Common Manifold Learning Methods: LDA and LLE

There are numerous common manifold learning methods, such as Locally Linear Embedding (LLE), Laplacian Eigenmaps (LE), Isometric Mapping (IsoMap), and more. However, we specifically focus on LDA (Linear Discriminant Analysis) and LLE methods in this implementation. This program is not only debugged and operational, but it's particularly suitable for beginners who want to learn manifold learning concepts. Through this implementation, you can easily understand the principles and implementation approaches of LDA and LLE. The LDA implementation demonstrates dimensionality reduction while maximizing class separability through scatter matrix calculations and eigenvalue decomposition. The LLE algorithm showcases neighborhood preservation by reconstructing local linear relationships and solving optimization problems for embedding. This program provides clear insights into the advantages and appropriate application scenarios of both methods, featuring code comments that explain key functions like neighborhood selection, weight matrix computation, and embedding optimization. You'll gain practical understanding of how these algorithms handle nonlinear dimensionality reduction and pattern recognition tasks.