MATLAB Code Implementation for Manifold Learning

Manifold learning is a technique used for dimensionality reduction of high-dimensional data. Algorithms such as Isomap, LLE, and LTSA are commonly employed methods for nonlinear data dimensionality reduction. These algorithms work by discovering the underlying manifold structure between data points in high-dimensional space and mapping the data to a lower-dimensional space, making data visualization and analysis more manageable. Key implementation aspects include: - Isomap uses geodesic distances computed through neighborhood graphs instead of Euclidean distances - LLE (Locally Linear Embedding) preserves local linear relationships by reconstructing weights from neighboring points - LTSA (Local Tangent Space Alignment) constructs local tangent spaces and aligns them to obtain global coordinates Manifold learning has been widely applied in fields such as image processing, natural language processing, and bioinformatics. MATLAB implementations typically involve constructing neighborhood graphs, computing distance matrices, and solving eigenvalue problems to obtain low-dimensional embeddings.