Paper Info
Title
A least squares formulation for canonical correlation analysis
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 binaryclass 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.
Year
DOI
Venue
2008
10.1145/1390156.1390285
ICML
Keywords
Field
DocType
high-dimensional data,multi-dimensional variable,cca extension,established equivalence relationship,proposed cca extension,sparse cca,canonical correlation analysis,multi-label classification,equivalence relationship,squares problem,multi-label data set,squares formulation,high dimensional data,least square
Least squares,Canonical correspondence analysis,Applied mathematics,Data set,Combinatorics,Dimensionality reduction,Pattern recognition,Canonical correlation,Regularization (mathematics),Equivalence (measure theory),Artificial intelligence,Mathematics
Conference
Citations 
PageRank 
References 
40
2.08
12
Authors
3
Name
Order
Citations
PageRank
Liang Sun150024.61
Shuiwang Ji22579122.25
Jieping Ye36943351.37