## A Least Squares Formulation for Canonical Correlation Analysis

published: Aug. 29, 2008,   recorded: July 2008,   views: 727
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# Slides

0:00 Slides Motivation - 1 Motivation - 2 Main Contributions Outline Background: CCA - 1 Background: CCA - 2 Background: CCA - 3 Background: Multivariate Linear Regression Background: MLR for Multi-label Classification CCA Versus Multivariate Linear Regression Notations and Definitions Computing CCA via Eigendecomposition Equivalence Relationship between CCA and MLR Notations and Definitions Equivalence Relationship between CCA and MLR CCA Extensions: Regularized CCA CCA Extensions: Sparse CCA CCA Extensions: Entire CCA Solution Path Experiment - Experimental Setup Equivalence Relationship Performance Comparison Sensitivity Study The Entire CCA Solution Path - Questions

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# Description

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