Incremental manifold learning by spectral embedding methods

Authors:
Housen Li;Hao Jiang;Roberto Barrio;Xiangke Liao;Lizhi Cheng;Fang Su
Affiliations:
College of Science, National University of Defense Technology, Changsha 410073, China;College of Science, National University of Defense Technology, Changsha 410073, China;Dpto. de Matemática Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain;College of Computer Science, National University of Defense Technology, Changsha 410073, China;College of Science, National University of Defense Technology, Changsha 410073, China;College of Science, National University of Defense Technology, Changsha 410073, China
Venue:
Pattern Recognition Letters
Year:
2011

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Abstract

Recent years have witnessed great success of manifold learning methods in understanding the structure of multidimensional patterns. However, most of these methods operate in a batch mode and cannot be effectively applied when data are collected sequentially. In this paper, we propose a general incremental learning framework, capable of dealing with one or more new samples each time, for the so-called spectral embedding methods. In the proposed framework, the incremental dimensionality reduction problem reduces to an incremental eigen-problem of matrices. Furthermore, we present, using this framework as a tool, an incremental version of Hessian eigenmaps, the IHLLE method. Finally, we show several experimental results on both synthetic and real world datasets, demonstrating the efficiency and accuracy of the proposed algorithm.