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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
h2 = self.fc1.forward(input)
h2 = self.relu1.forward(h2)
h3 = self.fc2.forward(h2)
h3 = self.relu2.forward(h3)
h4 = self.fc3.forward(h3)
self.prob = self.softmax.forward(h4)
return self.prob
def backward(self): # 神经网络的反向传播
dloss = self.softmax.backward()
dh3 = self.fc3.backward(dloss)
dh3 = self.relu2.backward(dh3)
dh2 = self.fc2.backward(dh3)
dh2 = self.relu1.backward(dh2)
dh2 = self.fc1.backward(dh2)
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__':
h2, h3, e = 128, 64, 20
mlp = MNIST_MLP(hidden1=h2, hidden2=h3,max_epoch=e)
mlp.load_data()
mlp.build_model()
mlp.init_model()
mlp.train()
mlp.save_model('mlp-%d-%d-%depoch.npy' % (h2,h3,e))
mlp.load_model('mlp-%d-%d-%depoch.npy' % (h2, h3, 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' % (h2, h3, 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__': h2, h3, 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
感谢各位的阅读，以上就是“Python如何利用三层神经网络实现手写数字分类”的内容了，经过本文的学习后，相信大家对Python如何利用三层神经网络实现手写数字分类这一问题有了更深刻的体会，具体使用情况还需要大家实践验证。这里是亿速云，小编将为大家推送更多相关知识点的文章，欢迎关注！
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