CPM: A covariance-preserving projection method

Jieping Ye; Tao Xiong; Ravi Janardan

doi:10.1137/1.9781611972764.3

CPM: A covariance-preserving projection method

Jieping Ye, Tao Xiong, Ravi Janardan

Computing, Informatics and Decision Systems Engineering, School of (CIDSE)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

Abstract

Dimension reduction is critical in many areas of data mining and machine learning. In this paper, a Covariance-preserving Projection Method (CPM for short) is proposed for dimension reduction. CPM maximizes the class discrimination and also preserves approximately the class covariance. The optimization involved in CPM can be formulated as low rank approximations of a collection of matrices, which can be solved iteratively. Our theoretical and empirical analysis reveals the relationship between CPM and Linear Discriminant Analysis (LDA), Sliced Average Variance Estimator (SAVE), and Heteroscedastic Discriminant Analysis (HDA). This gives us new insights into the nature of these different algorithms. We use both synthetic and real-world datasets to evaluate the effectiveness of the proposed algorithm.

Original language	English (US)
Title of host publication	Proceedings of the Sixth SIAM International Conference on Data Mining
Publisher	Society for Industrial and Applied Mathematics
Pages	24-34
Number of pages	11
ISBN (Print)	089871611X, 9780898716115
DOIs	https://doi.org/10.1137/1.9781611972764.3
State	Published - 2006
Event	Sixth SIAM International Conference on Data Mining - Bethesda, MD, United States Duration: Apr 20 2006 → Apr 22 2006

Publication series

Name	Proceedings of the Sixth SIAM International Conference on Data Mining
Volume	2006

Other

Other	Sixth SIAM International Conference on Data Mining
Country	United States
City	Bethesda, MD
Period	4/20/06 → 4/22/06

Keywords

Covariance
Dimension reduction
Heteroscedastic discriminant analysis
Linear discriminant analysis

ASJC Scopus subject areas

Engineering(all)

Access to Document

10.1137/1.9781611972764.3

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CPM : A covariance-preserving projection method. / Ye, Jieping; Xiong, Tao; Janardan, Ravi.

Proceedings of the Sixth SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2006. p. 24-34 (Proceedings of the Sixth SIAM International Conference on Data Mining; Vol. 2006).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ye, J, Xiong, T & Janardan, R 2006, CPM: A covariance-preserving projection method. in Proceedings of the Sixth SIAM International Conference on Data Mining. Proceedings of the Sixth SIAM International Conference on Data Mining, vol. 2006, Society for Industrial and Applied Mathematics, pp. 24-34, Sixth SIAM International Conference on Data Mining, Bethesda, MD, United States, 4/20/06. https://doi.org/10.1137/1.9781611972764.3

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