rbf神经网络二分类小批量训练

RBF神经网络的小批量训练是一种常用的训练方法，它可以加快训练速度并提高收敛性能。下面是一个使用小批量训练的RBF神经网络二分类示例：

首先，导入所需的库和模块：

import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import make_classification

然后，生成一个示例数据集进行训练：

# 生成示例数据集
X, y = make_classification(n_samples=1000, n_features=10, n_classes=2, random_state=42)

# 数据预处理
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

接下来，定义RBF神经网络的相关函数和参数：

def gaussian_rbf(x, c, s):
    return np.exp(-np.linalg.norm(x-c)**2 / (2 * s**2))

def initialize_centers(X, k):
    random_indices = np.random.choice(range(X.shape[0]), size=k)
    centers = X[random_indices]
    return centers

def compute_activations(X, centers, sigma):
    A = np.zeros((X.shape[0], centers.shape[0]))
    for i, x in enumerate(X):
        for j, c in enumerate(centers):
            A[i, j] = gaussian_rbf(x, c, sigma)
    return A

然后，定义小批量训练的函数：

def minibatch_train(X, y, k, sigma, lr, epochs, batch_size):
    centers = initialize_centers(X, k)
    for epoch in range(epochs):
        indices = np.random.permutation(X.shape[0])
        X = X[indices]
        y = y[indices]
        for i in range(0, X.shape[0], batch_size):
            X_batch = X[i:i+batch_size]
            y_batch = y[i:i+batch_size]
            A = compute_activations(X_batch, centers, sigma)
            W = np.linalg.inv(A.T @ A) @ A.T @ y_batch
            y_pred = A @ W
            error = y_pred - y_batch
            delta_W = - lr * (A.T @ error) / batch_size
            centers -= lr * (W.reshape(-1, 1) * (X_batch - centers)) / (sigma**2 * batch_size)
    return centers

最后，调用小批量训练函数进行训练并进行预测：

k = 10  # 隐藏层神经元数量
sigma = 1.0  # 高斯函数的标准差
lr = 0.01  # 学习率
epochs = 100  # 迭代次数
batch_size = 32  # 批量大小

# 小批量训练
centers = minibatch_train(X_scaled, y, k, sigma, lr, epochs, batch_size)

# 计算隐藏层的输出
A_test = compute_activations(X_scaled, centers, sigma)

# 预测测试集
y_pred = np.sign(A_test)

# 计算准确率
accuracy = np.mean(y_pred == y)

这是一个简单的使用小批量训练的RBF神经网络二分类示例。你可以根据需要调整参数和增加其他功能来进一步改进模型。