Python利用三层神经网络实现手写数字分类详解

前言

本文做的是基于三层神经网络实现手写数字分类，神经网络设计是设计复杂深度学习算法应用的基础，本文将介绍如何设计一个三层神经网络模型来实现手写数字分类。首先介绍如何利用高级编程语言Python搭建神经网络训练和推断框架来实现手写数字分类的训练和使用。

本文实验文档下载

一、神经网络组成

一个完整的神经网络通常由多个基本的网络层堆叠而成。本实验中的三层全连接神经网络由三个全连接层构成，在每两个全连接层之间会插入ReLU激活函数引入非线性变换，最后使用Softmax层计算交叉嫡损失，如下图所示。因此本实验中使用的基本单元包括全连接层、ReLU激活函数、Softmax损失函数。

二、代码实现

1.引入库

import numpy as np
import struct
import os

2.导入数据集

MNIST_DIR = "mnist_data"
TRAIN_DATA = "train-images-idx3-ubyte"
TRAIN_LABEL = "train-labels-idx1-ubyte"
TEST_DATA = "t10k-images-idx3-ubyte"
TEST_LABEL = "t10k-labels-idx1-ubyte"

数据集链接

数据集下载后一定记得解压

3.全连接层

class FullyConnectedLayer(object):
   def __init__(self, num_input, num_output):  # 全连接层初始化
       self.num_input = num_input
       self.num_output = num_output
   def init_param(self, std=0.01):  # 参数初始化
       self.weight = np.random.normal(loc=0, scale=std, size=(self.num_input, self.num_output))
       self.bias = np.zeros([1, self.num_output])
   def forward(self, input):  # 前向传播计算
       self.input = input
       self.output = np.dot(self.input,self.weight)+self.bias
       return self.output
   def backward(self, top_diff):  # 反向传播的计算
       self.d_weight =np.dot(self.input.T,top_diff)
       self.d_bias = top_diff #
       bottom_diff = np.dot(top_diff,self.weight.T)
       return bottom_diff
   def update_param(self, lr):  # 参数更新
       self.weight = self.weight - lr * self.d_weight  
       self.bias = self.bias - lr * self.d_bias    
   def load_param(self, weight, bias):  # 参数加载
       assert self.weight.shape == weight.shape
       assert self.bias.shape == bias.shape
       self.weight = weight
       self.bias = bias
   def save_param(self):  # 参数保存
       return self.weight, self.bias

4.ReLU激活函数层

class ReLULayer(object):
   def forward(self, input):  # 前向传播的计算
       self.input = input
       output = np.maximum(self.input,0)  
       return output
   def backward(self, top_diff):  # 反向传播的计算
       b = self.input
       b[b>0] =1
       b[b<0] = 0
       bottom_diff = np.multiply(b,top_diff)
       return bottom_diff

5.Softmax损失层

class SoftmaxLossLayer(object):
   def forward(self, input):  # 前向传播的计算
       input_max = np.max(input, axis=1, keepdims=True)
       input_exp = np.exp(input- input_max)#(64,10)
       partsum = np.sum(input_exp,axis=1)
       sum = np.tile(partsum,(10,1))
       self.prob = input_exp / sum.T
       return self.prob
   def get_loss(self, label):   # 计算损失
       self.batch_size = self.prob.shape[0]
       self.label_onehot = np.zeros_like(self.prob)
       self.label_onehot[np.arange(self.batch_size), label] = 1.0
       loss = -np.sum(self.label_onehot*np.log(self.prob)) / self.batch_size
       return loss
   def backward(self):  # 反向传播的计算
       bottom_diff = (self.prob - self.label_onehot)/self.batch_size
       return bottom_diff

6.网络训练与推断模块

class MNIST_MLP(object):
   def __init__(self, batch_size=64, input_size=784, hidden1=32, hidden2=16, out_classes=10, lr=0.01, max_epoch=1,print_iter=100):
       self.batch_size = batch_size
       self.input_size = input_size
       self.hidden1 = hidden1
       self.hidden2 = hidden2
       self.out_classes = out_classes
       self.lr = lr
       self.max_epoch = max_epoch
       self.print_iter = print_iter

def shuffle_data(self):
       np.random.shuffle(self.train_data)

