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Computer Science > Machine Learning

arXiv:2003.11205 (cs)
[Submitted on 25 Mar 2020]

Title:Generalized Canonical Correlation Analysis: A Subspace Intersection Approach

Authors:Mikael Sørensen, Charilaos I. Kanatsoulis, Nicholas D. Sidiropoulos
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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.
Subjects: Machine Learning (cs.LG); Information Retrieval (cs.IR); Signal Processing (eess.SP); Machine Learning (stat.ML)
Cite as: arXiv:2003.11205 [cs.LG]
  (or arXiv:2003.11205v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2003.11205
Related DOI: https://doi.org/10.1109/TSP.2021.3061218

Submission history

From: Charilaos Kanatsoulis [view email]
[v1] Wed, 25 Mar 2020 04:04:25 UTC (469 KB)
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