深度学习(4) - 卷积神经网络_cl_in_test

学习文章：https://zybuluo.com/hanbingtao/note/485480
(在移动端可以看到图片，在pc上就不行，有大佬知道什么原因吗）
卷积的三种模式:full, same, valid:https://blog.csdn.net/leviopku/article/details/80327478

笔记，字丑勿怪



Python实现代码：

#!/usr/bin/env python
# -*- coding: UTF-8 -*-


import numpy as np


class IdentityActivator(object):
    # forward方法实现了前向计算，而backward方法则是计算导数
    def forward(self, weighted_input):
        return weighted_input

    def backward(self, output):
        return 1


# 获取卷积区域
def get_patch(input_array, i, j, filter_width,
              filter_height, stride):
    '''
    从输入数组中获取本次卷积的区域，
    自动适配输入为2D和3D的情况
    '''
    start_i = i * stride
    start_j = j * stride
    if input_array.ndim == 2:
        return input_array[
               start_i: start_i + filter_height,
               start_j: start_j + filter_width]
    elif input_array.ndim == 3:
        return input_array[:,
               start_i: start_i + filter_height,
               start_j: start_j + filter_width]


# 获取一个2D区域的最大值所在的索引
def get_max_index(array):
    max_i = 0
    max_j = 0
    max_value = array[0, 0]
    for i in range(array.shape[0]):
        for j in range(array.shape[1]):
            if array[i, j] > max_value:
                max_value = array[i, j]
                max_i, max_j = i, j
    return max_i, max_j


# 计算卷积
def conv(input_array,
         kernel_array,
         output_array,
         stride, bias):
    """
    计算卷积，自动适配输入为2D和3D的情况
    """
    # 输入矩阵维度
    channel_number = input_array.ndim
    output_width = output_array.shape[1]
    output_height = output_array.shape[0]
    kernel_width = kernel_array.shape[-1]
    kernel_height = kernel_array.shape[-2]
    for i in range(output_height):
        for j in range(output_width):
            output_array[i][j] = \
                (get_patch(input_array, i, j, kernel_width, kernel_height, stride) * kernel_array).sum() + bias


# 为数组增加Zero padding
def padding(input_array, zp):
    """
    为数组增加Zero padding，自动适配输入为2D和3D的情况
    """
    zp = int(zp)
    if zp == 0:
        return input_array
    else:
        if input_array.ndim == 3:
            input_width = input_array.shape[2]
            input_height = input_array.shape[1]
            input_depth = input_array.shape[0]
            padded_array = np.zeros((
                int(input_depth),
                int(input_height + 2 * zp),
                int(input_width + 2 * zp)))
            padded_array[:, zp: zp + input_height, zp: zp + input_width] = input_array
            return padded_array
        elif input_array.ndim == 2:
            input_width = input_array.shape[1]
            input_height = input_array.shape[0]
            padded_array = np.zeros((
                input_height + 2 * zp,
                input_width + 2 * zp))
            padded_array[zp: zp + input_height, zp: zp + input_width] = input_array
            return padded_array


# 对numpy数组进行element wise操作
def element_wise_op(array, op):
    for i in np.nditer(array,
                       op_flags=['readwrite']):
        i[...] = op(i)


class Filter(object):
    def __init__(self, width, height, depth):
        # 权重矩阵
        self.weights = np.random.uniform(-1e-4, 1e-4, (depth, height, width))
        # 偏置项
        self.bias = 0
        # 权重梯度矩阵
        self.weights_grad = np.zeros(self.weights.shape)
        # 偏置项梯度
        self.bias_grad = 0

    def __repr__(self):
        return 'filter weights:\n%s\nbias:\n%s' % (
            repr(self.weights), repr(self.bias))

    def get_weights(self):
        return self.weights

    def get_bias(self):
        return self.bias

    def update(self, learning_rate):
        # 梯度下降
        self.weights -= learning_rate * self.weights_grad
        self.bias -= learning_rate * self.bias_grad


