用python来实现一个RBF径向基神经网络

使用python来实现一个RBF神经网络，代码如下：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans

class RBFNetwork:
    def __init__(self, num_centers, spread=1.0):
        """
        初始化 RBF 网络
        """
        self.num_centers = num_centers
        self.spread = spread
        self.centers = None
        self.weights = None
    def _gaussian_rbf(self, x, center):
        dist_sq = np.sum((x - center) ** 2, axis=1)        # 计算欧氏距离的平方
        return np.exp(-dist_sq / (2 * self.spread ** 2))   # 应用高斯函数

    def fit(self, X, y):  # 训练 RBF 网络
        N, D = X.shape
        
        kmeans = KMeans(n_clusters=self.num_centers, random_state=42, n_init=10)
        kmeans.fit(X)
        self.centers = kmeans.cluster_centers_
        G = np.zeros((N, self.num_centers))
        for j in range(self.num_centers):
            G[:, j] = self._gaussian_rbf(X, self.centers[j])
        self.weights = np.linalg.pinv(G).dot(y)

    def predict(self, X):            # 预测新数据
        N = X.shape
        G = np.zeros((N, self.num_centers))
        for j in range(self.num_centers):
            G[:, j] = self._gaussian_rbf(X, self.centers[j])
        
        return G.dot(self.weights)

# --- 函数拟合实例 ---
np.random.seed(42)
X_train = np.linspace(-5, 5, 100).reshape(-1, 1)
y_train = np.sin(X_train).ravel() + 0.5 * np.cos(3 * X_train).ravel() + 0.1 * np.random.randn(100)

# 训练 RBF 网络
num_hidden_neurons = 20  # 隐含层节点数
spread_param = 1.5       # 宽度参数，控制平滑度

rbf_net = RBFNetwork(num_centers=num_hidden_neurons, spread=spread_param)
rbf_net.fit(X_train, y_train)

# 预测
X_test = np.linspace(-5, 5, 200).reshape(-1, 1)
y_pred = rbf_net.predict(X_test)
y_true_test = np.sin(X_test).ravel() + 0.5 * np.cos(3 * X_test).ravel()

# 结果
plt.figure(figsize=(10, 6))
plt.scatter(X_train, y_train, color='blue', label='Training Data (Noisy)', alpha=0.6)
plt.plot(X_test, y_true_test, 'g-', label='True Function', linewidth=2)
plt.plot(X_test, y_pred, 'r--', label='RBF Prediction', linewidth=2)
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.grid(True)
plt.show()
print("训练完成。RBF 网络成功逼近了非线性函数。")

python运行上面的代码就可以了。