def build_model(self):  # 建立网络结构
       self.fc1 = FullyConnectedLayer(self.input_size, self.hidden1)
       self.relu1 = ReLULayer()
       self.fc2 = FullyConnectedLayer(self.hidden1, self.hidden2)  
       self.relu2 = ReLULayer()  
       self.fc3 = FullyConnectedLayer(self.hidden2, self.out_classes)
       self.softmax = SoftmaxLossLayer()
       self.update_layer_list = [self.fc1, self.fc2, self.fc3]

def init_model(self):
       for layer in self.update_layer_list:
           layer.init_param()

def forward(self, input):  # 神经网络的前向传播
       h1 = self.fc1.forward(input)
       h1 = self.relu1.forward(h1)
       h2 = self.fc2.forward(h1)  
       h2 = self.relu2.forward(h2)  
       h3 = self.fc3.forward(h2)  
       self.prob = self.softmax.forward(h3)
       return self.prob

def backward(self):  # 神经网络的反向传播
       dloss = self.softmax.backward()
       dh2 = self.fc3.backward(dloss)  
       dh2 = self.relu2.backward(dh2)  
       dh1 = self.fc2.backward(dh2)
       dh1 = self.relu1.backward(dh1)  
       dh1 = self.fc1.backward(dh1)

def update(self, lr):
       for layer in self.update_layer_list:
           layer.update_param(lr)

def load_mnist(self, file_dir, is_images='True'):
       bin_file = open(file_dir, 'rb')
       bin_data = bin_file.read()
       bin_file.close()
       if is_images:
           fmt_header = '>iiii'
           magic, num_images, num_rows, num_cols = struct.unpack_from(fmt_header, bin_data, 0)
       else:
           fmt_header = '>ii'
           magic, num_images = struct.unpack_from(fmt_header, bin_data, 0)
           num_rows, num_cols = 1, 1
       data_size = num_images * num_rows * num_cols
       mat_data = struct.unpack_from('>' + str(data_size) + 'B', bin_data, struct.calcsize(fmt_header))
       mat_data = np.reshape(mat_data, [num_images, num_rows * num_cols])
       return mat_data

def load_data(self):
       train_images = self.load_mnist(os.path.join(MNIST_DIR, TRAIN_DATA), True)
       train_labels = self.load_mnist(os.path.join(MNIST_DIR, TRAIN_LABEL), False)
       test_images = self.load_mnist(os.path.join(MNIST_DIR, TEST_DATA), True)
       test_labels = self.load_mnist(os.path.join(MNIST_DIR, TEST_LABEL), False)
       self.train_data = np.append(train_images, train_labels, axis=1)
       self.test_data = np.append(test_images, test_labels, axis=1)

def load_model(self, param_dir):
       params = np.load(param_dir).item()
       self.fc1.load_param(params['w1'], params['b1'])
       self.fc2.load_param(params['w2'], params['b2'])
       self.fc3.load_param(params['w3'], params['b3'])

def save_model(self, param_dir):
       params = {}
       params['w1'], params['b1'] = self.fc1.save_param()
       params['w2'], params['b2'] = self.fc2.save_param()
       params['w3'], params['b3'] = self.fc3.save_param()
       np.save(param_dir, params)

def train(self):
       max_batch_1 = self.train_data.shape[0] / self.batch_size
       max_batch = int(max_batch_1)
       for idx_epoch in range(self.max_epoch):
           mlp.shuffle_data()
           for idx_batch in range(max_batch):
               batch_images = self.train_data[idx_batch * self.batch_size:(idx_batch + 1) * self.batch_size, :-1]
               batch_labels = self.train_data[idx_batch * self.batch_size:(idx_batch + 1) * self.batch_size, -1]
               prob = self.forward(batch_images)
               loss = self.softmax.get_loss(batch_labels)
               self.backward()
               self.update(self.lr)
               if idx_batch ％ self.print_iter == 0:
                   print('Epoch ％d, iter ％d, loss: ％.6f' ％ (idx_epoch, idx_batch, loss))

def evaluate(self):
       pred_results = np.zeros([self.test_data.shape[0]])
       for idx in range(int(self.test_data.shape[0] / self.batch_size)):
           batch_images = self.test_data[idx * self.batch_size:(idx + 1) * self.batch_size, :-1]
           prob = self.forward(batch_images)
           pred_labels = np.argmax(prob, axis=1)
           pred_results[idx * self.batch_size:(idx + 1) * self.batch_size] = pred_labels
       accuracy = np.mean(pred_results == self.test_data[:, -1])
       print('Accuracy in test set: ％f' ％ accuracy)

