import numpy as np
import pandas as pd
import matplotlib
matplotlib.use('TkAgg')
import matplotlib.pyplot as plt
import ui
from scipy.io import loadmat
print('再次处理手写数字数据集，这次使用反向传播的前馈神经网络')
print('用的数据和 4_multi_classification.py 是一样的')
print("经典的 MNIST 手写数字识别")
ui.split_line1()
print("载入数据")
data = loadmat('data/ex3data1.mat')
print("预览载入的数据")
print(data)
print("数据的 X 和 y 的尺寸")
X = data['X']
y = data['y']
print(X.shape, y.shape)
print("对 y 标签做 one-hot 编码")
from sklearn.preprocessing import OneHotEncoder
encoder = OneHotEncoder(sparse=False)
y_onehot = encoder.fit_transform(y)
print('编码后 y 的尺寸')
print(y_onehot.shape)
print('对比原来的 y 和编码后的 y_onehot')
print(y[0], y_onehot[0, :])
print("定义 sigmoid 函数，前向传播函数和 cost 函数")
def sigmoid(z):
return 1 / (1 + np.exp(-z))
def forward_propagate(X, theta1, theta2):
m = X.shape[0]
a1 = np.insert(X, 0, values=np.ones(m), axis=1)
z2 = a1 * theta1.T
a2 = np.insert(sigmoid(z2), 0, values=np.ones(m), axis=1)
z3 = a2 * theta2.T
h = sigmoid(z3)
return a1, z2, a2, z3, h
def cost0(params, input_size, hidden_size, num_labels, X, y, learning_rate):
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
# reshape the parameter array into parameter matrices for each layer
theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
# run the feed-forward pass
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
# compute the cost
J = 0
for i in range(m):
first_term = np.multiply(-y[i,:], np.log(h[i,:]))
second_term = np.multiply((1 - y[i,:]), np.log(1 - h[i,:]))
J += np.sum(first_term - second_term)
J = J / m
return J
print('初始化设置')
input_size = 400
hidden_size = 25
num_labels = 10
learning_rate = 1
print('随机初始化完整网络参数大小的参数数组')
params = (np.random.random(size=hidden_size * (input_size + 1) + num_labels * (hidden_size + 1)) - 0.5) * 0.25
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
print('将参数数组解开为每个层的参数矩阵，大小为')
theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
print(theta1.shape, theta2.shape)
print('计算前向传播，结果的大小为')
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
print(a1.shape, z2.shape, a2.shape, z3.shape, h.shape)
print('计算 y 和 h 的总误差')
print(cost0(params, input_size, hidden_size, num_labels, X, y_onehot, learning_rate))
print('定义正则化损失函数')
def cost(params, input_size, hidden_size, num_labels, X, y, learning_rate):
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
# reshape the parameter array into parameter matrices for each layer
theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
# run the feed-forward pass
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
# compute the cost
J = 0
for i in range(m):
first_term = np.multiply(-y[i,:], np.log(h[i,:]))
second_term = np.multiply((1 - y[i,:]), np.log(1 - h[i,:]))
J += np.sum(first_term - second_term)
J = J / m
# add the cost regularization term
J += (float(learning_rate) / (2 * m)) * (np.sum(np.power(theta1[:,1:], 2)) + np.sum(np.power(theta2[:,1:], 2)))
return J
print('再计算一次总误差')
print(cost(params, input_size, hidden_size, num_labels, X, y_onehot, learning_rate))
print('定义反向传播相关函数')
def sigmoid_gradient(z):
return np.multiply(sigmoid(z), (1 - sigmoid(z)))
def backprop(params, input_size, hidden_size, num_labels, X, y, learning_rate):
m = X.shape[0]
X = np.matrix(X)
y = np.matrix(y)
# reshape the parameter array into parameter matrices for each layer
theta1 = np.matrix(np.reshape(params[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
theta2 = np.matrix(np.reshape(params[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
# run the feed-forward pass
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
# initializations
J = 0
delta1 = np.zeros(theta1.shape) # (25, 401)
delta2 = np.zeros(theta2.shape) # (10, 26)
# compute the cost
for i in range(m):
first_term = np.multiply(-y[i,:], np.log(h[i,:]))
second_term = np.multiply((1 - y[i,:]), np.log(1 - h[i,:]))
J += np.sum(first_term - second_term)
J = J / m
# add the cost regularization term
J += (float(learning_rate) / (2 * m)) * (np.sum(np.power(theta1[:,1:], 2)) + np.sum(np.power(theta2[:,1:], 2)))
# perform backpropagation
for t in range(m):
a1t = a1[t,:] # (1, 401)
z2t = z2[t,:] # (1, 25)
a2t = a2[t,:] # (1, 26)
ht = h[t,:] # (1, 10)
yt = y[t,:] # (1, 10)
d3t = ht - yt # (1, 10)
z2t = np.insert(z2t, 0, values=np.ones(1)) # (1, 26)
d2t = np.multiply((theta2.T * d3t.T).T, sigmoid_gradient(z2t)) # (1, 26)
delta1 = delta1 + (d2t[:,1:]).T * a1t
delta2 = delta2 + d3t.T * a2t
delta1 = delta1 / m
delta2 = delta2 / m
# add the gradient regularization term
delta1[:,1:] = delta1[:,1:] + (theta1[:,1:] * learning_rate) / m
delta2[:,1:] = delta2[:,1:] + (theta2[:,1:] * learning_rate) / m
# unravel the gradient matrices into a single array
grad = np.concatenate((np.ravel(delta1), np.ravel(delta2)))
return J, grad
print('尝试计算一步反向传播')
J, grad = backprop(params, input_size, hidden_size, num_labels, X, y_onehot, learning_rate)
print(J, grad.shape)
print('进行模型训练')
from scipy.optimize import minimize
# minimize the objective function
fmin = minimize(fun=backprop, x0=params, args=(input_size, hidden_size, num_labels, X, y_onehot, learning_rate),
method='TNC', jac=True, options={'maxiter': 250})
print('结果为', fmin)
print('使用优化后的参数进行预测')
X = np.matrix(X)
theta1 = np.matrix(np.reshape(fmin.x[:hidden_size * (input_size + 1)], (hidden_size, (input_size + 1))))
theta2 = np.matrix(np.reshape(fmin.x[hidden_size * (input_size + 1):], (num_labels, (hidden_size + 1))))
a1, z2, a2, z3, h = forward_propagate(X, theta1, theta2)
y_pred = np.array(np.argmax(h, axis=1) + 1)
print('y 的预测值为')
print(y_pred)
print('评估准确率')
correct = [1 if a == b else 0 for (a, b) in zip(y_pred, y)]
accuracy = (sum(map(int, correct)) / float(len(correct)))
print ('accuracy = {0}%'.format(accuracy * 100))
