import math import random import string import os from Pillow import Image import numpy as np
random.seed(0)
def rand(a, b): return (b - a) * random.random() + a
def makeMatrix(I, J, fill=0.0): m = [] for i in range(I): m.append([fill] * J) return m
def sigmoid(x): return math.tanh(x)
def dsigmoid(y): return 1.0 - y ** 2
class NN: ''' 三层反向传播神经网络 '''
def __init__(self, ni, nh, no):
# 输入层、隐藏层、输出层的节点（数）
self.ni = ni + 1 # 增加一个偏差节点
self.nh = nh
self.no = no
# 激活神经网络的所有节点（向量）
self.ai = [1.0] * self.ni
self.ah = [1.0] * self.nh
self.ao = [1.0] * self.no
# 建立权重（矩阵）
self.wi = makeMatrix(self.ni, self.nh)
self.wo = makeMatrix(self.nh, self.no)
# 设为随机值
for i in range(self.ni):
for j in range(self.nh):
self.wi[i][j] = rand(-0.2, 0.2)
for j in range(self.nh):
for k in range(self.no):
self.wo[j][k] = rand(-2.0, 2.0)
# 最后建立动量因子（矩阵）
self.ci = makeMatrix(self.ni, self.nh)
self.co = makeMatrix(self.nh, self.no)
def update(self, inputs):
if len(inputs) != self.ni - 1:
raise ValueError('与输入层节点数不符！')
# 激活输入层
for i in range(self.ni - 1):
# self.ai[i] = sigmoid(inputs[i])
self.ai[i] = inputs[i]
# 激活隐藏层
for j in range(self.nh):
sum1 = 0.0
for i in range(self.ni):
sum1 = sum1 + self.ai[i] * self.wi[i][j]
self.ah[j] = sigmoid(sum1)
# 激活输出层
for k in range(self.no):
sum2 = 0.0
for j in range(self.nh):
sum2 = sum2 + self.ah[j] * self.wo[j][k]
self.ao[k] = sigmoid(sum2)
return self.ao[:]
def backPropagate(self, targets, N, M):
''' 反向传播 '''
if len(targets) != self.no:
raise ValueError('与输出层节点数不符！')
# 计算输出层的误差
output_deltas = [0.0] * self.no
for k in range(self.no):
error = targets[k] - self.ao[k]
output_deltas[k] = dsigmoid(self.ao[k]) * error
# 计算隐藏层的误差
hidden_deltas = [0.0] * self.nh
for j in range(self.nh):
error = 0.0
for k in range(self.no):
error = error + output_deltas[k] * self.wo[j][k]
hidden_deltas[j] = dsigmoid(self.ah[j]) * error
# 更新输出层权重
for j in range(self.nh):
for k in range(self.no):
change = output_deltas[k] * self.ah[j]
self.wo[j][k] = self.wo[j][k] + N * change + M * self.co[j][k]
self.co[j][k] = change
# print(N*change, M*self.co[j][k])
# 更新输入层权重
for i in range(self.ni):
for j in range(self.nh):
change = hidden_deltas[j] * self.ai[i]
self.wi[i][j] = self.wi[i][j] + N * change + M * self.ci[i][j]
self.ci[i][j] = change
# 计算误差
error = 0.0
for k in range(len(targets)):
error = error + 0.5 * (targets[k] - self.ao[k]) ** 2
return error
def test(self, patterns):
for p in patterns:
print(p[0], '->', self.update(p[0]))
def weights(self):
print('输入层权重:')
for i in range(self.ni):
print(self.wi[i])
print()
print('输出层权重:')
for j in range(self.nh):
print(self.wo[j])
def train(self, patterns, iterations=1000, N=0.5, M=0.1):
# N: 学习速率(learning rate)
# M: 动量因子(momentum factor)
for i in range(iterations):
error = 0.0
for p in patterns:
inputs = p[0]
targets = p[1]
self.update(inputs)
error = error + self.backPropagate(targets, N, M)
if i % 100 == 0:
print('误差 %-.5f' % error)
def demo(): # 一个演示：教神经网络学习逻辑异或（XOR）------------可以换成你自己的数据试试 pat = [ [[0, 0], [0]], [[0, 1], [1]], [[1, 0], [1]], [[1, 1], [0]] ]
# 创建一个神经网络：输入层有两个节点、隐藏层有两个节点、输出层有一个节点
n = NN(2, 2, 1)
# 用一些模式训练它
n.train(pat)
# 测试训练的成果（不要吃惊哦）
n.test(pat)
# 看看训练好的权重（当然可以考虑把训练好的权重持久化）
# n.weights()
if name == 'main': demo()
def load_data(): # Return a new array of given shape and type, without initializing entries. data = np.empty((42000, 1, 28, 28), dtype='float32') label = np.empty((42000,), dtype='uint8') # o s.listdir(filename)返回filename中所有文件的文件名列表 imgs = os.listdir('mnist') num = len(imgs) for i in range(num): # PIL 的 open() 函数用于创建 PIL 图像对象 img = Image.open('mnist/'+imgs[i]) # Convert the input to an array arr = np.asarray(img, dtype='float32') data[i, :, :, :] = arr label[i] = int(imgs[i].split('.')[0]) return data, label