Nonlinear Manifold Learning 6 . 454 Summary
Manifold learning is the process of estimating a low-dimensional structure which underlies a collection of high-dimensional data. Here we review two popular methods for nonlinear dimensionality reduction, locally linear embedding (LLE, [1]) and IsoMap [2]. We also discuss their roots in principal component analysis and multidimensional scaling, and provide a brief comparison of the underlying assumptions, strengths, and weaknesses of each algorithm.