Stable local dimensionality reduction approaches

Authors:
Chenping Hou;Changshui Zhang;Yi Wu;Yuanyuan Jiao
Affiliations:
Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073, China and State Key Laboratory of Intelligent Technology and Systems, Tsinghua National L ...;State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100 ...;Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073, China;Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073, China
Venue:
Pattern Recognition
Year:
2009

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Abstract

Dimensionality reduction is a big challenge in many areas. A large number of local approaches, stemming from statistics or geometry, have been developed. However, in practice these local approaches are often in lack of robustness, since in contrast to maximum variance unfolding (MVU), which explicitly unfolds the manifold, they merely characterize local geometry structure. Moreover, the eigenproblems that they encounter, are hard to solve. We propose a unified framework that explicitly unfolds the manifold and reformulate local approaches as the semi-definite programs instead of the above-mentioned eigenproblems. Three well-known algorithms, locally linear embedding (LLE), laplacian eigenmaps (LE) and local tangent space alignment (LTSA) are reinterpreted and improved within this framework. Several experiments are presented to demonstrate the potential of our framework and the improvements of these local algorithms.