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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 429451, 21 pages
http://dx.doi.org/10.1155/2014/429451
Research Article

EVD Dualdating Based Online Subspace Learning

1School of Aeronautics and Astronautics, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, China
2School of Information Science and Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China

Received 10 April 2014; Accepted 25 June 2014; Published 24 July 2014

Academic Editor: Yan Liang

Copyright © 2014 Bo Jin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Conventional incremental PCA methods usually only discuss the situation of adding samples. In this paper, we consider two different cases: deleting samples and simultaneously adding and deleting samples. To avoid the NP-hard problem of downdating SVD without right singular vectors and specific position information, we choose to use EVD instead of SVD, which is used by most IPCA methods. First, we propose an EVD updating and downdating algorithm, called EVD dualdating, which permits simultaneous arbitrary adding and deleting operation, via transforming the EVD of the covariance matrix into a SVD updating problem plus an EVD of a small autocorrelation matrix. A comprehensive analysis is delivered to express the essence, expansibility, and computation complexity of EVD dualdating. A mathematical theorem proves that if the whole data matrix satisfies the low-rank-plus-shift structure, EVD dualdating is an optimal rank-k estimator under the sequential environment. A selection method based on eigenvalues is presented to determine the optimal rank k of the subspace. Then, we propose three incremental/decremental PCA methods: EVDD-IPCA, EVDD-DPCA, and EVDD-IDPCA, which are adaptive to the varying mean. Finally, plenty of comparative experiments demonstrate that EVDD-based methods outperform conventional incremental/decremental PCA methods in both efficiency and accuracy.