深度学习入门（10）：卷积神经网络（CNN）

卷积层和池化层的实现

四维数组

from collections import OrderedDict

import numpy as np
from torch import nn

x = np.random.rand(10,1,27,28)#随机生成数据
# x.shape
x[0,0]

基于im2col（image to column）的展开

def im2col(input_data, filter_h, filter_w, stride=1, pad=0):
    """

    Parameters
    ----------
    input_data : 由(数据量, 通道, 高, 长)的4维数组构成的输入数据
    filter_h : 滤波器的高
    filter_w : 滤波器的长
    stride : 步幅
    pad : 填充

    Returns
    -------
    col : 2维数组
    """
    N, C, H, W = input_data.shape
    out_h = (H + 2*pad - filter_h)//stride + 1
    out_w = (W + 2*pad - filter_w)//stride + 1

    img = np.pad(input_data, [(0,0), (0,0), (pad, pad), (pad, pad)], 'constant')
    col = np.zeros((N, C, filter_h, filter_w, out_h, out_w))

    for y in range(filter_h):
        y_max = y + stride*out_h
        for x in range(filter_w):
            x_max = x + stride*out_w
            col[:, :, y, x, :, :] = img[:, :, y:y_max:stride, x:x_max:stride]

    col = col.transpose(0, 4, 5, 1, 2, 3).reshape(N*out_h*out_w, -1)
    return col

x1 = np.random.rand(1,3,7,7)
col1 = im2col(x1, 5, 5, stride=1, pad=0)
print(col1.shape)
x2 = np.random.rand(10,3,7,7)
col2 = im2col(x2, 5, 5, stride=1, pad=0)
print(col2.shape)

卷积层

class Convolution:
    def __init__(self,W,b,stride=1,pad=0):
        self.W = W
        self.b = b
        self.stride = stride
        self.pad = pad

    def forward(self,x):
        FN,C,FH,FW = x.shape
        N,C,H,W = x.shape
        out_h = (H + 2*self.pad - FH)//self.stride + 1
        out_w = (W + 2*self.pad - FW)//self.stride + 1

        col = im2col(x,FH,FW,stride=self.stride,pad=self.pad)
        col_W = self.W.reshape(FN,-1).T
        out = np.dot(col,col_W) + self.b

        out = out.reshape(N,out_h,out_w,-1).transpose(0,3,1,2)

        return out

池化层

class Pooling:
    def __init__(self,pool_h,pool_w,stride=1,pad=0):
        self.pool_h = pool_h
        self.pool_w = pool_w
        self.stride = stride
        self.pad = pad

    def forward(self,x):
        N,C,H,W = x.shape
        out_h = (H + 2*self.pad - self.pool_h)//self.stride + 1
        out_w = (W + 2*self.pad - self.pool_w)//self.stride + 1

        #展开（1）
        col = im2col(x,self.pool_h,self.pool_w,stride=self.stride,pad=self.pad)
        col = col.reshape(-1,self.pool_h*self.pool_w)

        #最大值（2）
        out = np.max(col,axis=1)
        #转换（3）
        out = out.reshape(N,out_h,out_w,C).transpose(0,3,1,2)

        return out

CNN的实现

class Affine:
    def __init__(self,W,b):
        self.W = W
        self.b = b
        self.x = None
        self.dW = None
        self.db = None

    def forward(self,x):
        self.x = x
        out = np.dot(x,self.W) + self.b

        return out

    def backward(self,dout):
        dx = np.dot(dout,self.W.T)
        self.dW = np.dot(self.x.T,dout)
        self.db = np.sum(dout,axis=0)

        return dx

class SoftmaxWithLoss:
    def __init__(self):
        self.loss = None #损失
        self.y = None #softmax的输出
        self.t = None #监督数据

    def forward(self,x,t):
        self.t = t
        self.y = softmax(x)
        self.loss = cross_entropy_error(self.y,self.t)

        return self.loss

    def backward(self,dout=1):
        batch_size = self.t.shape[0]
        dx = (self.y - self.t) / batch_size

        return dx

class SimpleConvNet:
    def __init__(self, input_dim=(1, 28, 28),
    conv_param={'filter_num':30, 'filter_size':5,
    'pad':0, 'stride':1},
    hidden_size=100, output_size=10, weight_init_std=0.01):
     filter_num = conv_param['filter_num']
     filter_size = conv_param['filter_size']
     filter_pad = conv_param['pad']
     filter_stride = conv_param['stride']
     input_size = input_dim[1]
     conv_output_size = (input_size - filter_size + 2*filter_pad) / \
     filter_stride + 1
     pool_output_size = int(filter_num * (conv_output_size/2)*(conv_output_size/2))
     #参数的初始化
     self.params={}
     self.params['w1'] = weight_init_std * \
                         np.random.randn(filter_num, filter_size, filter_size, filter_num)
     self.params['b1']=np.zeros(filter_num)
     self.params['w2']=weight_init_std*\
         np.random.randn(pool_output_size, hidden_size)
     self.params['b2']=np.zeros(hidden_size)
     self.params['w3']=weight_init_std* np.random.randn(output_size, hidden_size)
     self.params['b3']=np.zeros(hidden_size)

     #生成必要的层
     self.layers = OrderedDict()
     self.layers['conv1'] = Convolution(self.params['w1'],self.params['b1'],stride=conv_param['stride'],pad=conv_param['pad'])
     self.layers['Relu1']=nn.ReLU()
     self.layers['Pool1']=Pooling(pool_h=2,pool_w=2,stride=2)
     self.layers['Affine']=Affine(self.params['w2'],self.params['b2'])
     self.layers['Relu2']=nn.ReLU()
     self.layers['Affine2']=Affine(self.params['w3'],self.params['b3'])
     self.last_layer = SoftmaxWithLoss()

     def predict(self,x):
         for layer in self.layers.values():
             x = layer.forward(x)
         return x

     def loss(self,x,t):
        y = self.predict(x)
        return self.lastLayer.forward(y,t)

     def gradient(self, x, t):
         # forward
         self.loss(x, t)

         # backward
         dout = 1
         dout = self.lastLayer.backward(dout)
         layers = list(self.layers.values())
         layers.reverse()
         for layer in layers:
             dout = layer.backward(dout)

         # 设定
         grads = {}
         grads['W1'] = self.layers['Conv1'].dW
         grads['b1'] = self.layers['Conv1'].db
         grads['W2'] = self.layers['Affine1'].dW
         grads['b2'] = self.layers['Affine1'].db
         grads['W3'] = self.layers['Affine2'].dW
         grads['b3'] = self.layers['Affine2'].db

         return grads

参考资料

《深度学习入门：基于python的理论与实践》