基于BP神经网络的手写数字识别
基于BP神经网络的手写数字识别运行结果视频：https://pan.baidu.com/s/1x2wGGBZ8iBIEYU2IZRv0OQ
"""
Created on Sun May 20 21:38:45 2018
@author: ysw
"""
#-*- coding: utf-8 -*-
#from PIL import Image
import numpy as np
from scipy import io as spio
from scipy import optimize
from matplotlib import pyplot as plt
#from sklearn import datasets
#from sklearn.preprocessing import StandardScaler
import time
# BP
def BPneuralNetwork(X, y, input_layer_size,hidden_layer_size,out_put_layer):
m,n = X.shape
## 随机显示几行数据
rand_indices = ]# 生成100个0-m的随机数
display_data(X) # 显示100个数字
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
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)
'''可视化 Theta1'''
length = result.shape
Theta1 = result.reshape(hidden_layer_size,input_layer_size+1)
Theta2 = result.reshape(out_put_layer,hidden_layer_size+1)
return Theta1, Theta2
# 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 = imgData.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(np.transpose(display_array),cmap='gray') #显示灰度图像
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 # theta的中长度
# 还原theta1和theta2
Theta1 = nn_params.reshape(hidden_layer_size,input_layer_size+1)
Theta2 = nn_params.reshape(num_labels,hidden_layer_size+1)
m = X.shape
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
Theta1_x = Theta1[:,1:Theta1_colCount]
Theta2_colCount = Theta2.shape
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
Theta1 = nn_params.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.reshape(num_labels,hidden_layer_size+1).copy()
m = X.shape
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
Theta1_x = Theta1[:,1:Theta1_colCount]
Theta2_colCount = Theta2.shape
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 = (h-class_y)*sigmoidGradient(z3)# 均方误差的误差率
delta3 = h-class_y # 交叉熵误差率
Theta2_grad = Theta2_grad+np.dot(np.transpose(delta3.reshape(1,-1)),a2.reshape(1,-1))
delta2 = np.dot(delta3.reshape(1,-1),Theta2_x)*sigmoidGradient(z2)
Theta1_grad = Theta1_grad+np.dot(np.transpose(delta2.reshape(1,-1)),a1.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theta
def randInitializeWeights(L_in,L_out):
W = np.zeros((L_out,1+L_in)) # 对应theta的权重
epsilon_init = (6.0/(L_out+L_in))**0.5
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
return W
# 预测
def predict(Theta1, Theta2, X):
m = X.shape
num_labels = Theta2.shape
#p = np.zeros((m,1))
'''正向传播，预测结果'''
X = np.hstack((np.ones((m,1)),X))
h1 = sigmoid(np.dot(X,np.transpose(Theta1)))
h1 = np.hstack((np.ones((m,1)),h1))
h2 = sigmoid(np.dot(h1,np.transpose(Theta2)))
'''
返回h中每一行最大值所在的列号
- 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）
- 最后where找到的最大概率所在的列号（列号即是对应的数字）
'''
#np.savetxt("h2.csv",h2,delimiter=',')
p = np.array(np.where(h2 == np.max(h2, axis=1)))
for i in np.arange(1, m):
t = np.array(np.where(h2 == np.max(h2, axis=1)))
p = np.vstack((p,t))
return p
# 加载mat文件
def loadmat_data(fileName):
return spio.loadmat(fileName)
if __name__ == "__main__":
# 加载数据
data_img = loadmat_data("data_digits.mat")
X = data_img['X']
y = data_img['y']
input_layer_size = 400;
hidden_layer_size = 25;
out_put_layer = 10;
start = time.time()
Theta1, Theta2 = BPneuralNetwork(X, y, input_layer_size, hidden_layer_size, out_put_layer)
print ('\n')
print ('\n')
print ( '执行时间：' )
print ( time.time()-start )
'''预测'''
p = predict(Theta1,Theta2,X)
print ('预测准确度为：')
print ( np.mean(np.float64(p == y.reshape(-1,1))*100) )
res = np.hstack((p,y.reshape(-1,1)))
np.savetxt("predict.csv", res, delimiter=',')
百度网盘链接：链接：https://pan.baidu.com/s/1wyldRyUqMasP2uGfQ402Eg 密码：uidi
页:
[1]