Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Kernel independent component analysis
The Journal of Machine Learning Research
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
A least squares formulation for canonical correlation analysis
Proceedings of the 25th international conference on Machine learning
Overview and recent advances in partial least squares
SLSFS'05 Proceedings of the 2005 international conference on Subspace, Latent Structure and Feature Selection
A shared-subspace learning framework for multi-label classification
ACM Transactions on Knowledge Discovery from Data (TKDD)
A scalable two-stage approach for a class of dimensionality reduction techniques
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Face recognition using two-dimensional CCA and PLS
International Journal of Biometrics
Feature Fusion Using Multiple Component Analysis
Neural Processing Letters
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Canonical correlation analysis (CCA) and partial least squares (PLS) are well-known techniques for feature extraction from two sets of multi-dimensional 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.