使用Python构建三层BP神经网络实现鸢尾花分类

以下是一个示例代码，实现了一个三层的BP神经网络，输入层为4个特征，隐层大小为10，输出层为3个分类。使用iris数据集进行训练和测试，输出了模型的损失值和准确率曲线变化。

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

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

# 将标签转为one-hot编码
Y = np.zeros((len(y), 3))
for i in range(len(y)):
    Y[i][y[i]] = 1

# 将数据集分为训练集和测试集
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.2)

# 定义sigmoid函数和它的导数
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def sigmoid_prime(x):
    return sigmoid(x) * (1 - sigmoid(x))

# 定义BP神经网络类
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

        # 初始化权重矩阵和偏置向量
        self.W1 = np.random.randn(self.input_size, self.hidden_size)
        self.b1 = np.zeros((1, self.hidden_size))
        self.W2 = np.random.randn(self.hidden_size, self.output_size)
        self.b2 = np.zeros((1, self.output_size))

    # 前向传播
    def forward(self, X):
        self.z1 = np.dot(X, self.W1) + self.b1
        self.a1 = sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.W2) + self.b2
        self.a2 = sigmoid(self.z2)
        return self.a2

    # 反向传播
    def backward(self, X, Y, output):
        delta3 = (output - Y) * sigmoid_prime(self.z2)
        dW2 = np.dot(self.a1.T, delta3)
        db2 = np.sum(delta3, axis=0, keepdims=True)

        delta2 = np.dot(delta3, self.W2.T) * sigmoid_prime(self.z1)
        dW1 = np.dot(X.T, delta2)
        db1 = np.sum(delta2, axis=0)

        # 更新权重矩阵和偏置向量
        self.W2 -= 0.1 * dW2
        self.b2 -= 0.1 * db2
        self.W1 -= 0.1 * dW1
        self.b1 -= 0.1 * db1

    # 训练模型
    def train(self, X, Y):
        for i in range(10000):
            output = self.forward(X)
            self.backward(X, Y, output)

    # 预测
    def predict(self, X):
        output = self.forward(X)
        return np.argmax(output, axis=1)

# 创建BP神经网络模型
nn = NeuralNetwork(input_size=4, hidden_size=10, output_size=3)

# 训练模型
nn.train(X_train, Y_train)

# 在测试集上评估模型
Y_hat = nn.predict(X_test)
accuracy = np.mean(Y_hat == np.argmax(Y_test, axis=1))
print('Accuracy:', accuracy)

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

losses = []
accuracies = []
for i in range(10000):
    output = nn.forward(X_train)
    loss = np.mean((output - Y_train) ** 2)
    losses.append(loss)
    Y_hat = nn.predict(X_test)
    accuracy = np.mean(Y_hat == np.argmax(Y_test, axis=1))
    accuracies.append(accuracy)
    nn.backward(X_train, Y_train, output)

plt.subplot(2, 1, 1)
plt.plot(losses)
plt.title('Loss')

plt.subplot(2, 1, 2)
plt.plot(accuracies)
plt.title('Accuracy')

plt.show()

运行代码后，可以得到如下的损失值和准确率曲线变化图：