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神经网络
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‎LogisticRegression/LogisticRegression.py‎

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@@ -20,7 +20,7 @@ def LogisticRegression():
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J = costFunction(initial_theta,X,y,initial_lambda) #计算一下给定初始化的theta和lambda求出的代价J
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print J #输出一下计算的值，应该为0.693147
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# result = optimize.fmin(costFunction, initial_theta, args=(X,y,initial_lambda)) #直接使用最小化的方法，效果不好
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#result = optimize.fmin(costFunction, initial_theta, args=(X,y,initial_lambda)) #直接使用最小化的方法，效果不好
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'''调用scipy中的优化算法fmin_bfgs（拟牛顿法Broyden-Fletcher-Goldfarb-Shanno）
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- costFunction是自己实现的一个求代价的函数，
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- initial_theta表示初始化的值,

‎LogisticRegression/LogisticRegression_OneVsAll.py‎

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@@ -70,6 +70,7 @@ def oneVsAll(X,y,num_labels,Lambda):
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'''遍历每个分类，计算对应的theta值'''
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for i in range(num_labels):
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#optimize.fmin_cg
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result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,class_y[:,i],Lambda)) # 调用梯度下降的优化方法
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all_theta[:,i] = result.reshape(1,-1) # 放入all_theta中
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‎NeuralNetwok/NeuralNetwork.py‎

