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Equivalence between LDA/QR and Direct LDA

Equivalence between LDA/QR and Direct LDA

Rong-Hua Li, Shuang Liang, George Baciu, Eddie Chan
Copyright: © 2013 |Pages: 16
ISBN13: 9781466624764|ISBN10: 1466624760|EISBN13: 9781466624771
DOI: 10.4018/978-1-4666-2476-4.ch021
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MLA

Li, Rong-Hua, et al. "Equivalence between LDA/QR and Direct LDA." Cognitive Informatics for Revealing Human Cognition: Knowledge Manipulations in Natural Intelligence, edited by Yingxu Wang, IGI Global, 2013, pp. 338-353. https://doi.org/10.4018/978-1-4666-2476-4.ch021

APA

Li, R., Liang, S., Baciu, G., & Chan, E. (2013). Equivalence between LDA/QR and Direct LDA. In Y. Wang (Ed.), Cognitive Informatics for Revealing Human Cognition: Knowledge Manipulations in Natural Intelligence (pp. 338-353). IGI Global. https://doi.org/10.4018/978-1-4666-2476-4.ch021

Chicago

Li, Rong-Hua, et al. "Equivalence between LDA/QR and Direct LDA." In Cognitive Informatics for Revealing Human Cognition: Knowledge Manipulations in Natural Intelligence, edited by Yingxu Wang, 338-353. Hershey, PA: IGI Global, 2013. https://doi.org/10.4018/978-1-4666-2476-4.ch021

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Abstract

Singularity problems of scatter matrices in Linear Discriminant Analysis (LDA) are challenging and have obtained attention during the last decade. Linear Discriminant Analysis via QR decomposition (LDA/QR) and Direct Linear Discriminant analysis (DLDA) are two popular algorithms to solve the singularity problem. This paper establishes the equivalent relationship between LDA/QR and DLDA. They can be regarded as special cases of pseudo-inverse LDA. Similar to LDA/QR algorithm, DLDA can also be considered as a two-stage LDA method. Interestingly, the first stage of DLDA can act as a dimension reduction algorithm. The experiment compares LDA/QR and DLDA algorithms in terms of classification accuracy, computational complexity on several benchmark datasets and compares their first stages. The results confirm the established equivalent relationship and verify their capabilities in dimension reduction.

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