NeuralNetwok神经网络（numpy实现）.zip

#-*- coding: utf-8 -*- import numpy as np from scipy import io as spio from matplotlib import pyplot as plt from scipy import optimize from matplotlib.font_manager import FontProperties 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 from sklearn import datasets from sklearn.preprocessing import StandardScaler import time def neuralNetwork(input_layer_size,hidden_layer_size,out_put_layer): data_img = loadmat_data("data_digits.mat") X = data_img['X'] y = data_img['y'] '''scaler = StandardScaler() scaler.fit(X) X = scaler.transform(X)''' m,n = X.shape """digits = datasets.load_digits() X = digits.data y = digits.target m,n = X.shape scaler = StandardScaler() scaler.fit(X) X = scaler.transform(X)""" ##　随机显示几行数据 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 display_data(X[rand_indices,:]) # 显示100个数字 #nn_params = np.vstack((Theta1.reshape(-1,1),Theta2.reshape(-1,1))) Lambda = 1 initial_Theta1 = randInitializeWeights(input_layer_size,hidden_layer_size); initial_Theta2 = randInitializeWeights(hidden_layer_size,out_put_layer) initial_nn_params = np.vstack((initial_Theta1.reshape(-1,1),initial_Theta2.reshape(-1,1))) #展开theta #np.savetxt("testTheta.csv",initial_nn_params,delimiter=",") start = time.time() result = optimize.fmin_cg(nnCostFunction, initial_nn_params, fprime=nnGradient, args=(input_layer_size,hidden_layer_size,out_put_layer,X,y,Lambda), maxiter=100) print (u'执行时间：',time.time()-start) print (result) '''可视化 Theta1''' length = result.shape[0] Theta1 = result[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1) Theta2 = result[hidden_layer_size*(input_layer_size+1):length].reshape(out_put_layer,hidden_layer_size+1) display_data(Theta1[:,1:length]) display_data(Theta2[:,1:length]) '''预测''' p = predict(Theta1,Theta2,X) print (u"预测准确度为：%f%%"%np.mean(np.float64(p == y.reshape(-1,1))*100)) res = np.hstack((p,y.reshape(-1,1))) np.savetxt("predict.csv", res, delimiter=',') # 加载mat文件 def loadmat_data(fileName): return spio.loadmat(fileName) # 显示100个数字 def display_data(imgData): sum = 0 ''' 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） - 初始化一个二维数组 - 将每行的数据调整成图像的矩阵，放进二维数组 - 显示即可 ''' m,n = imgData.shape width = np.int32(np.round(np.sqrt(n))) height = np.int32(n/width); rows_count = np.int32(np.floor(np.sqrt(m))) cols_count = np.int32(np.ceil(m/rows_count)) pad = 1 display_array = -np.ones((pad+rows_count*(height+pad),pad+cols_count*(width+pad))) for i in range(rows_count): for j in range(cols_count): if sum >= m: #超过了行数，退出当前循环 break; 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 sum += 1 if sum >= m: #超过了行数，退出当前循环 break; plt.imshow(display_array,cmap='gray') #显示灰度图像 plt.axis('off') plt.show() # 代价函数 def nnCostFunction(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda): length = nn_params.shape[0] # theta的中长度 # 还原theta1和theta2 Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1) Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1) # np.savetxt("Theta1.csv",Theta1,delimiter=',') m = X.shape[0] 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 # 映射y for i in range(num_labels): class_y[:,i] = np.int32(y==i).reshape(1,-1) # 注意reshape(1,-1)才可以赋值 '''去掉theta1和theta2的第一列，因为正则化时从1开始''' Theta1_colCount = Theta1.shape[1] Theta1_x = Theta1[:,1:Theta1_colCount] Theta2_colCount = Theta2.shape[1] Theta2_x = Theta2[:,1:Theta2_colCount] # 正则化向theta^2 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)))) '''正向传播,每次需要补上一列1的偏置bias''' a1 = np.hstack((np.ones((m,1)),X)) z2 = np.dot(a1,np.transpose(Theta1)) a2 = sigmoid(z2) a2 = np.hstack((np.ones((m,1)),a2)) z3 = np.dot(a2,np.transpose(Theta2)) h = sigmoid(z3) '''代价''' 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 #temp1 = (h.reshape(-1,1)-class_y.reshape(-1,1)) #temp2 = (temp1**2).sum() #J = 1/(2*m)*temp2 return np.ravel(J) # 梯度 def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda): length = nn_params.shape[0] Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1).copy() # 这里使用copy函数，否则下面修改Theta的值，nn_params也会一起修改 Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1).copy() m = X.shape[0] 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 # 映射y for i in range(num_labels): class_y[:,i] = np.int32(y==i).reshape(1,-1) # 注意reshape(1,-1)才可以赋值 '''去掉theta1和theta2的第一列，因为正则化时从1开始''' Theta1_colCount = Theta1.shape[1] Theta1_x = Theta1[:,1:Theta1_colCount] Theta2_colCount = Theta2.shape[1] Theta2_x = Theta2[:,1:Theta2_colCount] Theta1_grad = np.zeros((Theta1.shape)) #第一层到第二层的权重 Theta2_grad = np.zeros((Theta2.shape)) #第二层到第三层的权重 '''正向传播，每次需要补上一列1的偏置bias''' a1 = np.hstack((np.ones((m,1)),X)) z2 = np.dot(a1,np.transpose(Theta1)) a2 = sigmoid(z2) a2 = np.hstack((np.ones((m,1)),a2)) z3 = np.dot(a2,np.transpose(Theta2)) h = sigmoid(z3) '''反向传播，delta为误差，''' delta3 = np.zeros((m,num_labels)) delta2 = np.zeros((m,hidden_layer_size)) for i in range(m): #delta3[i,:] = (h[i,:]-class_y[i,:])*sigmoidGradient(z3[i,:]) # 均方误差的误差率 delta3[i,:] = h[i,:]-class_y[i,:] # 交叉熵误差率 Theta2_grad = Theta2_grad+np.dot(np.transpose(delta3[i,:].reshape(1,-1)),a2[i,:].reshape(1,-1)) delta2[i,:] = np.dot(delta3[i,:].reshape(1,-1),Theta2_x)*sigmoidGradient(z2[i,:]) Theta1_grad = Theta1_grad+np.dot(np.transpose(delta2[i,:].reshape(1,-1)),a1[i,:].reshape(1,-1)) Theta1[:,0] = 0 Theta2[:,0] = 0 '''梯度''' 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 return np.ravel(grad) # S型函数 def sigmoid(z): h = np.zeros((len(z),1)) # 初始化，与z的长度一致 h = 1.0/(1.0+np.exp(-z)) return h # S型函数导数 def sigmoidGradient(z): g = sigmoid(z)*(1-sigmoid(z)) return g # 随机初始化权重th