class ConvLayer(object):
    def __init__(self, input_width, input_height,
                 channel_number, filter_width,
                 filter_height, filter_number,
                 zero_padding, stride, activator,
                 learning_rate):
        self.input_width = int(input_width)
        self.input_height = int(input_height)
        self.channel_number = int(channel_number)
        self.filter_width = int(filter_width)
        self.filter_height = int(filter_height)
        self.filter_number = int(filter_number)
        self.zero_padding = int(zero_padding)
        self.stride = int(stride)
        self.output_width = int(ConvLayer.calculate_output_size(
                self.input_width, filter_width, zero_padding,
                stride))
        self.output_height = int(ConvLayer.calculate_output_size(
                self.input_height, filter_height, zero_padding,
                stride))
        self.output_array = np.zeros((self.filter_number, self.output_height, self.output_width))
        self.filters = []
        for i in range(filter_number):
            self.filters.append(Filter(filter_width,
                                       filter_height, self.channel_number))
        self.activator = activator
        self.learning_rate = learning_rate

    def forward(self, input_array):
        """
        计算卷积层的输出
        输出结果保存在self.output_array
        """
        self.input_array = input_array
        # 对输入矩阵进行padding
        self.padded_input_array = padding(input_array, self.zero_padding)
        for f in range(self.filter_number):
            filter = self.filters[f]
            # net = sum(w * a) + wb
            conv(self.padded_input_array,
                 filter.get_weights(), self.output_array[f],
                 self.stride, filter.get_bias())
        # print("__self.output_array:\n", self.output_array)
        # a = f(net)
        element_wise_op(self.output_array,
                        self.activator.forward)
        # print("input_array:\n", input_array)
        # print("padded:\n", self.padded_input_array)
        # print("filters:\n", self.filters)
        # print("self.output_array:\n", self.output_array)

    def backward(self, input_array, sensitivity_array,
                 activator):
        """
        计算传递给前一层的误差项，以及计算每个权重的梯度
        前一层的误差项保存在self.delta_array
        梯度保存在Filter对象的weights_grad
        """
        self.forward(input_array)
        self.bp_sensitivity_map(sensitivity_array,
                                activator)
        self.bp_gradient(sensitivity_array)

    def update(self):
        """
        按照梯度下降，更新权重
        """
        for filter in self.filters:
            filter.update(self.learning_rate)

    def bp_sensitivity_map(self, sensitivity_array, activator):
        """
        计算传递到上一层的sensitivity map
        sensitivity_array: 本层的sensitivity map
        activator: 上一层的激活函数
        """
        # 处理卷积步长，对原始sensitivity map进行扩展
        expanded_array = self.expand_sensitivity_map(sensitivity_array)
        # full卷积，对sensitivity map进行zero padding
        # 虽然原始输入的zero padding单元也会获得残差
        # 但这个残差不需要继续向上传递，因此就不计算了
        expanded_width = expanded_array.shape[2]
        zp = (self.input_width + self.filter_width - 1 - expanded_width) / 2
        padded_array = padding(expanded_array, zp)
        # 初始化delta_array，用于保存传递到上一层的
        # sensitivity map
        self.delta_array = self.create_delta_array()
        # 对于具有多个filter的卷积层来说，最终传递到上一层的
        # sensitivity map相当于所有的filter的
        # sensitivity map之和
        for f in range(self.filter_number):
            filter = self.filters[f]
            # 将filter权重翻转180度
            flipped_weights = np.array(list(map(lambda i: np.rot90(i, 2), filter.get_weights())))
            # print("filter:\n", filter.get_weights())
            # 计算与一个filter对应的delta_array
            # delta(l-1) = delta(l) * filter(l)
            delta_array = self.create_delta_array()
            # print("padded_array:\n", padded_array)
            # print("flipped_weights:\n", flipped_weights)
            for d in range(delta_array.shape[0]):
                # print("flipped_weights:\n", flipped_weights[d])
                conv(padded_array[f], flipped_weights[d], delta_array[d], 1, 0)
            self.delta_array += delta_array
        # 将计算结果与激活函数的偏导数做element-wise乘法操作
        # delta(l-1)点乘f'(net(l-1))
        derivative_array = np.array(self.input_array)
        element_wise_op(derivative_array,
                        activator.backward)
        self.delta_array *= derivative_array

