A Least Squares Formulation for Canonical Correlation Analysis

author: Shuiwang Ji, The Biodesign Institute, Arizona State University
published: Aug. 29, 2008,   recorded: July 2008,   views: 846
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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

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Comment1 an baiguo, October 8, 2008 at 3:56 a.m.:

very good

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