多核高斯核函数的TCA的python代码

以下是多核高斯核函数的TCA的Python代码：

import numpy as np

def gaussian_kernel(X, Y, sigma):
    """
    计算高斯核矩阵
    :param X: numpy array, shape (n_samples_X, n_features)
    :param Y: numpy array, shape (n_samples_Y, n_features)
    :param sigma: float, 高斯核参数
    :return: numpy array, shape (n_samples_X, n_samples_Y)
    """
    n_samples_X = X.shape[0]
    n_samples_Y = Y.shape[0]
    K = np.zeros((n_samples_X, n_samples_Y))
    for i in range(n_samples_X):
        for j in range(n_samples_Y):
            diff = X[i] - Y[j]
            K[i, j] = np.exp(-np.dot(diff, diff) / (2 * sigma ** 2))
    return K

def multi_kernel_TCA(Xs, sigma_list):
    """
    多核TCA
    :param Xs: list of numpy array, 每个numpy array的shape为(n_samples, n_features)，表示源域数据
    :param sigma_list: list of float, 每个float表示对应的高斯核参数
    :return: list of numpy array, 每个numpy array的shape为(n_samples, n_components)，表示TCA后的源域数据
    """
    n_domains = len(Xs)
    n_samples_list = [X.shape[0] for X in Xs]
    n_samples = sum(n_samples_list)
    n_features = Xs[0].shape[1]
    H = np.zeros((n_samples, n_samples))
    for i in range(n_domains):
        Xi = Xs[i]
        sigma_i = sigma_list[i]
        Ki = gaussian_kernel(Xi, Xi, sigma_i)
        n_samples_i = n_samples_list[i]
        Hii = np.identity(n_samples_i) - np.ones((n_samples_i, n_samples_i)) / n_samples_i
        Xi_centered = np.dot(Hii, Xi)
        for j in range(i + 1, n_domains):
            Xj = Xs[j]
            sigma_j = sigma_list[j]
            Kj = gaussian_kernel(Xj, Xj, sigma_j)
            n_samples_j = n_samples_list[j]
            Hjj = np.identity(n_samples_j) - np.ones((n_samples_j, n_samples_j)) / n_samples_j
            Xj_centered = np.dot(Hjj, Xj)
            Kij = gaussian_kernel(Xi, Xj, sigma_i)
            Kji = gaussian_kernel(Xj, Xi, sigma_j)
            Hij = np.zeros((n_samples_i, n_samples_j))
            for k in range(n_samples_i):
                for l in range(n_samples_j):
                    Hij[k, l] = -Kij[k, l] / (n_samples_i * n_samples_j)
            Hji = np.zeros((n_samples_j, n_samples_i))
            for k in range(n_samples_j):
                for l in range(n_samples_i):
                    Hji[k, l] = -Kji[k, l] / (n_samples_i * n_samples_j)
            H[np.ix_(range(sum(n_samples_list[:i]), sum(n_samples_list[:i+1])), range(sum(n_samples_list[:j]), sum(n_samples_list[:j+1])))] = Hij
            H[np.ix_(range(sum(n_samples_list[:j]), sum(n_samples_list[:j+1])), range(sum(n_samples_list[:i]), sum(n_samples_list[:i+1])))] = Hji
    H = np.dot(H, H)
    eigvals, eigvecs = np.linalg.eig(H)
    eigvals_sorted_indices = np.argsort(eigvals)[::-1]
    eigvecs_sorted = eigvecs[:, eigvals_sorted_indices]
    Zs = []
    for i in range(n_domains):
        Xi = Xs[i]
        n_samples_i = n_samples_list[i]
        Hi = np.identity(n_samples_i) - np.ones((n_samples_i, n_samples_i)) / n_samples_i
        Xi_centered = np.dot(Hi, Xi)
        Ki = gaussian_kernel(Xi_centered, Xi_centered, sigma_list[i])
        Z = np.dot(Ki, eigvecs_sorted[:, :n_features])
        Zs.append(Z)
    return Zs

其中，multi_kernel_TCA函数实现了多核TCA算法，其中sigma_list是高斯核参数的列表，Xs是源域数据的列表，Zs是TCA后的源域数据的列表。需要注意的是，该代码只适用于两个源域的情况，如果需要扩展到多个源域，需要进一步修改。