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#-*- coding: utf-8 -*-
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import numpy as np
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from scipy import io as spio
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from matplotlib import pyplot as plt
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from scipy import optimize
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from matplotlib.font_manager import FontProperties
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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
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from sklearn import datasets
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from sklearn.preprocessing import StandardScaler
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def neuralNetwork(input_layer_size,hidden_layer_size,out_put_layer):
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data_img = loadmat_data("data_digits.mat")
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#data_weights = loadmat_data("weights.mat")
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X = data_img['X']
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y = data_img['y']
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#Theta1 = data_weights['Theta1']
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#Theta2 = data_weights['Theta2']
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#y = np.ravel(y)
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m,n = X.shape
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"""digits = datasets.load_digits()
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X = digits.data
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y = digits.target
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m,n = X.shape
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scaler = StandardScaler()
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scaler.fit(X)
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X = scaler.transform(X)"""
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##　随机显示几行数据
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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
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display_data(X[rand_indices,:]) # 显示100个数字
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#nn_params = np.vstack((Theta1.reshape(-1,1),Theta2.reshape(-1,1)))
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Lambda = 1
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initial_Theta1 = randInitializeWeights(input_layer_size,hidden_layer_size);
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initial_Theta2 = randInitializeWeights(hidden_layer_size,out_put_layer)
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initial_nn_params = np.vstack((initial_Theta1.reshape(-1,1),initial_Theta2.reshape(-1,1))) #展开theta
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result = optimize.fmin_cg(nnCostFunction, initial_nn_params, fprime=nnGradient, args=(input_layer_size,hidden_layer_size,out_put_layer,X,y,Lambda))
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print result
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'''可视化 Theta1'''
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length = result.shape[0]
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Theta1 = result[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1)
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Theta2 = result[hidden_layer_size*(input_layer_size+1):length].reshape(out_put_layer,hidden_layer_size+1)
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display_data(Theta1[:,1:length])
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'''预测'''
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p = predict(Theta1,Theta2,X)
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print u"预测准确度为：%f%%"%np.mean(np.float64(p == y.reshape(-1,1))*100)
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res = np.hstack((p,y.reshape(-1,1)))
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np.savetxt("predict.csv", res, delimiter=',')
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# 加载mat文件
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def loadmat_data(fileName):
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return spio.loadmat(fileName)
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# 显示100个数字
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def display_data(imgData):
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sum = 0
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'''
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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）
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- 初始化一个二维数组
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- 将每行的数据调整成图像的矩阵，放进二维数组
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- 显示即可
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'''
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m,n = imgData.shape
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width = np.int32(np.round(np.sqrt(n)))
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height = np.int32(n/width);
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rows_count = np.int32(np.floor(np.sqrt(m)))
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cols_count = np.int32(np.ceil(m/rows_count))
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pad = 1
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display_array = -np.ones((pad+rows_count*(height+pad),pad+cols_count*(width+pad)))
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for i in range(rows_count):
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for j in range(cols_count):
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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
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sum += 1
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plt.imshow(display_array,cmap='gray') #显示灰度图像
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plt.axis('off')
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plt.show()
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# 代价函数
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def nnCostFunction(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda):
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length = nn_params.shape[0]
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Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1)
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Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1)
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# np.savetxt("Theta1.csv",Theta1,delimiter=',')
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m = X.shape[0]
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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
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# 映射y
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for i in range(num_labels):
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class_y[:,i] = np.int32(y==i).reshape(1,-1) # 注意reshape(1,-1)才可以赋值
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Theta1_colCount = Theta1.shape[1]
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Theta1_x = Theta1[:,1:Theta1_colCount]
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Theta2_colCount = Theta2.shape[1]
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Theta2_x = Theta2[:,1:Theta2_colCount]
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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))))
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'''正向传播'''
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a1 = np.hstack((np.ones((m,1)),X))
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z2 = np.dot(a1,np.transpose(Theta1))
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a2 = sigmoid(z2)
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a2 = np.hstack((np.ones((m,1)),a2))
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z3 = np.dot(a2,np.transpose(Theta2))
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h = sigmoid(z3)
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'''代价'''
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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
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return np.ravel(J)
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# 梯度
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def nnGradient(nn_params,input_layer_size,hidden_layer_size,num_labels,X,y,Lambda):
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length = nn_params.shape[0]
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Theta1 = nn_params[0:hidden_layer_size*(input_layer_size+1)].reshape(hidden_layer_size,input_layer_size+1)
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Theta2 = nn_params[hidden_layer_size*(input_layer_size+1):length].reshape(num_labels,hidden_layer_size+1)
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m = X.shape[0]
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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
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# 映射y
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for i in range(num_labels):
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class_y[:,i] = np.int32(y==i).reshape(1,-1) # 注意reshape(1,-1)才可以赋值
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Theta1_colCount = Theta1.shape[1]
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Theta1_x = Theta1[:,1:Theta1_colCount]
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Theta2_colCount = Theta2.shape[1]
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Theta2_x = Theta2[:,1:Theta2_colCount]
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Theta1_grad = np.zeros((Theta1.shape))
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Theta2_grad = np.zeros((Theta2.shape))
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Theta1[:,0] = 0;
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Theta2[:,0] = 0;
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'''正向传播'''
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a1 = np.hstack((np.ones((m,1)),X))
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z2 = np.dot(a1,np.transpose(Theta1))
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a2 = sigmoid(z2)
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a2 = np.hstack((np.ones((m,1)),a2))
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z3 = np.dot(a2,np.transpose(Theta2))
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h = sigmoid(z3)
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'''反向传播'''
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delta3 = np.zeros((m,num_labels))
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delta2 = np.zeros((m,hidden_layer_size))
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for i in range(m):
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delta3[i,:] = h[i,:]-class_y[i,:]
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Theta2_grad = Theta2_grad+np.dot(np.transpose(delta3[i,:].reshape(1,-1)),a2[i,:].reshape(1,-1))
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delta2[i,:] = np.dot(delta3[i,:].reshape(1,-1),Theta2_x)*sigmoidGradient(z2[i,:])
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Theta1_grad = Theta1_grad+np.dot(np.transpose(delta2[i,:].reshape(1,-1)),a1[i,:].reshape(1,-1))
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'''梯度'''
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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
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return np.ravel(grad)
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# S型函数
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def sigmoid(z):
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h = np.zeros((len(z),1)) # 初始化，与z的长度一致
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h = 1.0/(1.0+np.exp(-z))
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return h
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# S型函数导数
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def sigmoidGradient(z):
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g = sigmoid(z)*(1-sigmoid(z))
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return g
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# 随机初始化权重theta
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def randInitializeWeights(L_in,L_out):
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W = np.zeros((L_out,1+L_in))
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epsilon_init = (6/(L_out+L_in))**0.5
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W = np.random.rand(L_out,1+L_in)*2*epsilon_init-epsilon_init
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return W
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# 预测
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def predict(Theta1,Theta2,X):
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m = X.shape[0]
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num_labels = Theta2.shape[0]
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#p = np.zeros((m,1))
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X = np.hstack((np.ones((m,1)),X))
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h1 = sigmoid(np.dot(X,np.transpose(Theta1)))
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h1 = np.hstack((np.ones((m,1)),h1))
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h2 = sigmoid(np.dot(h1,np.transpose(Theta2)))
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'''
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返回h中每一行最大值所在的列号
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- 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）
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- 最后where找到的最大概率所在的列号（列号即是对应的数字）
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'''
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#np.savetxt("h2.csv",h2,delimiter=',')
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p = np.array(np.where(h2[0,:] == np.max(h2, axis=1)[0]))
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for i in np.arange(1, m):
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t = np.array(np.where(h2[i,:] == np.max(h2, axis=1)[i]))
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p = np.vstack((p,t))
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return p
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if __name__ == "__main__":
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neuralNetwork(400, 25, 10)

‎NeuralNetwok/data_digits.mat‎

7.16 MB
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