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An approximate closed-form solution to correlation similarity discriminant analysis
Taiping Zhang1; Yuan Yan Tang2; C.L. Philip Chen2; Zhaowei Shang1; Bin Fang1
2014-07-05
Source PublicationNeurocomputing
ISSN0925-2312
Volume135Pages:284-298
Abstract

High-dimensional data often lie on relatively low-dimensional manifold, while the nonlinear geometry of that manifold is often embedded in the similarities between the data points. Correlation as a similarity measure is able to capture these similarity structures. In this paper, we present a new correlation-based similarity discriminant analysis (CSDA) method for class separability problem. Firstly, a new formula based on the trace of matrix is proposed for computing the correlation between data points. Then a criterion maximizing the difference between within-class correlation and between-class correlation is proposed to achieve maximum class separability. The optimization of the criterion function can be transformed to an eigen-problem and an approximate closed-form solution can be obtained. Theoretical analysis shows that CSDA can be interpreted in the framework of graph-based learning. Furthermore, we also show how to extend CSDA to a nonlinear case through kernel-based mapping. Extensive experiments on different data sets are reported to illustrate the effectiveness of the proposed method in comparison with other competing methods. 

KeywordCorrelation Feature Extraction Linear Discriminant Analysis Similarity Discriminant Analysis Similarity Measure
DOIhttps://doi.org/10.1016/j.neucom.2013.12.015
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science
WOS SubjectComputer Science, Artificial Intelligence
WOS IDWOS:000335871200032
PublisherELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
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Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF COMPUTER AND INFORMATION SCIENCE
Corresponding AuthorTaiping Zhang
Affiliation1.College of Computer Science, Chongqing University, Chongqing 400030, China
2.Faculty of Science and Technology, University of Macau, Macau, China
Recommended Citation
GB/T 7714
Taiping Zhang,Yuan Yan Tang,C.L. Philip Chen,et al. An approximate closed-form solution to correlation similarity discriminant analysis[J]. Neurocomputing,2014,135:284-298.
APA Taiping Zhang,Yuan Yan Tang,C.L. Philip Chen,Zhaowei Shang,&Bin Fang.(2014).An approximate closed-form solution to correlation similarity discriminant analysis.Neurocomputing,135,284-298.
MLA Taiping Zhang,et al."An approximate closed-form solution to correlation similarity discriminant analysis".Neurocomputing 135(2014):284-298.
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