贪玩ML系列之一个BP玩一天

手写串行BP算法，可调batch_size

既要：1、输入层f(x)=x  隐藏层sigmoid 输出层f(x)=x

2、run函数实现单条数据的一次前馈

3、train函数读入所有数据for循环处理每条数据。

循环中：

首先调用run函数，得到各层的值

self.input_nodes_value

self.hidden_nodes_value

self.output_nodes_value

然后计算输出层误差和delta

4、关键函数：用于前馈的sigmoid和用于反馈的sigmoid的导数

 self.activation_function = lambda x : 1/(1+np.exp(-x))  # sigmoid函数，用于正向传播
 self.delta_activation_function = lambda x: x-x**2 # sigmoid一阶导，用于反向传播

inputs = np.array([[0.5, -0.2, 0.1]])
targets = np.array([[0.4]])
test_w_i_h = np.array([[0.1, -0.2],
                       [0.4, 0.5],
                       [-0.3, 0.2]])
test_w_h_o = np.array([[0.3],
                       [-0.1]])
batch_size=1

# 输入层没有激活函数f(x)=x，隐藏层激活函数sigmoid，输出层激活函数f(x)=x
class NeuralNetwork(object):
    def __init__(self, input_nodes, hidden_nodes, output_nodes, learning_rate):

        # Set number of nodes in input, hidden and output layers.
        self.input_nodes = input_nodes
        self.hidden_nodes = hidden_nodes
        self.output_nodes = output_nodes

#         创建三个一维数组存放三层节点的值
#         print(str(self.input_nodes)+" "+str(self.hidden_nodes)+" "+str(self.output_nodes))
        self.input_nodes_value=[1.0]*input_nodes
        self.hidden_nodes_value=[1.0]*hidden_nodes
        self.output_nodes_value=[1.0]*output_nodes

        # Initialize weights
        self.weights_input_to_hidden = np.random.normal(0.0, self.input_nodes**-0.5,
                                       (self.input_nodes, self.hidden_nodes))

        self.weights_hidden_to_output = np.random.normal(0.0, self.hidden_nodes**-0.5,
                                       (self.hidden_nodes, self.output_nodes))
        self.learning_rate = learning_rate

        #### TODO: Set self.activation_function to your implemented sigmoid function ####

        self.activation_function = lambda x : 1/(1+np.exp(-x))  # sigmoid函数，用于正向传播
        self.delta_activation_function = lambda x: x-x**2 # sigmoid一阶导，用于反向传播

        self.change_to_fix_weights_h2o=[[0.0]*self.output_nodes]*self.hidden_nodes
        self.change_to_fix_weights_i2h=[[0.0]*self.hidden_nodes]*self.input_nodes
#         print("xxxx")
#         print(self.change_to_fix_weights_h2o)
#         print(self.change_to_fix_weights_i2h)

    def train(self, features, targets):#完成n条数据的一次前向传递
        ‘‘‘ Train the network on batch of features and targets. 

            Arguments
            ---------

            features: 2D array, each row is one data record, each column is a feature
            targets: 1D array of target values

        ‘‘‘

        ####################modify by zss###############################################

        n=features.shape[0]#数据条数
#         print(features)
#         print(targets)

        counter=batch_size
        for ii in range(0,n):
            print("######",ii)
            print(self.weights_input_to_hidden)
            print(self.weights_hidden_to_output)
#             print(self.run(features[ii]))
#             print(targets[ii])

            error_o=[0.0]*self.output_nodes#输出层误差
            error_h=[0.0]*self.hidden_nodes#隐藏层误差
            output_deltas=[0.0]*self.output_nodes
            hidden_deltas=[0.0]*self.hidden_nodes

            for o in range(self.output_nodes): # 输 出 层
                error_o[o]=targets[ii][o]-self.output_nodes_value[o]#计算输出层误差
                output_deltas[o]=self.delta_activation_function(self.output_nodes_value[o])*error_o[o]

            for h in range(self.hidden_nodes): # 隐 藏 层
                for o in range(self.output_nodes):
                    error_h[h]+=output_deltas[o]*self.weights_hidden_to_output[h][o]
                hidden_deltas[h]=self.delta_activation_function(self.hidden_nodes_value[h])*error_h[h]

            for h in range(self.hidden_nodes):
                for o in range(self.output_nodes):
                    self.change_to_fix_weights_h2o[h][o]+=output_deltas[o]*self.hidden_nodes_value[h]

            for i in range(self.input_nodes):
                for h in range(self.hidden_nodes):
                    self.change_to_fix_weights_i2h[i][h]+=hidden_deltas[h]*self.input_nodes_value[i]

            counter-=1
            if counter==0:#当counter=0，进行一次权重修改
                #调整隐藏层--输出层权重
                for h in range(self.hidden_nodes):
                    for o in range(self.output_nodes):
                        self.weights_hidden_to_output[h][o] += self.learning_rate*self.change_to_fix_weights_h2o[h][o]

                #调整输入层--隐藏层权重
                for i in range(self.input_nodes):
                    for h in range(self.hidden_nodes):
                        self.weights_input_to_hidden[i][h] += self.learning_rate*self.change_to_fix_weights_i2h[i][h]

                self.change_to_fix_weights_h2o=[[0.0]*self.output_nodes]*self.hidden_nodes
                self.change_to_fix_weights_i2h=[[0.0]*self.hidden_nodes]*self.input_nodes
                counter=batch_size
        return self.weights_hidden_to_output

    def run(self, features):#完成一条数据的一次前向传递
        ‘‘‘
            features: 1D array of feature values
        ‘‘‘        

        print(features)

        for i in range(self.input_nodes):
            self.input_nodes_value[i]=features[i]
#             self.input_nodes_value[i]=self.activation_function(features[i])

        for h in range(self.hidden_nodes):
            temp=0
            for i in range(self.input_nodes):
                temp+=self.input_nodes_value[i]*self.weights_input_to_hidden[i][h]
            temp=self.activation_function(temp)
            self.hidden_nodes_value[h]=temp

        for o in range(self.output_nodes):
            temp=0
            for h in range(self.hidden_nodes):
                temp+=self.hidden_nodes_value[h]*self.weights_hidden_to_output[h][o]
#             temp=self.activation_function(temp)
            self.output_nodes_value[o]=temp
        return

def test_run():
    # Test correctness of run method
    network = NeuralNetwork(3, 2, 1, 0.5)
    network.weights_input_to_hidden = test_w_i_h.copy()
    network.weights_hidden_to_output = test_w_h_o.copy()

    print("#####"+str(network.run(np.array([0.5, -0.2, 0.1]))))
    print(np.allclose(network.run(np.array([0.5, -0.2, 0.1])), 0.09998924))
    return

def test_train():
    # Test that weights are updated correctly on training
    network = NeuralNetwork(3, 2, 1, 0.5)
    network.weights_input_to_hidden = test_w_i_h.copy()
    network.weights_hidden_to_output = test_w_h_o.copy()
    network.train(inputs, targets)

    print(np.allclose(network.weights_hidden_to_output,
                                np.array([[ 0.37275328],
                                            [-0.03172939]])))
    print(np.allclose(network.weights_input_to_hidden,
                                np.array([[ 0.10562014, -0.20185996],
                                            [0.39775194, 0.50074398],
                                            [-0.29887597, 0.19962801]])))
test_train()

可以看出结果比较接近，但是还是不满足allclose 5%的要求，因为只迭代了一次，多迭代几次精确率就会进一步上升，未完待续

allclose结果为false

原文地址：https://www.cnblogs.com/zealousness/p/9351799.html