期刊
PATTERN RECOGNITION
卷 42, 期 9, 页码 2054-2066出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.patcog.2008.12.009
关键词
Dimensionality reduction; Manifold learning; Locally linear embedding; Laplacian eigenmaps; Local tangent space alignment
资金
- National Basic Research Program of China [2005CB321800]
- National Natural Science Foundation of China [60673090, 60721003]
- National University of Defense Technology [13070201]
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. (C) 2008 Elsevier Ltd. All rights reserved.
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