2020机器学习卷积神经网(1)

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卷积神经网在当下流行深度学习框架如 tensorflow mxnet 都提供 API 很容就能够实现卷积神经网，但是为了更好的掌握和理解卷积神经网，今天要自己试着实现一个卷积神经网。仅使用 NumPy 来实现一个卷积神经网(CNN)。
我们要做的卷积神经网(CNN)包括卷积层（conv）、激活函数用 ReLU 和一个使用 max 的池化层

# 导入依赖
%matplotlib inline
import skimage.data
import matplotlib.pyplot as plt
import numpy as np

准备数据

# print(img)
# 读取图片
img = skimage.data.chelsea()
# 将图片转换为黑白
img = skimage.color.rgb2gray(img)
plt.imshow(img,cmap='gray')

<matplotlib.image.AxesImage at 0x1c242e5090>

output_3_1.png

ll_filter = np.zeros((2,3,3))

用 numpy.zeros 创建 的矩阵作为卷积核集合，这里 2 表示有两个卷积核，卷积核大小都是 因为输入灰度图，也就是只有一个通道，所以个卷积就够了。如果图片是 RGB 3 个通道，我们就需要适当增加卷积核的深度或者用 3 个卷积核来提取特征。

ll_filter[0,:,:] = np.array([[
    [-1,0,1],
    [-1,0,1],
    [-1,0,1]
]])
ll_filter[1,:,:] = np.array([[
    [1,1,1],
    [0,0,0],
    [-1,-1,-1]
]])
print(ll_filter.shape)
print(len(ll_filter.shape))
curr_filter = ll_filter[0, :] 
print(curr_filter)
print(len(curr_filter.shape))

(2, 3, 3)
3
[[-1.  0.  1.]
 [-1.  0.  1.]
 [-1.  0.  1.]]
2

def conv(img, conv_filter):
    # 检测图片数据矩阵 3 维 卷积核深度和图片深度是否一致
    if len(img.shape) > 2 or len(conv_filter.shape) > 3:  
        if img.shape[-1] != conv_filter.shape[-1]:  
            print("Error: Number of channels in both image and filter must match.")  
            sys.exit()  
    # 检查卷积核矩阵是否为方阵    
    if conv_filter.shape[1] != conv_filter.shape[2]: 
        print('Error: Filter must be a square matrix. I.e. number of rows and columns must match.')  
        sys.exit()  
    # 检查矩阵是否为偶数矩阵     
    if conv_filter.shape[1]%2==0: 
        print('Error: Filter must have an odd size. I.e. number of rows and columns must be odd.')  
        sys.exit()  
  
    # 初始化 feature map 来保存过滤后图片数据    
    feature_maps = numpy.zeros((img.shape[0]-conv_filter.shape[1]+1,   
                                img.shape[1]-conv_filter.shape[1]+1,   
                                conv_filter.shape[0]))  
  
    # 使用过滤器来提取图片特征
    # 卷积核数量数量，分别遍历卷积核    
    for filter_num in range(conv_filter.shape[0]):  
        print("Filter ", filter_num + 1)  
        # 获取每一个卷积核（过滤器)         
        curr_filter = conv_filter[filter_num, :] 
        #          
        if len(curr_filter.shape) > 2:  #非单通道的卷积核
            conv_map = conv_(img[:, :, 0], curr_filter[:, :, 0]) 
            for ch_num in range(1, curr_filter.shape[-1]):   
                conv_map = conv_map + conv_(img[:, :, ch_num],   
                                  curr_filter[:, :, ch_num])  
        else: # 单一通道卷积核  
            conv_map = conv_(img, curr_filter)  
        feature_maps[:, :, filter_num] = conv_map 
    return feature_maps 

首先要做的工作是检查每个滤波器的深度等于图像通道的数量。然后再进一步检查图片和过滤器最后一维是否相等。

if len(img.shape) > 2 or len(conv_filter.shape) > 3:  
        if img.shape[-1] != conv_filter.shape[-1]:  
            print("Error: Number of channels in both image and filter must match.")  
            sys.exit() 
            

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