Python 西瓜书编程实现标准BP算法和累积BP算法+loss可视化

由于没有给出数据集，这里只提供标准BP算法和累积BP算法的代码和loss可视化方法。

标准BP算法代码：

import numpy as np

class BP:
    def __init__(self, input_size, hidden_size, output_size, learning_rate=0.01):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        self.learning_rate = learning_rate
        
        self.W1 = np.random.randn(input_size, hidden_size)
        self.b1 = np.zeros((1, hidden_size))
        self.W2 = np.random.randn(hidden_size, output_size)
        self.b2 = np.zeros((1, output_size))
        
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    def forward(self, X):
        self.z1 = np.dot(X, self.W1) + self.b1
        self.a1 = self.sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.W2) + self.b2
        self.a2 = self.sigmoid(self.z2)
        return self.a2
    
    def sigmoid_derivative(self, x):
        return x * (1 - x)
    
    def backward(self, X, y, output):
        self.error = y - output
        self.a2_delta = self.error * self.sigmoid_derivative(output)
        self.a1_error = np.dot(self.a2_delta, self.W2.T)
        self.a1_delta = self.a1_error * self.sigmoid_derivative(self.a1)
        
        self.W1 += self.learning_rate * np.dot(X.T, self.a1_delta)
        self.b1 += self.learning_rate * np.sum(self.a1_delta, axis=0, keepdims=True)
        self.W2 += self.learning_rate * np.dot(self.a1.T, self.a2_delta)
        self.b2 += self.learning_rate * np.sum(self.a2_delta, axis=0, keepdims=True)
        
    def train(self, X, y, epochs):
        self.loss = []
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, output)
            self.loss.append(np.mean(np.abs(self.error)))
            
            if i % 1000 == 0:
                print("Epoch:", i, " Loss:", np.mean(np.abs(self.error)))
                
    def predict(self, X):
        return self.forward(X)

累积BP算法代码：

import numpy as np

class Accumulative_BP:
    def __init__(self, input_size, hidden_size, output_size, learning_rate=0.01):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        self.learning_rate = learning_rate
        
        self.W1 = np.random.randn(input_size, hidden_size)
        self.b1 = np.zeros((1, hidden_size))
        self.W2 = np.random.randn(hidden_size, output_size)
        self.b2 = np.zeros((1, output_size))
        
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    def forward(self, X):
        self.z1 = np.dot(X, self.W1) + self.b1
        self.a1 = self.sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.W2) + self.b2
        self.a2 = self.sigmoid(self.z2)
        return self.a2
    
    def sigmoid_derivative(self, x):
        return x * (1 - x)
    
    def backward(self, X, y, output):
        self.error = y - output
        self.a2_delta = self.error * self.sigmoid_derivative(output)
        self.a1_error = np.dot(self.a2_delta, self.W2.T)
        self.a1_delta = self.a1_error * self.sigmoid_derivative(self.a1)
        
        self.W1 += self.learning_rate * np.dot(X.T, self.a1_delta)
        self.b1 += self.learning_rate * np.sum(self.a1_delta, axis=0, keepdims=True)
        self.W2 += self.learning_rate * np.dot(self.a1.T, self.a2_delta)
        self.b2 += self.learning_rate * np.sum(self.a2_delta, axis=0, keepdims=True)
        
    def train(self, X, y, epochs):
        self.loss = []
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, output)
            self.loss.append(np.mean(np.abs(self.error)))
            
            if i % 1000 == 0:
                print("Epoch:", i, " Loss:", np.mean(np.abs(self.error)))
                
    def predict(self, X):
        return self.forward(X)

loss可视化方法：

import matplotlib.pyplot as plt

plt.plot(bp.loss)
plt.title("Standard BP Loss")
plt.xlabel("Epochs")
plt.ylabel("Loss")
plt.show()

plt.plot(abp.loss)
plt.title("Accumulative BP Loss")
plt.xlabel("Epochs")
plt.ylabel("Loss")
plt.show()