MATLAB Implementation of Manifold Learning

In the field of machine learning, manifold learning is a crucial technique that helps identify low-dimensional latent structures within high-dimensional data. Among various approaches, the HE (Hessian Eigenmaps) algorithm stands as one of the most classical methods in manifold learning, serving as a fundamental linear subspace learning technique widely applied in domains like image processing and speech recognition. By implementing manifold learning through MATLAB code, users can better understand and execute the HE algorithm, achieving improved results in practical applications. The MATLAB implementation typically involves constructing neighborhood graphs, computing Hessian matrices, and performing eigenvalue decomposition to extract meaningful low-dimensional embeddings. Key functions often include pdist2 for distance calculation, eigs for sparse eigenvalue computation, and optimization routines for handling large-scale datasets efficiently.