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：常规化的共生关系分析(CARGCA)是多区块数据分析的一般统计框架,它能够破译数组变量和子集之间的关系,许多众所周知的多变分析方法是特殊情况,然而,共生关系分析只涉及矢量价值区块,而忽视其可能存在的更高级结构,本文介绍了Tensor GGCA(TGCA),这是分析高阶高压控控控载器的新方法,允许直角级RCP分解。此外,根据是否强制实行分立的共变异结构,还提出了两套TGCA的算法,同时提供了趋同保证,根据模拟和真实数据对TGCCA的效率和有用性进行了评价,并与最新方法进行了比较。