Tensor Generalized Canonical Correlation Analysis
This work addresses the problem of multi-block data analysis for researchers and practitioners in fields like machine learning and statistics, offering a novel extension to handle tensor structures, though it is incremental as it builds upon existing RGCCA frameworks.
The paper tackles the limitation of RGCCA in handling only vector-valued data by introducing Tensor GCCA (TGCCA), a method for analyzing higher-order tensors with orthogonal rank-R CP decomposition, and demonstrates its efficiency and usefulness through favorable comparisons with state-of-the-art approaches on simulated and real data.
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.