTPVlWe1A+sW24H2p3YYsTab7oNiawsbGxgE3pSl0\nP16rebP+uH7d51n9rcDOamkT2KQpyF3fSDpFYK/F0bf0eIvjzpxWbFqHE43aMVr+TNs0gXpltujH\npfwS6+eV5ZppqbiWB7OFVmlBNAFMh6Xrr1CL/9ov0I/mFjDPLTFfmwKNyZxjfX0wrmRuVOXMzHPP\nPXd4Vk8wQD+9N82nUQ/PFgE2Po899tjMnLTC5p+YOZ+T5hOtNtvTiAfF1hQ2NjYOuClNoQzX8mk9\nx8eoq/9C9+31auOHQEPoHo+G0HwA1wqL0mqagXk9I7aS2+u94hWvOMhIG8FYPbNu6XGytDhITyXg\nUjGY+jp4RrNAadPcuN64rnkNZ05zc62gbOM0Zs5zDTafQvfGzR9Zb9Q3vvGNh2caz+eff35mTnPe\nojPr+9fShfURgGv+MP7qp/YU6DWuNAJ9pNnK5bjaJlruzrtcLeRa+cAHxdYUNjY2DrgpTaFedc2r\nWEut65R4X9sA+23X8mikAWAyGob9/rWVHhrlhlEwcC3eMyebgrb5QLhHv1588cWZObF1I+b8bdl3\nmkQ9Gsm47jlrp8FYPS0gQzWp+m24T7v1CNR+vQxnztnXeNRfA/N7NtuB+W/cAfbl51FZzEdPN1a0\neG+zOXuW68jYwrSPP/74zJzY3V/XG+/f+73fO7S/2hTqldtTKG3RgJqB60GxNYWNjY0DbkpTsJ/q\n/rzxBZjT/mxdEbEllsCOzQBtta3luR53l7wBZ65bnX1eC9LWa62l08H+8eGHH56Z85OUsnll85wy\nb0u3z5wY7lrcQQvC9pnG13iZI99jcVqM5xiXdc56+tA4CVZ2Mhk37FtvQnNLK9EH4+l8vwVZV5uC\nMaxG1ELD9b6kMXgPjYPThSeeeOJwff9qvzkfZk62hEZSmlfvTzXru2JrChsbGwfclKZgP18vQczg\nexrFq171qpk5MmAty9iicQOYvp5ontWMRGXf7tO11yzRM+e+91jESu9eDEkGbTTDr2fW56L1MaA+\n/uu1ZRttN5qxtpP6ZUAzMPuM7S9lJOret3VAG3fw6le/emZOrKzNagZkwNI0hGbyouWtpyD8BdqP\n9dRk5rxWCU2JjwTZm+vAuDduhfZL1nWcPv3pT8/M+dz46x1u9a+7YmsKGxsbB9yUpmDltuKV9a/l\nNFzZyn79hRdemJnTyo3ZtEHbKKs2L6QVvrHprV5lz9wqPTMnJsQGtI9WUcJUGNBf1nO2htoWMAOZ\namu4VD+jdRyanYgsZDOuPSFqnEa9TjGlccfma+alegFqi+bYPXQjMM2BueY7QXb7+lZjJmtzPK4y\n1F5RmIOeiFSTFLdAVuOL/b3rxksfV5uG/xeNFqXNrJm11jbuiq0pbGxsHHBTmkLP3bES20HP1j/w\ngQ8cPs+cNAT3Wk2xBos1dvD95z73uZk5reRkwXCNQGwMfveU6yqN2euBh01b+RrjYzzXt3ZgKzrT\nLMpqPq/7Yf3EttrsODQPRf0NaGBY3TP0Vd+05/c1XqVWcr81D6R+0loa8eq9abajejb6XV/JtOaA\n9KxG3VZjbA1O0O9PfOITM3Ne8am+OMbR+PJzWGWiUTXnR/ND6ue1TF9fDFtT2NjYOOCmNIXWxGv0\nW/Mpiou3Gs+cVnKs+eijj87MaVVtJCG27l4PW1l969FYaz2m9XfNmdATChbn7o3107Nch/FYpBsT\nca3KMjQ/wcxpLDFU6za06rbx6Fl5/Tt6coLdsD7mWzWvtV7izIktWx2aZsQPwXiIgqydxxxgVuf4\nNC7tmnMepjPnWY2MXU+hapcwbk6vGs8DcjA2JuSShgD6xx5W71D2CWNfG8ODYmsKGxsbB+xFYWNj\n44Cb2j5Q46hcLYvud6rnM888MzPH8F2/Va1tgpKWnqu623Tp18KR6857KXDG1oUKTVXUhi0Hg5t+\nO0KrUcqWp8VwanACsltyh9oAAATXSURBVK+qLFnI0CS5tjzuoR43Eatnub59amJXfVmT0HRsqcO2\nR55N7adaU5eFGdtGeE88y7hQ6X0PLeM3c1420JamSVb6XmnrWgh+v28Bm2vG6Jnz405jWJf1S2N8\nF2xNYWNj44Cb0hQYUrriWX3rcON4EfPOnBhMaKoVvo5QTWhi5a6raNsFsmGtpiFfgYE4IWH4Bg+R\nsQbEJu7oER42b7p2qPF07b/xaIm+psCnQfVo0Vy5zv1+p+1o75JRtEFGWFrbWLgl/cjOOAeYVLvt\nf9OuXzLQNmS87ws0II7GRHvV3wa3mbMnn3xyZk4aQUPyV62mwWvu0aZrvYP7SHJjY+MlwU1pCtjF\nCmgv2bLpVnF79R/5kR/5QhsYz+qJVSTUaHqxFkwFbO73pgSzGjeRaZ19Zk5HXZ6NNVr01u/uJXv3\nxsbHfdprIRZwFLfumf27ruMNtqqNwDhUZppU29OX2mYulbCDlt4z/57h9x7lSmt3yW155qSBdB+v\nj02quo5DUwFWVtf1CLsFaOtW791oMFzTBKxtsaU0VaAxrsv6XbE1hY2NjQNuSlPAHhigBUat8PZr\nVvZL6disntpkd2jq97r71o0VSzVVV5mwyUZXhxzXNhFtE5k0UYu2mjwDC7WE2bVQ2bqPz5xb4slW\nlu0JgNBeMvkew9E0fG4Bm57WXOpHxxrLtriLEOq6KftrDjyTLNzmsTb70ypHk916L5pkVhv602I3\nDVZq4JO5J5vn0UBW+5FrfKeNuqr3ZOOu2JrCxsbGATelKbSEmRUQ+9S63tOKmfOkH1b/nu03JLo2\nAWzlumuJSntWrL2VCV1Tv4IWZCF7C9f0ZKMJbZt8tvtWsq4nKNd8GhrY0wQuPntGE7lqr3vtpqNf\n97vdp7eYrfHwmf2HfQMj8lPoiVKT29