EVD dualdating based online subspace learning
type: Item
instance of: scholarly article
title: EVD dualdating based online subspace learning
zbMATH Open document ID: 1407.62217
DOI: 10.1155/2014/429451
author: Bo Jin
author: Zhongliang Jing
author: Hai-Tao Zhao
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 62H25
zbMATH DE Number: 7016425
describes a project that uses: AR face
describes a project that uses: FERET
describes a project that uses: COIL-100
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/429451
OpenAlex ID: W1988829994
Wikidata QID: Q59067114
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description: scientific article; zbMATH DE number 7016425