On the equivalence between canonical correlation analysis and orthonormalized partial least squares

Liang Sun, Shuiwang Ji, Shipeng Yu, Jieping Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

37 Scopus citations

Abstract

Canonical correlation analysis (CCA) and partial least squares (PLS) are well-known techniques for feature extraction from two sets of multidimensional variables. The fundamental difference between CCA and PLS is that CCA maximizes the correlation while PLS maximizes the covariance. Although both CCA and PLS have been applied successfully in various applications, the intrinsic relationship between them remains unclear. In this paper, we attempt to address this issue by showing the equivalence relationship between CCA and orthonormalized partial least squares (OPLS), a variant of PLS. We further extend the equivalence relationship to the case when regularization is employed for both sets of variables. In addition, we show that the CCA projection for one set of variables is independent of the regularization on the other set of variables. We have performed experimental studies using both synthetic and real data sets and our results confirm the established equivalence relationship. The presented analysis provides novel insights into the connection between these two existing algorithms as well as the effect of the regularization.

Original languageEnglish (US)
Title of host publicationIJCAI-09 - Proceedings of the 21st International Joint Conference on Artificial Intelligence
PublisherInternational Joint Conferences on Artificial Intelligence
Pages1230-1235
Number of pages6
ISBN (Print)9781577354260
StatePublished - Jan 1 2009
Event21st International Joint Conference on Artificial Intelligence, IJCAI 2009 - Pasadena, United States
Duration: Jul 11 2009Jul 16 2009

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823

Conference

Conference21st International Joint Conference on Artificial Intelligence, IJCAI 2009
CountryUnited States
CityPasadena
Period7/11/097/16/09

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ASJC Scopus subject areas

  • Artificial Intelligence

Cite this

Sun, L., Ji, S., Yu, S., & Ye, J. (2009). On the equivalence between canonical correlation analysis and orthonormalized partial least squares. In IJCAI-09 - Proceedings of the 21st International Joint Conference on Artificial Intelligence (pp. 1230-1235). (IJCAI International Joint Conference on Artificial Intelligence). International Joint Conferences on Artificial Intelligence.