Block structure-based covariance tensor decomposition for group identification in matrix variables

In research fields such as financial market analysis and social network research, understanding variable grouping relationships is fundamental to effective data analysis. This study describes the concept of the covariance tensor and emphasizes its significant role in analyzing matrix variable groupings through block structures. We propose a novel tensor decomposition-based method to exploit these structures for group identification. In addition, we explore the asymptotic properties of our estimators, focusing on the precision of the estimation of the number of groups and the asymptotic convergence of classification error rates to zero. We validate the effectiveness of the method through extensive numerical simulations across diverse data volumes and complexities, affirming its capability in variable grouping.