神经网络-手写字体识别

3层神经网络，自定义输入节点、隐藏层、输出节点的个数，使用sigmoid函数作为激活函数，梯度下降法进行权重的优化。

使用MNIST数据集，进行手写数字识别

#!/usr/bin/env python
# -*- coding:utf-8 -*-

#!/usr/bin/env python
# -*- coding:utf-8 -*-

import numpy
import scipy.special


#手写数字识别神经网络
class NeuralNetwork():
    def __init__(self,inputnodes,hiddennodes,outputnodes,learningrate):
        '''
        神经网络初始化
        :param inputnodes: 输入节点的数量
        :param hiddennodes: 隐藏层节点的数量
        :param outputnodes: 输出节点的数量
        :param learningrate: 学习率
        :return:
        '''
        self.inodes = inputnodes
        self.hnodes = hiddennodes
        self.onodes = outputnodes
        self.learn = learningrate
        self.wih = numpy.random.rand(self.hnodes,self.inodes) - 0.5
        self.who = numpy.random.rand(self.onodes,self.hnodes) - 0.5
        # self.wih = numpy.random.normal(0.0,pow(self.hnodes,-0.5),(self.inodes,self.inodes))
        # self.who = numpy.random.normal(0.0,pow(self.onodes,-0.5),(self.hnodes,self.hnodes))
        self.activate_function = lambda x : scipy.special.expit(x)
        # print(self.who)
        # print(self.wih)
    def train(self,input_list,target_list):
        '''
        训练神经网络首先计算样本输出，然后在与目标值进行对比，更新权重
        :param input_list: 输入值
        :param target_list: 目标值
        :return:
        '''
        #针对样本计算输出，与query函数一样
        inputs = numpy.array(input_list).T
        targets = numpy.array(target_list).T
        hidden_inputs = numpy.dot(self.wih,inputs)
        hidden_outputs = self.activate_function(hidden_inputs)
        final_inputs = numpy.dot(self.who,hidden_outputs)
        final_outpust = self.activate_function(final_inputs)

        #将计算得到的输出与目标值对比，更新权重
        output_error = targets - final_outpust
        hidden_error = numpy.dot(self.who.T,output_error)

        # print(output_error.shape)
        # print(final_outpust.shape)
        # print(hidden_outputs.T.shape)
        # self.who += self.learn*numpy.dot((output_error*final_outpust*(1.0-final_outpust)),numpy.transpose(hidden_outputs))
        # self.wih += self.learn*numpy.dot((hidden_error*hidden_outputs*(1.0-hidden_outputs)),numpy.transpose(inputs))

        self.who += self.learn*numpy.dot((output_error*final_outpust*(1.0-final_outpust)).reshape((self.onodes,1)),hidden_outputs.reshape((1,self.hnodes)))
        self.wih += self.learn*numpy.dot((hidden_error*hidden_outputs*(1.0-hidden_outputs)).reshape((self.hnodes,1)),inputs.reshape((1,self.inodes)))



    def query(self,input_list):
        '''
        计算输出
        :param input_list:
        :return:
        '''
        inputs = numpy.array(input_list).T
        hidden_inputs = numpy.dot(self.wih,inputs)
        hidden_outputs = self.activate_function(hidden_inputs)
        final_inputs = numpy.dot(self.who,hidden_outputs)
        final_outpust = self.activate_function(final_inputs)

        return final_outpust

#初始化一个神经网络对象
n = NeuralNetwork(784,100,10,0.5)

#训练数据
with open('dataset/mnist_train.csv','r') as f:
    train_data = f.readlines()

#训练神经网络
for line in train_data:
    data = line.split(',')
    inputs = (numpy.asfarray(data[1:]) / 255 * 0.99) + 0.01
    targets = numpy.zeros(n.onodes)+0.01
    targets[int(data[0])] = 0.99

    n.train(inputs,targets)


#测试神经网络
with open('dataset/mnist_test_10.csv','r') as f:
    test_data = f.readlines()

for line in test_data:
    label = int(line[0])
    data = line.split(',')
    input_list = numpy.asfarray(data[1:])
    output = n.query(input_list)

    print(label)
    print(output)

代码实现了手写数字的识别，可以在此基础上，进行改进研究，比如调节学习率、初始化权重的方式，激活函数等变化时对结果的影响。