BP 神经网络

Posted 2020-11-28 heimazaifei

代码：

import numpy as np
from utils.features import prepare_for_training
from utils.hypothesis import sigmoid, sigmoid_gradient

class MultilayerPerceptron:
    def __init__(self,data,labels,layers,normalize_data =False):
        data_processed = prepare_for_training(data,normalize_data = normalize_data)[0]
        self.data= data_processed
        self.labels= labels
        self.layers= layers #pixexls(784)  hiddenLayer(25)  output(10)
        self.normalize_data= normalize_data
        self.thetas = MultilayerPerceptron.thetas_init(layers) # weight
        
    def predict(self,data):
        data_processed = prepare_for_training(data,normalize_data = self.normalize_data)[0]
        num_examples = data_processed.shape[0]
        predictions = MultilayerPerceptron.feedforward_propagation(data_processed,self.thetas,self.layers)
        return np.argmax(predictions,axis=1).reshape((num_examples,1))

    def train(self,max_iterations=1000,alpha=0.1):
        unrolled_theta = MultilayerPerceptron.thetas_unroll(self.thetas)
        (optimized_theta,cost_history) = MultilayerPerceptron.gradient_descent(self.data,self.labels,unrolled_theta,self.layers,max_iterations,alpha)
        self.thetas = MultilayerPerceptron.thetas_roll(optimized_theta,self.layers)
        return self.thetas,cost_history
         
    @staticmethod  # 该方法不强制要求传递参数，如下声明一个静态方法
    def thetas_init(layers):
        num_layers = len(layers)  #3
        thetas = {}
        """
        会执行两次，得到两组参数矩阵：25*(784+1) , 10*26 
        layers[0] = 784
        layers[1] = 25
        layers[2] = 10
        """
        for layer_index in range(num_layers - 1):
            in_count = layers[layer_index]
            out_count = layers[layer_index+1]
            # 这里需要考虑到偏置项，记住一点偏置的个数跟输出的结果是一致的
            thetas[layer_index] = np.random.rand(out_count,in_count+1)*0.05 #随机进行初始化操作，值尽量小一点
            #example: rand(2,3)
            #[0.12  0.08  0.17]
            #[0.53  0.13  0.98]
        return thetas
    
    @staticmethod
    def thetas_unroll(thetas):
        num_theta_layers = len(thetas)# thetas[0],thetas[1]
        unrolled_theta = np.array([])
        for theta_layer_index in range(num_theta_layers):
            unrolled_theta = np.hstack((unrolled_theta,thetas[theta_layer_index].flatten()))
            #arr1=np.array([1,2,3]) , arr2=np.array([4,5,6])  np.hstack(arr1,arr2) is [1,2,3,4,5,6]
            #a=array([[1,2],[3,4],[5,6]])  , a.flatten() : array([1,2,3,4,5,6])
        return unrolled_theta
    
    @staticmethod
    def gradient_descent(data,labels,unrolled_theta,layers,max_iterations,alpha):
        optimized_theta = unrolled_theta
        cost_history = []
        for _ in range(max_iterations):
            cost = MultilayerPerceptron.cost_function(data,labels,MultilayerPerceptron.thetas_roll(optimized_theta,layers),layers)
            cost_history.append(cost)
            theta_gradient = MultilayerPerceptron.gradient_step(data,labels,optimized_theta,layers)
            optimized_theta = optimized_theta - alpha* theta_gradient
        return optimized_theta,cost_history
                        
    @staticmethod 
    def gradient_step(data,labels,optimized_theta,layers):
        theta = MultilayerPerceptron.thetas_roll(optimized_theta,layers)
        thetas_rolled_gradients = MultilayerPerceptron.back_propagation(data,labels,theta,layers)
        thetas_unrolled_gradients = MultilayerPerceptron.thetas_unroll(thetas_rolled_gradients)
        return thetas_unrolled_gradients
    
    @staticmethod 
    def back_propagation(data,labels,thetas,layers):  # 反向传播
        num_layers = len(layers)
        (num_examples,num_features) = data.shape
        num_label_types = layers[-1]
        
