Tensor Canonical Correlation Analysis for Multi-View Dimension Reduction

Luo, Y; Tao, D; Ramamohanarao, K; Xu, C; Wen, Y

Tensor Canonical Correlation Analysis for Multi-View Dimension Reduction

Luo, Y Tao, D

Ramamohanarao, K Xu, C Wen, Y

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Knowledge and Data Engineering, 2015, 27 (11), pp. 3111 - 3124
Issue Date:: 2015-11-01

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Field	Value	Language
dc.contributor.author	Luo, Y	en_US
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.contributor.author	Ramamohanarao, K	en_US
dc.contributor.author	Xu, C	en_US
dc.contributor.author	Wen, Y	en_US
dc.date.issued	2015-11-01	en_US
dc.identifier.citation	IEEE Transactions on Knowledge and Data Engineering, 2015, 27 (11), pp. 3111 - 3124	en_US
dc.identifier.issn	1041-4347	en_US
dc.identifier.uri	http://hdl.handle.net/10453/35425
dc.description.abstract	© 2015 IEEE. Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multi-view data, it ignores the high order statistics (correlation information) which can only be discovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the canonical correlation of multiple (more than two) views. Crucially, we prove that the main problem of multi-view canonical correlation maximization is equivalent to finding the best rank-1 approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained. In addition, a non-linear extension of TCCA is presented. Experiments on various challenge tasks, including large scale biometric structure prediction, internet advertisement classification, and web image annotation, demonstrate the effectiveness of the proposed method.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP140102164
dc.relation	http://purl.org/au-research/grants/arc/FT130101457
dc.relation.ispartof	IEEE Transactions on Knowledge and Data Engineering	en_US
dc.relation.isbasedon	10.1109/TKDE.2015.2445757	en_US
dc.subject.classification	Information Systems	en_US
dc.title	Tensor Canonical Correlation Analysis for Multi-View Dimension Reduction	en_US
dc.type	Journal Article
utslib.citation.volume	11	en_US
utslib.citation.volume	27	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	08 Information and Computing Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access
pubs.issue	11	en_US
pubs.publication-status	Published	en_US
pubs.volume	27	en_US

Abstract:

© 2015 IEEE. Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multi-view data, it ignores the high order statistics (correlation information) which can only be discovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the canonical correlation of multiple (more than two) views. Crucially, we prove that the main problem of multi-view canonical correlation maximization is equivalent to finding the best rank-1 approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained. In addition, a non-linear extension of TCCA is presented. Experiments on various challenge tasks, including large scale biometric structure prediction, internet advertisement classification, and web image annotation, demonstrate the effectiveness of the proposed method.

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http://hdl.handle.net/10453/35425