AsaRLVzGZOTE+j0kZtSzQm/a6/R8sOdvxabrAu2uv73NSB\nTf1HG77k43AXbE1hY2PjgJvSFFpg1gpoFcb6Zbl1L9ikJ1Zo12JtzOYZVl/7+p4Tl81a0gzL9IRh\n5sQu1wrlNtS1QUcYvuXTao2vJgH22KsGgTXZN3o608S03Ts30Yfx8n1L3Qtiw/prwFhtCE0Xb5x8\n7ikL+1CfieWrWdEQfPaurD4ILUB0rVhr7Rz+smO0SEzT3/W0qh6RawAWG5TvyO+dben5XTZuY2Pj\nJcFNaQpWTyyLXay6ZRCMu54YXEqNPXNaRVsoo7YGrGPFb9FXaNEUMnefP3Ne7quWbZ/tBcsS2sIm\n7muqeKzVMuiXipwYW/c2hVltAz1taBLdWt+bQq9a0OpFWM+77oXJoB89pSF7k8vqW+NYAHvTKNaT\nBYxNG2lcDuhPvW+bhq6errQS73D7eCkxDpuBtlzb92SneN/Y2HhJ8dD/Ng30S4l79+69/EJsbHyJ\n4/79+w9UR25rChsbGwfchKawsbFxO9iawsbGxgF7UdjY2DhgLwobGxsH7EVhY2PjgL0obGxsHLAX\nhY2NjQP2orCxsXHAXhQ2NjYO2IvCxsbGAXtR2NjYOGAvChsbGwfsRWFjY+OAvShsbGwcsBeFjY2N\nA/aisLGxccBeFDY2Ng7Yi8LGxsYBe1HY2Ng4YC8KGxsbB+xFYWNj44C9KGxsbBywF4WNjY0D9qKw\nsbFxwP8B6J7OEsYQJhkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18076e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c15e198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "预测准确度为：87.140000%\n"
     ]
    }
   ],
   "source": [
    "def neuralNetwork(input_layer_size,hidden_layer_size,out_put_layer):\n",
    "    data_img = spio.loadmat(\"../data/3-neural_network/data_digits.mat\")\n",
    "    X = data_img['X']\n",
    "    y = data_img['y']\n",
    "    m,n = X.shape\n",
    "\n",
    "    ##　随机显示几行数据\n",
    "    rand_indices = [t for t in [np.random.randint(x-x, m) for x in range(100)]]  # 生成100个0-m的随机数\n",
    "    display_data(X[rand_indices,:])     # 显示100个数字    \n",
    "    \n",
    "    #nn_params = np.vstack((Theta1.reshape(-1,1),Theta2.reshape(-1,1)))\n",
    "    Lambda = 1\n",
    "    \n",
    "    initial_Theta1 = randInitializeWeights(input_layer_size,hidden_layer_size)\n",
    "    initial_Theta2 = randInitializeWeights(hidden_layer_size,out_put_layer)\n",
    "    \n",
    "    initial_nn_params = np.vstack((initial_Theta1.reshape(-1,1),initial_Theta2.reshape(-1,1)))  # 展开theta\n",
    "    #np.savetxt(\"testTheta.csv\",initial_nn_params,delimiter=\",\")\n",
    "    start = time.time()\n",
    "    result = optimize.fmin_cg(nnCostFunction, initial_nn_params, fprime=nnGradient, args=(input_layer_size,hidden_layer_size,out_put_layer,X,y,Lambda))\n",
    "    print (u'执行时间：',time.time()-start)\n",
    "    print (result)\n",
    "    '''可视化 Theta1'''\n",
    "    length = result.shape[0]\n",
    "    Theta1 = result[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1)\n",
    "    Theta2 = result[hidden_layer_size*(input_layer_size+1):length].reshape(out_put_layer,hidden_layer_size+1)    \n",
    "    display_data(Theta1[:,1:length])\n",
    "    display_data(Theta2[:,1:length])\n",
    "    '''预测'''\n",
    "    p = predict(Theta1,Theta2,X)\n",
    "    print (u\"预测准确度为：%f%%\" % np.mean((p == y.reshape(-1,1))*100))\n",
    "    res = np.hstack((p,y.reshape(-1,1)))\n",
    "    np.savetxt(\"predict.csv\", res, delimiter=',')\n",
    "\n",
    "neuralNetwork(400, 25, 10)"
   ]
  }
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