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.

翻译：正则化广义典型相关分析（RGCCA）是一种用于多块数据分析的通用统计框架。RGCCA能够揭示多组变量之间的关系，并涵盖许多经典多变量分析方法作为特例。然而，RGCCA仅处理向量形式的数据块，忽略了其可能具有的高阶结构。本文提出张量GCCA（TGCCA），一种用于分析高阶张量的新方法，其典型向量满足秩为R的正交CP分解。此外，本文基于是否施加可分离协方差结构，提出了两种TGCCA算法，并提供了收敛性保证。通过模拟数据和真实数据评估了TGCCA的效率和实用性，并与现有先进方法进行了比较，结果显示出优越性。