第一步定义卷积核类:
class Filter(object): # 滤波器类 对卷积核进行初始化 def __init__(self,width,height,depth): # initialize the filter parameter self.weights=np.random.uniform(-1e-4,1e-4,(depth,height,width)) self.bias=0 self.weights_grad=np.zeros(self.weights.shape) self.bias_grad=0 def get_weights(self): return self.weights def get_bias(self): return self.bias def update_weight(self,learning_rate): self.weights-=self.weights_grad*learning_rate self.bias-=self.bias_grad*learning_rate
定义卷积层
def conv(input_array,kernel_array,output_array,stride,bias): 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):
# get_patch 得到i,j位置对应的图像的块 output_array[i][j]=(get_patch(input_array,i,j,kernel_width,kernel_height,stride)*kernel_array).sum()+bias
定义padding 函数:根据扩展的大小进行0填充
def padding(input_array, zero_padding): if zero_padding == 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((input_depth, input_height + 2 * zero_padding, input_width + 2 * zero_padding)) padded_array[:, zero_padding:zero_padding + input_height, zero_padding:zero_padding + input_width] = input_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 * zero_padding, input_width + 2 * zero_padding)) padded_array[zero_padding:zero_padding + input_width, zero_padding:zero_padding + input_height] = input_array return padded_array
定义卷积类:
def calculate_output_size(input_size,filter_size,zero_padding,stride): return (input_size-filter_size+2*zero_padding)/stride+1
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=input_width self.input_height=input_height self.channel_number=channel_number self.filter_width=filter_width self.filter_height=filter_height self.filter_number=filter_number self.zero_padding=zero_padding self.stride=stride
# 根据(f-w+2p)/2+1 self.outpu_width=ConvLayer.calculate_output_size(self.input_width, filter_width,zero_padding,stride) self.output_height=ConvLayer.calculate_output_size(self.input_height, filter_height,zero_padding, stride)
# 得到padding 后的图像 self.output_array=np.zeros(self.filter_number,self.output_width,self.output_height) # the output of the convolution
# 初始化filters
self.filters=[] # initialize 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 # 对 灵敏度图进行扩充 def expand_sentivity_map(self,sensitivity_array): depth=sensitivity_array.shape[0] expanded_width=(self.input_width-self.filter_width+2*self.zero_padding+1) expanded_height=(self.input_height-self.filter_height+2*self.zero_padding+1) expand_array=np.zeros((depth,expanded_height,expanded_width)) 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
# 创建灵敏度矩阵 def create_delta_array(self): return np.zeros((self.channnel_number,self.input_height,self.input_width)) # 前向传递 def forward(self,input_array): self.input_array=input_array # first pad image to the size needed self.padded_input_array=padding(input_array,self.zero_padding) for f in range(self.filter_number): filter=self.filters[f] conv(self.paded_input_array,filter.get_weights(),filter.get_bias()) element_wise_op(self.output_array,self.acitator.forward) # 反向传递
def bp_sensitivity_map(self, sensitivity_array,activator): # padding sensitivity map expanded_array=self.expand_sentivity_map(sensitivity_array) expanded_width=expanded_array.shape[2] zp=(self.input_width+self.filter_width-1-expanded_width)/2 padded_array=padding(expanded_array,zp) self.delta_array=self.create_delta_array() for f in range(self.filter_number): filter=self.filter[f] filpped_weights=np.array(map(lambda i: np.rot90(i,2),filter.get_weights())) delta_array=self.create_delta_array() for d in range(delta_array.shape[0]) conv(padded_array[f],filpped_weights[d],delta_array[d],1,0) self.delta_array+=delta_array derivative_array=np.array(self.input_array) element_wise_op(derivative_array,activator.backward) self.delta_array*=derivative_array
# 参数的梯度是 输入乘以灵敏度矩阵 def bp_gradient(self,sensitivity_array): expanded_array=self.expand_sensitivity_map(sensitivity_array) for f in range(self.filter_number): filter=self.filter[f] for d in range(filter.weights.shape[0]): conv(self.padded_input_array[d],expanded_array[f],filter.weights_grad[d],1,0) filter.bias_grad=expanded_array[f].sum()
# 对参数进行update def update(self): for filter in self.filters: filter.update(self.learning_rate)