Incremental Laplacian eigenmaps by preserving adjacent information between data points

Authors:
Peng Jia;Junsong Yin;Xinsheng Huang;Dewen Hu
Affiliations:
Department of Automatic Control, College of Mechatronics and Automation, National University of Defense Technology, Changsha, Hunan 410073, China;Beijing Institute of Electronic System Engineering, 100141, China;Department of Automatic Control, College of Mechatronics and Automation, National University of Defense Technology, Changsha, Hunan 410073, China;Department of Automatic Control, College of Mechatronics and Automation, National University of Defense Technology, Changsha, Hunan 410073, China
Venue:
Pattern Recognition Letters
Year:
2009

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Abstract

Traditional nonlinear manifold learning methods have achieved great success in dimensionality reduction and feature extraction, most of which are batch modes. However, if new samples are observed, the batch methods need to be calculated repeatedly, which is computationally intensive, especially when the number or dimension of the input samples are large. This paper presents incremental learning algorithms for Laplacian eigenmaps, which computes the low-dimensional representation of data set by optimally preserving local neighborhood information in a certain sense. Sub-manifold analysis algorithm together with an alternative formulation of linear incremental method is proposed to learn the new samples incrementally. The locally linear reconstruction mechanism is introduced to update the existing samples' embedding results. The algorithms are easy to be implemented and the computation procedure is simple. Simulation results testify the efficiency and accuracy of the proposed algorithms.