7.完整流程

if __name__ == '__main__':
   h1, h2, e = 128, 64, 20
   mlp = MNIST_MLP(hidden1=h1, hidden2=h2,max_epoch=e)
   mlp.load_data()
   mlp.build_model()
   mlp.init_model()
   mlp.train()
   mlp.save_model('mlp-％d-％d-％depoch.npy' ％ (h1,h2,e))
   mlp.load_model('mlp-％d-％d-％depoch.npy' ％ (h1, h2, e))
   mlp.evaluate()

三、代码debug

pycharm在初次运行时，会在以下代码报错：

mlp.load_model('mlp-％d-％d-％depoch.npy' ％ (h1, h2, e))

ValueError: Object arrays cannot be loaded when allow_pickle=False

经过上网查看原因后，发现是numpy版本太高引起

解决方法：

点击报错处，进入源代码（.py），注释掉693行：

#if not allow_pickle:
   #raise ValueError("Object arrays cannot be loaded when "
                  #  "allow_pickle=False")

# Now read the actual data.
   if dtype.hasobject:
       # The array contained Python objects. We need to unpickle the data.
       #if not allow_pickle:
           #raise ValueError("Object arrays cannot be loaded when "
                          #  "allow_pickle=False")
       if pickle_kwargs is None:
           pickle_kwargs = {}
       try:
           array = pickle.load(fp, **pickle_kwargs)
       except UnicodeError as err:
           if sys.version_info[0] >= 3:
               # Friendlier error message

四、结果展示

在不改变网络结构的条件下我通过自行调节参数主要体现在：

if __name__ == '__main__':
   h1, h2, e = 128, 64, 20

class MNIST_MLP(object):
   def __init__(self, batch_size=64, input_size=784, hidden1=32, hidden2=16, out_classes=10, lr=0.01, max_epoch=1,print_iter=100):

为了提高准确率，当然你可以从其他方面进行修改，以下是我得出的输出结果：

补充

ValueError: Object arrays cannot be loaded when allow_pickle=False解决方案

在读.npz文件时报下面错误：

population_data=np.load("./data/populations.npz")
print(population_data.files)#里面有两个数组   data  feature_names
data=population_data['data']
print(data)
print(population_data['feature_names'])

报错：

['data', 'feature_names']
Traceback (most recent call last):
 File "E:/pycharm file/使用scikit-learn构建模型/构建一元线性模型.py", line 32, in <module>
   data=population_data['data']
 File "E:\pycharm file\venv\lib\site-packages\numpy\lib\npyio.py", line 262, in __getitem__
   pickle_kwargs=self.pickle_kwargs)
 File "E:\pycharm file\venv\lib\site-packages\numpy\lib\format.py", line 692, in read_array
   raise ValueError("Object arrays cannot be loaded when "
ValueError: Object arrays cannot be loaded when allow_pickle=False

报错为：numpy版本太高，我用的是1.16.3，应该降级为1.16.2

两种解决方案：

Numpy 1.16.3几天前发布了。从发行版本中说明：“函数np.load（）和np.lib.format.read_array（）采用allow_pickle关键字，现在默认为False以响应CVE-2019-6446 < nvd.nist.gov/vuln/detail / CVE-2019-6446 >“。降级到1.16.2对我有帮助，因为错误发生在一些library内部

第一种：点击报错处，进入源代码（.py），注释掉693行：

#if not allow_pickle:
   #raise ValueError("Object arrays cannot be loaded when "
                  #  "allow_pickle=False")

# Now read the actual data.
   if dtype.hasobject:
       # The array contained Python objects. We need to unpickle the data.
       #if not allow_pickle:
           #raise ValueError("Object arrays cannot be loaded when "
                          #  "allow_pickle=False")
       if pickle_kwargs is None:
           pickle_kwargs = {}
       try:
           array = pickle.load(fp, **pickle_kwargs)
       except UnicodeError as err:
           if sys.version_info[0] >= 3:
               # Friendlier error message

修改后成功解决了问题，但改掉源码不知道会不会有后遗症

第二种：降级numpy版本

pip install numpy==1.16.2

上述两种方法都可以成功解决报错问题

来源：https://blog.csdn.net/qq_50492541/article/details/121459607