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。
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
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原文链接：https://blog.csdn.net/qq_50492541/article/details/121459607