        deltas = {}
        #初始化操作
        for layer_index in range(num_layers -1 ):
            in_count = layers[layer_index]
            out_count = layers[layer_index+1]
            deltas[layer_index] = np.zeros((out_count,in_count+1)) #25*785 10*26
        for example_index in range(num_examples):
            layers_inputs = {}
            layers_activations = {}
            layers_activation = data[example_index,:].reshape((num_features,1))#785*1 加入偏置项
            layers_activations[0] = layers_activation
            #逐层计算
            for layer_index in range(num_layers - 1):
                layer_theta = thetas[layer_index] #得到当前权重参数值 25*785   10*26
                layer_input = np.dot(layer_theta,layers_activation) #第一次得到25*1  第二次10*1
                layers_activation = np.vstack((np.array([[1]]),sigmoid(layer_input)))
                layers_inputs[layer_index + 1] = layer_input #后一层计算结果
                layers_activations[layer_index + 1] = layers_activation #后一层经过激活函数后的结果
            output_layer_activation = layers_activation[1:,:]
            
            delta = {}
            #标签处理
            bitwise_label = np.zeros((num_label_types,1))
            bitwise_label[labels[example_index][0]] = 1
            #计算输出层和真实值之间的差异（当前样本）
            delta[num_layers - 1] = output_layer_activation - bitwise_label
            
            #遍历循环 L L-1 L-2 ...2
            for layer_index in range(num_layers - 2,0,-1): # (start,stop,step) 计算一次
                layer_theta = thetas[layer_index] # 当前theta
                next_delta = delta[layer_index+1] # 下一层 变化
                layer_input = layers_inputs[layer_index]
                layer_input = np.vstack((np.array((1)),layer_input))# 加入偏置项
                #按照公式进行计算
                delta[layer_index] = np.dot(layer_theta.T,next_delta)*sigmoid_gradient(layer_input)
                #过滤掉偏置参数
                delta[layer_index] = delta[layer_index][1:,:]
            for layer_index in range(num_layers-1):  # 计算梯度值
                layer_delta = np.dot(delta[layer_index+1],layers_activations[layer_index].T)
                deltas[layer_index] = deltas[layer_index] + layer_delta #第一次25*785  第二次10*26
                
        for layer_index in range(num_layers -1):
               
            deltas[layer_index] = deltas[layer_index] * (1/num_examples)
            
        return deltas
            
    @staticmethod        
    def cost_function(data,labels,thetas,layers):
        num_layers = len(layers)  # 3
        num_examples = data.shape[0] # 第一维度 数值[[1,2,3],[1,2,4]].shape[0] is 2 
        num_labels = layers[-1] # output
        
        #前向传播走一次
        predictions = MultilayerPerceptron.feedforward_propagation(data,thetas,layers)
        #制作标签，每一个样本的标签都得是one-hot
        bitwise_labels = np.zeros((num_examples,num_labels)) # 1700 * 10  e.g  [0 0 0 0 0 0 0 0 1 0] ... 
        for example_index in range(num_examples):
            bitwise_labels[example_index][labels[example_index][0]] = 1
        bit_set_cost = np.sum(np.log(predictions[bitwise_labels == 1]))   # here 1 is np.ones(bitwise_labels.shape()) 
        bit_not_set_cost = np.sum(np.log(1-predictions[bitwise_labels == 0]))
        cost = (-1/num_examples) *(bit_set_cost+bit_not_set_cost)
        return cost
                
    @staticmethod        
    def feedforward_propagation(data,thetas,layers):    
        num_layers = len(layers)
        num_examples = data.shape[0] 
        in_layer_activation = data  # input  1700  x 784+1  ,+1预处理后，偏置项b
        
        # 逐层计算
        for layer_index in range(num_layers - 1):
            theta = thetas[layer_index]
            out_layer_activation = sigmoid(np.dot(in_layer_activation,theta.T))  #矩阵乘法 dot（ 1700x185 ，185x25^） = shape[1700,25]
            # 正常计算完之后是num_examples*25,但是要考虑偏置项 变成num_examples*(25 +1)   +1 为偏置项
            out_layer_activation = np.hstack((np.ones((num_examples,1)),out_layer_activation))
            in_layer_activation = out_layer_activation
            
        #返回输出层结果,结果中不要偏置项了 [0 位置] 
        return in_layer_activation[:,1:]
                   
    @staticmethod       
    def thetas_roll(unrolled_thetas,layers):    
        num_layers = len(layers)
        thetas = {}
        unrolled_shift = 0
        for layer_index in range(num_layers - 1):
            in_count = layers[layer_index]
            out_count = layers[layer_index+1]
            
            thetas_width = in_count + 1
            thetas_height = out_count
            thetas_volume = thetas_width * thetas_height
            start_index = unrolled_shift
            end_index = unrolled_shift + thetas_volume
            layer_theta_unrolled = unrolled_thetas[start_index:end_index]
            thetas[layer_index] = layer_theta_unrolled.reshape((thetas_height,thetas_width))
            unrolled_shift = unrolled_shift+thetas_volume
        
        return thetas