【pythonでCNN#7】Pooling層

投稿者 Dken2021年9月30日2021年9月30日

記事の目的

pythonでCNN(畳み込みニューラルネットワーク)を実装する上で必要になるPooling層を実装していきます。ここにある全てのコードは、コピペで再現することが可能です。

目次

max pooling概要
im2col関数とcol2im関数
モPooling実装
Pooling層

1 max pooling概要

2 im2col関数とcol2im関数

# In[1]
import numpy as np
np.random.seed(1)

# In[2]
def im2col(x, fil_size, y_size, stride, pad):
    x_b, x_c, x_h, x_w = x.shape
    fil_h, fil_w = fil_size, fil_size
    y_h, y_w = y_size, y_size
    index = -1
    
    x_pad = np.pad(x, [(0, 0), (0, 0), (pad, pad), (pad, pad)], "constant")
    x_col = np.zeros((fil_h*fil_w, x_b, x_c, y_h, y_w))
    
    for h in range(fil_h):
        h2 = h + y_h*stride
        for w in range(fil_w):
            index += 1
            w2 = w + y_w*stride
            x_col[index,:,:,:,:] = x_pad[:,:,h:h2:stride,w:w2:stride]
    x_col = x_col.transpose(2,0,1,3,4).reshape(x_c*fil_h*fil_w, x_b*y_h*y_w)
    
    return x_col

def col2im(dx_col, x_shape, fil_size, y_size, stride, pad):
    x_b, x_c, x_h, x_w = x_shape
    fil_h, fil_w = fil_size, fil_size
    y_h, y_w = y_size, y_size
    index = -1
    
    dx_col = dx_col.reshape(x_c, fil_h*fil_w, x_b, y_h, y_w).transpose(1,2,0,3,4)
    dx = np.zeros((x_b, x_c, x_h+2*pad+stride-1, x_w+2*pad+stride-1))
    
    for h in range(fil_h):
        h2 = h + y_h*stride
        for w in range(fil_w):
            index += 1
            w2 = w + y_w*stride
            dx[:,:,h:h2:stride,w:w2:stride] += dx_col[index,:,:,:,:]
    
    return dx[:,:,pad:x_h+pad, pad:x_w+pad]

3 Pooling実装

# In[3]
x = np.random.randint(0,10,2*3*4*4).reshape(2,3,4,4)
x

# In[4]
x_col = im2col(x,2,2,2,0).T.reshape(-1,4)
x_col

# In[5]
y = np.max(x_col, axis=1)
y

# In[6]
y = y.reshape(2, 2, 2, 3).transpose(0,3,1,2)
y

# In[7]
max_index = np.argmax(x_col, axis=1)
max_index

# In[8]
dy = np.ones(y.shape).transpose(0,2,3,1)
dy

# In[9]
dx = np.zeros((2*2, dy.size))
dx

# In[10]
dx[max_index.reshape(-1), np.arange(dy.size)] = dy.reshape(-1)
dx

# In[11]
dx = dx.reshape(2, 2, 2, 2, 2, 3).transpose(5,0,1,2,3,4).reshape(3*2*2, 2*2*2)
dx

# In[12]
col2im(dx, x.shape, 2, 2, 2, 0)

4 Pooling層

# in[13]
class Pooling:
    
    def __init__(self, pool):
        self.pool = pool
        
    def forward(self, x):
        self.xshape = x.shape
        self.x_b, self.x_c, self.x_h, self.x_w = x.shape
        self.y_h = self.x_h//self.pool if self.x_h%self.pool==0 else self.x_h//self.pool+1
        self.y_w = self.x_w//self.pool if self.x_w%self.pool==0 else self.x_w//self.pool+1
        
        x_col = im2col(x, self.pool, self.y_h, self.pool, 0).T.reshape(-1,self.pool*self.pool)
        y = np.max(x_col, axis=1)
        self.y = y.reshape(self.x_b, self.y_h, self.y_w, self.x_c).transpose(0,3,1,2)
        self.max_index = np.argmax(x_col, axis=1)
        return self.y
    
    def backward(self, dy):
        dy = dy.transpose(0,2,3,1)
        dx = np.zeros((self.pool*self.pool, dy.size))
        dx[self.max_index.reshape(-1), np.arange(dy.size)] = dy.reshape(-1)
        dx = dx.reshape(self.pool, self.pool, self.x_b, self.y_h, self.y_w, self.x_c)
        dx = dx.transpose(5,0,1,2,3,4)
        dx = dx.reshape(self.x_c*self.pool*self.pool, self.x_b*self.y_h*self.y_w)
        self.dx = col2im(dx, self.xshape, self.pool, self.y_h, self.pool, 0)
        return self.dx

# in[14]
pool = Pooling(2)

# in[15]
x.shape

# in[16]
y = pool.forward(x)
y