拉普拉斯特征映射 matlab代码

以下是拉普拉斯特征映射的 MATLAB 代码实现：

function Y = laplacian_eigenmaps(X, n_components, k, gamma)
% Laplacian Eigenmaps algorithm for dimensionality reduction.
%
% Parameters:
% -----------
% X: matrix, shape (n_samples, n_features)
%     The input data to reduce dimensionality.
% n_components: int
%     The number of components to keep.
% k: int, optional (default=5)
%     Number of neighbors to use when constructing the adjacency matrix.
% gamma: float, optional (default=0.1)
%     Parameter controlling the strength of the affinity matrix.
%
% Returns:
% --------
% Y: matrix, shape (n_samples, n_components)
%     The reduced data.

% Compute pairwise euclidean distances
D = pdist2(X, X);
[~, indices] = sort(D, 2);
indices = indices(:, 2:k+1);
W = exp(-gamma * D.^2);
W(sub2ind(size(W), repmat((1:size(W,1))', [1 k]), indices)) = 0;

% Compute the degree matrix
D = sum(W, 2);
D = spdiags(D, 0, size(W, 1), size(W, 1));

% Compute the unnormalized Laplacian
L = D - W;

% Compute the normalized Laplacian
D_inv_sqrt = spdiags(1 ./ sqrt(D), 0, size(W, 1), size(W, 1));
L_norm = D_inv_sqrt * L * D_inv_sqrt;

% Compute the eigenvectors and eigenvalues of L_norm
options.disp = 0;
[eigenvectors, eigenvalues] = eigs(L_norm, n_components+1, 'SM', options);

% Sort the eigenvectors by eigenvalues
[~, idx] = sort(diag(eigenvalues));
eigenvectors = eigenvectors(:, idx);

% Remove the first eigenvector (eigenvalue=0)
eigenvectors = eigenvectors(:, 2:n_components+1);

% Normalize the eigenvectors
Y = normr(eigenvectors);

end

这个实现使用了 MATLAB 的 `pdist2` 函数计算邻居之间的距离，使用了 `spdiags` 函数来构造对角线矩阵，使用了 `eigs` 函数计算特征向量和特征值，并使用 `normr` 函数对特征向量进行归一化。