Tensor Generalized Canonical Correlation Analysis

• URL: http://arxiv.org/abs/2302.05277v1
• Date: Fri, 10 Feb 2023 14:41:12 GMT
• Title: Tensor Generalized Canonical Correlation Analysis
• Authors: Fabien Girka, Arnaud Gloaguen, Laurent Le Brusquet, Violetta Zujovic, Arthur Tenenhaus
• Abstract summary: Generalized Generalized Canonical Correlation Analysis (RGCCA) is a general statistical framework for multi-block data analysis. This paper presents TGCCA, a new method for analyzing higher-order tensors with admitting an canonical rank-R decomposition. The efficiency and usefulness of TGCCA are evaluated on simulated and real data and compared favorably to state-of-the-art approaches.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Regularized Generalized Canonical Correlation Analysis (RGCCA) is a general statistical framework for multi-block data analysis. RGCCA enables deciphering relationships between several sets of variables and subsumes many well-known multivariate analysis methods as special cases. However, RGCCA only deals with vector-valued blocks, disregarding their possible higher-order structures. This paper presents Tensor GCCA (TGCCA), a new method for analyzing higher-order tensors with canonical vectors admitting an orthogonal rank-R CP decomposition. Moreover, two algorithms for TGCCA, based on whether a separable covariance structure is imposed or not, are presented along with convergence guarantees. The efficiency and usefulness of TGCCA are evaluated on simulated and real data and compared favorably to state-of-the-art approaches.

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