用python创建的神经网络--mnist手写数字识别率达到98%

遵循Tariq Rashid的指导，使用纯Python编写了一个三层神经网络，对MNIST手写数字识别进行训练。经过参数调优，该模型在测试集上的识别率达到了98%。调优过程包括特定的输入输出范围优化，不改变S曲线激活函数。最后，通过添加旋转图像训练，准确率提升至97.9%。

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周末根据Tariq Rashid大神的指导，没有使用tensorflow等框架，用python编写了一个三层神经网络，并应用再mnist手写库识别上，经过多方面参数调优，识别率竟然达到了98%。调优比较难，经验感觉特别宝贵，为避免时间长了忘记，记录整理如下。

具体过程记录

一、加载所需要的库

# Code for a 3-layer neural network, and code for learning the MNIST dataset
# Zhouxw@ebscn.com,2018.8  Studying to write neural network by python
# license is GPLv2

import numpy
# scipy.special for the sigmoid function expit()
import scipy.special
import matplotlib.pyplot
# ensure the plots are inside this jupyter notebook, not an external window
%matplotlib inline

# helper to load data from PNG image files
import imageio
# glob helps select multiple files using patterns
import glob

二、定义神经网络类

# neural network class definition （3 layers）
class neuralNetwork:
    # initialise the neural network
    def __init__(self,inputnodes,hiddennodes,outputnodes,learningrate):
        # set number of nodes in each input,hidden,output layer
        self.inodes = inputnodes
        self.hnodes = hiddennodes
        self.onodes = outputnodes
        # learning rate
        self.lr = learningrate
        
        # link weight matrices ,wih and who
        # weithg inside the arrays are w_i_j, where link is from node i to node j in the next layer
        # w11 w21
        # w12 w22 etc
        self.wih = (numpy.random.normal(0.0, pow(self.hnodes,-0.5), (self.hnodes,self.inodes) )  )
        self.who = (numpy.random.normal(0.0, pow(self.onodes,-0.5), (self.onodes,self.hnodes) )  )
        
        # activation function is the sigmoid function
        self.activation_function = lambda x: scipy.special.expit(x)

        pass
    
    # train the neural network
    def train(self,inputs_list,targets_list):
        # convert inputs list to 2d array        
        inputs = numpy.array(inputs_list,ndmin=2).T
        targets = numpy.array(targets_list,ndmin=2).T
        
        # calculate signals into hidden