Geometric Methods for Feature Extraction and Dimensional Reduction - A Guided Tour

A self-contained review of the concepts and mathematics underlying several geometric methods for feature extraction and dimensional reduction, and the Nystrom method, which links several of the algorithms, is reviewed.

Abstract

We give a tutorial overview of several geometric methods for feature extractionand dimensional reduction. We divide the methods into projective methods and methods thatmodel the manifold on which the data lies. For projective methods, we review projectionpursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, and orientedPCA; and for the manifold methods, we review multidimensional scaling (MDS), landmarkMDS, Isomap, locally linear embedding, Laplacian eigenmaps and spectral clustering. TheNyström method, which links several of the algorithms, is also reviewed. The goal is to providea self-contained review of the concepts and mathematics underlying these algorithms.