Generalized Canonical Correlation Analysis: A Subspace Intersection Approach

• URL: http://arxiv.org/abs/2003.11205v1
• Date: Wed, 25 Mar 2020 04:04:25 GMT
• Title: Generalized Canonical Correlation Analysis: A Subspace Intersection Approach
• Authors: Mikael S{\o}rensen, Charilaos I. Kanatsoulis, and Nicholas D. Sidiropoulos
• Abstract summary: Generalized Canonical Correlation Analysis (GCCA) is an important tool that finds numerous applications in data mining, machine learning, and artificial intelligence. This paper offers a fresh algebraic perspective of GCCA based on a (bi-linear) generative model that naturally captures its essence. A novel GCCA algorithm is proposed based on subspace intersection, which scales up to handle large GCCA tasks.
• Score: 30.475159163815505
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generalized Canonical Correlation Analysis (GCCA) is an important tool that finds numerous applications in data mining, machine learning, and artificial intelligence. It aims at finding `common' random variables that are strongly correlated across multiple feature representations (views) of the same set of entities. CCA and to a lesser extent GCCA have been studied from the statistical and algorithmic points of view, but not as much from the standpoint of linear algebra. This paper offers a fresh algebraic perspective of GCCA based on a (bi-)linear generative model that naturally captures its essence. It is shown that from a linear algebra point of view, GCCA is tantamount to subspace intersection; and conditions under which the common subspace of the different views is identifiable are provided. A novel GCCA algorithm is proposed based on subspace intersection, which scales up to handle large GCCA tasks. Synthetic as well as real data experiments are provided to showcase the effectiveness of the proposed approach.

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