The connections between principal component analysis and dimensionality reduction methods of manifolds

Authors:
Bo Li;Jin Liu
Affiliations:
College of Computer Science and Technology, Wuhan University of Science and Technology, Wuhan, China;State Key Lab. of Software Engineering, Wuhan, China
Venue:
ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing Theories and Applications: with aspects of artificial intelligence
Year:
2011

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Abstract

Isometric feature mapping (ISOMAP), locally linear embedding (LLE) and Laplacian eigenmaps (LE) are recently proposed nonlinear dimensionality reduction methods of manifolds. When these methods are satisfied with some specific constraints, some hidden connections can be found between principal component analysis (PCA) and those manifolds learning based approaches. In this paper, some derivations are presented to validate the idea and then some conclusions are drawn.