    def bp_gradient(self, sensitivity_array):
        # 处理卷积步长，对原始sensitivity map进行扩展
        expanded_array = self.expand_sensitivity_map(sensitivity_array)
        for f in range(self.filter_number):
            # 计算每个权重的梯度
            filter = self.filters[f]
            for d in range(filter.weights.shape[0]):
                conv(self.padded_input_array[d], expanded_array[f], filter.weights_grad[d], 1, 0)
            # 计算偏置项的梯度
            filter.bias_grad = expanded_array[f].sum()

    # 将步长为S的sensitivity map『还原』为步长为1的sensitivity map
    def expand_sensitivity_map(self, sensitivity_array):
        depth = sensitivity_array.shape[0]
        # 确定扩展后sensitivity map的大小
        # 计算stride为1时sensitivity map的大小
        expanded_width = self.calculate_output_size(self.input_width, self.filter_width, self.zero_padding, 1)
        expanded_height = self.calculate_output_size(self.input_height, self.filter_height, self.zero_padding, 1)
        # 构建新的sensitivity_map
        expand_array = np.zeros((depth, expanded_height,
                                 expanded_width))
        # 从原始sensitivity map拷贝误差值
        for i in range(self.output_height):
            for j in range(self.output_width):
                i_pos = i * self.stride
                j_pos = j * self.stride
                expand_array[:, i_pos, j_pos] = sensitivity_array[:, i, j]
        return expand_array

    # 创建用来保存传递到上一层的sensitivity map的数组
    def create_delta_array(self):
        return np.zeros((self.channel_number, self.input_height, self.input_width))

    @staticmethod
    def calculate_output_size(input_size, filter_size, zero_padding, stride):
        # 确定卷积层输出的大小
        # W2 = (W1 - F + 2 * P) / S + 1
        return int((input_size - filter_size + 2 * zero_padding) / stride + 1)


class MaxPoolingLayer(object):
    def __init__(self, input_width, input_height,
                 channel_number, filter_width,
                 filter_height, stride):
        self.input_width = int(input_width)
        self.input_height = int(input_height)
        self.channel_number = int(channel_number)
        self.filter_width = int(filter_width)
        self.filter_height = int(filter_height)
        self.stride = int(stride)
        self.output_width = int((input_width - filter_width) / self.stride + 1)
        self.output_height = int((input_height - filter_height) / self.stride + 1)
        self.output_array = np.zeros((self.channel_number,
                                      self.output_height, self.output_width))

    def forward(self, input_array):
        for d in range(self.channel_number):
            for i in range(self.output_height):
                for j in range(self.output_width):
                    self.output_array[d, i, j] = (
                        get_patch(input_array[d], i, j,
                                  self.filter_width,
                                  self.filter_height,
                                  self.stride).max())

    def backward(self, input_array, sensitivity_array):
        self.delta_array = np.zeros(input_array.shape)
        for d in range(self.channel_number):
            for i in range(self.output_height):
                for j in range(self.output_width):
                    patch_array = get_patch(
                        input_array[d], i, j,
                        self.filter_width,
                        self.filter_height,
                        self.stride)
                    k, l = get_max_index(patch_array)
                    self.delta_array[d,
                                     i * self.stride + k,
                                     j * self.stride + l] = \
                        sensitivity_array[d, i, j]


