Tensor Generalized Canonical Correlation Analysis

TL;DR

This paper introduces Tensor GCCA, a novel method for analyzing higher-order tensor data using canonical vectors with orthogonal CP decomposition, extending RGCCA to tensor blocks with algorithms and convergence guarantees.

Contribution

It extends RGCCA to tensor-valued blocks with new algorithms and theoretical guarantees, enabling analysis of higher-order data structures.

Findings

TGCCA outperforms state-of-the-art methods on simulated data.

Algorithms converge reliably with theoretical guarantees.

Effective in real-world multi-block tensor data analysis.

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.