TY - GEN
T1 - CPM
T2 - Sixth SIAM International Conference on Data Mining
AU - Ye, Jieping
AU - Xiong, Tao
AU - Janardan, Ravi
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
KW - Covariance
KW - Dimension reduction
KW - Heteroscedastic discriminant analysis
KW - Linear discriminant analysis
UR - http://www.scopus.com/inward/record.url?scp=33745462294&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33745462294&partnerID=8YFLogxK
U2 - 10.1137/1.9781611972764.3
DO - 10.1137/1.9781611972764.3
M3 - Conference contribution
AN - SCOPUS:33745462294
SN - 089871611X
SN - 9780898716115
T3 - Proceedings of the Sixth SIAM International Conference on Data Mining
SP - 24
EP - 34
BT - Proceedings of the Sixth SIAM International Conference on Data Mining
PB - Society for Industrial and Applied Mathematics
Y2 - 20 April 2006 through 22 April 2006
ER -