Earlier work has shown that no extension of the Eckart–Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart–Young SVD approximation theorem to the orthogonal rank tensor decomposition, answering an open question previously posed by Kolda [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 243–355].

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between lowrank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the residual. We prove convergence to the globally optimal solution under natural incoh...

We present a hybrid clustering algorithm of multiple information sources via tensor decomposition, which can be regarded an extension of the spectral clustering based on modularity maximization. This hybrid clustering can be solved by the truncated higher-order singular value decomposition (HOSVD). Experimental results conducted on the synthetic data have demonstrated the effectiveness. keyword...

We analyze the decomposition of tensor products between infinite dimensional (unitary) and finite-dimensional (non-unitary) representations of SL(2,R). Using classical results on indefinite inner product spaces, we derive explicit decomposition formulae, true modulo a natural cohomological reduction, for the tensor products. PACS: 02.20.-a, 03.65Fd, 11-30.-j

Let V be the 7-dimensional irreducible representations of G2. We decompose the tensor power V ⊗n into irreducible representations of G2 and obtain all irreducible representations of G2 in the decomposition. This generalizes Weyl’s work on the construction of irreducible representations and decomposition of tensor products for classical groups to the exceptional group G2.

This article introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one mode and several tabular modes. The problem is motivated by high-order longitudinal data analysis. Our model assumes observed to be random realization of an approximate CP low-rank measured on discrete time grid. Incorporating algebra theory reproducing ...