基于Python实现鸢尾花分类的3层BP神经网络

本文将使用Python语言构建一个3层BP神经网络，并使用经典的鸢尾花数据集进行分类实验。该网络包含4个输入特征（花萼长度、花萼宽度、花瓣长度、花瓣宽度）、10个隐藏神经元和3个输出类别（山鸢尾、变色鸢尾、维吉尼亚鸢尾）。我们将通过反向传播算法训练模型，最终实现对鸢尾花的准确分类。

代码实现

import numpy as np
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split

# sigmoid函数
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# sigmoid函数的导数
def sigmoid_derivative(x):
    return x * (1 - x)

# 构建神经网络
class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        
        # 随机初始化权重
        self.weights1 = np.random.randn(self.input_size, self.hidden_size)
        self.weights2 = np.random.randn(self.hidden_size, self.output_size)
        
        # 初始化偏置
        self.bias1 = np.zeros((1, self.hidden_size))
        self.bias2 = np.zeros((1, self.output_size))
        
    # 前向传播
    def forward(self, X):
        self.z1 = np.dot(X, self.weights1) + self.bias1
        self.a1 = sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.weights2) + self.bias2
        self.a2 = sigmoid(self.z2)
        return self.a2
    
    # 反向传播
    def backward(self, X, y, output):
        self.output_error = y - output
        self.output_delta = self.output_error * sigmoid_derivative(output)
        
        self.hidden_error = np.dot(self.output_delta, self.weights2.T)
        self.hidden_delta = self.hidden_error * sigmoid_derivative(self.a1)
        
        self.weights1 += np.dot(X.T, self.hidden_delta)
        self.weights2 += np.dot(self.a1.T, self.output_delta)
        
        self.bias1 += np.sum(self.hidden_delta, axis=0)
        self.bias2 += np.sum(self.output_delta, axis=0)
    
    # 训练模型
    def train(self, X, y, epochs):
        self.loss = []
        self.accuracy = []
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, output)
            loss = np.mean(np.square(y - output))
            predicted_class = np.argmax(output, axis=1)
            true_class = np.argmax(y, axis=1)
            accuracy = np.mean(predicted_class == true_class)
            self.loss.append(loss)
            self.accuracy.append(accuracy)
            if i % 100 == 0:
                print('Epoch:', i, 'Loss:', loss, 'Accuracy:', accuracy)

# 加载数据集
iris = load_iris()
X = iris.data
y = iris.target

# 将标签转换为独热编码
n_classes = 3
y_onehot = np.zeros((len(y), n_classes))
for i in range(len(y)):
    y_onehot[i, y[i]] = 1

# 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X, y_onehot, test_size=0.2, random_state=0)

# 构建神经网络
input_size = 4
hidden_size = 10
output_size = 3
nn = NeuralNetwork(input_size, hidden_size, output_size)

# 训练模型
epochs = 1000
nn.train(X_train, y_train, epochs)

# 绘制损失函数和准确率的曲线变化
import matplotlib.pyplot as plt

plt.plot(range(epochs), nn.loss)
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.show()

plt.plot(range(epochs), nn.accuracy)
plt.xlabel('Epochs')
plt.ylabel('Accuracy')
plt.show()

# 在测试集上评估模型
output = nn.forward(X_test)
predicted_class = np.argmax(output, axis=1)
true_class = np.argmax(y_test, axis=1)
accuracy = np.mean(predicted_class == true_class)
print('Accuracy on test set:', accuracy)

实验结果

Epoch: 0 Loss: 0.2358100833960581 Accuracy: 0.4083333333333333
Epoch: 100 Loss: 0.05034545262871095 Accuracy: 0.9583333333333334
Epoch: 200 Loss: 0.041641629105006495 Accuracy: 0.975
Epoch: 300 Loss: 0.03440676453880626 Accuracy: 0.975
Epoch: 400 Loss: 0.028630343852315764 Accuracy: 0.975
Epoch: 500 Loss: 0.02455513306488438 Accuracy: 0.975
Epoch: 600 Loss: 0.02158420473621269 Accuracy: 0.9833333333333333
Epoch: 700 Loss: 0.019338783402717488 Accuracy: 0.9916666666666667
Epoch: 800 Loss: 0.017564335944329147 Accuracy: 0.9916666666666667
Epoch: 900 Loss: 0.016100101928982987 Accuracy: 0.9916666666666667Accuracy on test set: 1.0

可以看到，模型在训练过程中损失函数逐渐下降，准确率逐渐提高，最终在测试集上实现了100%的准确率。

总结

本文成功构建并训练了一个3层BP神经网络，并使用鸢尾花数据集进行了分类实验。实验结果表明，该模型能够有效地对鸢尾花进行分类，最终在测试集上达到了100%的准确率。这证明了BP神经网络在解决分类问题的有效性。