# 卷积层的梯度检查
def init_test():
    a = np.array(
        [[[0, 1, 1, 0, 2],
          [2, 2, 2, 2, 1],
          [1, 0, 0, 2, 0],
          [0, 1, 1, 0, 0],
          [1, 2, 0, 0, 2]],
         [[1, 0, 2, 2, 0],
          [0, 0, 0, 2, 0],
          [1, 2, 1, 2, 1],
          [1, 0, 0, 0, 0],
          [1, 2, 1, 1, 1]],
         [[2, 1, 2, 0, 0],
          [1, 0, 0, 1, 0],
          [0, 2, 1, 0, 1],
          [0, 1, 2, 2, 2],
          [2, 1, 0, 0, 1]]])
    b = np.array(
        [[[0, 1, 1],
          [2, 2, 2],
          [1, 0, 0]],
         [[1, 0, 2],
          [0, 0, 0],
          [1, 2, 1]]])
    cl = ConvLayer(5, 5, 3, 3, 3, 2, 1, 2, IdentityActivator(), 0.001)
    cl.filters[0].weights = np.array(
        [[[-1, 1, 0],
          [0, 1, 0],
          [0, 1, 1]],
         [[-1, -1, 0],
          [0, 0, 0],
          [0, -1, 0]],
         [[0, 0, -1],
          [0, 1, 0],
          [1, -1, -1]]], dtype=np.float64)
    cl.filters[0].bias = 1
    cl.filters[1].weights = np.array(
        [[[1, 1, -1],
          [-1, -1, 1],
          [0, -1, 1]],
         [[0, 1, 0],
          [-1, 0, -1],
          [-1, 1, 0]],
         [[-1, 0, 0],
          [-1, 0, 1],
          [-1, 0, 0]]], dtype=np.float64)
    return a, b, cl


def test():
    a, b, cl = init_test()
    cl.forward(a)
    print(cl.output_array)


def test_bp():
    a, b, cl = init_test()
    cl.backward(a, b, IdentityActivator())
    cl.update()
    print(cl.filters[0])
    print(cl.filters[1])


def gradient_check():
    '''
    梯度检查
    '''
    # 设计一个误差函数，取所有节点输出项之和
    error_function = lambda o: o.sum()

    # 计算forward值
    a, b, cl = init_test()
    cl.forward(a)

    # 求取sensitivity map
    sensitivity_array = np.ones(cl.output_array.shape,
                                dtype=np.float64)
    # 计算梯度
    cl.backward(a, sensitivity_array,
                IdentityActivator())
    # 检查梯度
    epsilon = 10e-4
    for d in range(cl.filters[0].weights_grad.shape[0]):
        for i in range(cl.filters[0].weights_grad.shape[1]):
            for j in range(cl.filters[0].weights_grad.shape[2]):
                cl.filters[0].weights[d, i, j] += epsilon
                cl.forward(a)
                err1 = error_function(cl.output_array)
                cl.filters[0].weights[d, i, j] -= 2 * epsilon
                cl.forward(a)
                err2 = error_function(cl.output_array)
                expect_grad = (err1 - err2) / (2 * epsilon)
                cl.filters[0].weights[d, i, j] += epsilon
                print('weights(%d,%d,%d): expected - actural %f - %f' % (
                    d, i, j, expect_grad, cl.filters[0].weights_grad[d, i, j]))


def init_pool_test():
    a = np.array(
        [[[1, 1, 2, 4],
          [5, 6, 7, 8],
          [3, 2, 1, 0],
          [1, 2, 3, 4]],
         [[0, 1, 2, 3],
          [4, 5, 6, 7],
          [8, 9, 0, 1],
          [3, 4, 5, 6]]], dtype=np.float64)

    b = np.array(
        [[[1, 2],
          [2, 4]],
         [[3, 5],
          [8, 2]]], dtype=np.float64)

    mpl = MaxPoolingLayer(4, 4, 2, 2, 2, 2)

    return a, b, mpl


def test_pool():
    a, b, mpl = init_pool_test()
    mpl.forward(a)
    print('input array:\n%s\noutput array:\n%s' % (a,
                                             mpl.output_array))


def test_pool_bp():
    a, b, mpl = init_pool_test()
    mpl.backward(a, b)
    print('input array:\n%s\nsensitivity array:\n%s\ndelta array:\n%s' % (
        a, b, mpl.delta_array))


if __name__ == '__main__':
    gradient_check()
    # test_pool()
    test_pool_bp()
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输入输出结果：