A least squares formulation for canonical correlation analysis

Liang Sun, Shuiwang Ji, Jieping Ye

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

63 Scopus citations

Abstract

Canonical Correlation Analysis (CCA) is a well-known technique for finding the correlations between two sets of multi-dimensional variables. It projects both sets of variables into a lower-dimensional space in which they are maximally correlated. CCA is commonly applied for supervised dimensionality reduction, in which one of the multi-dimensional variables is derived from the class label. It has been shown that CCA can be formulated as a least squares problem in the binary-class case. However, their relationship in the more general setting remains unclear. In this paper, we show that, under a mild condition which tends to hold for high-dimensional data, CCA in multi-label classifications can be formulated as a least squares problem. Based on this equivalence relationship, we propose several CCA extensions including sparse CCA using 1-norm regularization. Experiments on multi-label data sets confirm the established equivalence relationship. Results also demonstrate the effectiveness of the proposed CCA extensions.

Original languageEnglish (US)
Title of host publicationProceedings of the 25th International Conference on Machine Learning
PublisherAssociation for Computing Machinery (ACM)
Pages1024-1031
Number of pages8
ISBN (Print)9781605582054
DOIs
StatePublished - Jan 1 2008
Event25th International Conference on Machine Learning - Helsinki, Finland
Duration: Jul 5 2008Jul 9 2008

Publication series

NameProceedings of the 25th International Conference on Machine Learning

Other

Other25th International Conference on Machine Learning
CountryFinland
CityHelsinki
Period7/5/087/9/08

ASJC Scopus subject areas

  • Artificial Intelligence
  • Human-Computer Interaction
  • Software

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