We show how to construct nonnegative low-rank approximations of tensors in Tucker and tensor train formats. use alternating projections between the orthant set tensors, using STHOSVD TTSVD algorithms, respectively, further accelerate randomized sketching. The numerical experiments on both synthetic data hyperspectral images decay negative elements that error resulting approximation is close ini...

We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H-eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H-eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors. We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H-eigenva...

A novel tensor decomposition called pattern or P-decomposition is proposed to make it possible to identify replicating structures in complex data, such as textures and patterns in music spectrograms. In order to establish a computational framework for this paradigm, we adopt a multiway (tensor) approach. To this end, a novel tensor product is introduced, and the analysis of its properties shows...

In the paper we derive and discuss a wide class of algorithms for 3D Super-symmetric nonnegative Tensor Factorization (SNTF) or nonnegative symmetric PARAFAC, and as a special case: Symmetric Nonnegative Matrix Factorization (SNMF) that have many potential applications, including multi-way clustering, feature extraction, multisensory or multi-dimensional data analysis, and nonnegative neural sp...

We are interested in finding a solution to the tensor complementarity problem with strong M-tensor, which we call M-tensor problem. propose lower dimensional linear equation approach solve that At each iteration, only system of needs be solved. The coefficient matrices systems independent iteration after finitely many iterations. show starting from zero or some nonnegative point, method generat...

Abstract A decomposition theorem is established for a class of closed Riemannian submanifolds immersed in space form the constant sectional curvature. In particular, it shown that if M has nonnegative curvature and admits Codazzi tensor with “parallel mean curvature”, then locally isometric to direct product irreducible factors determined by spectrum tensor. This global when simply connected, g...

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with N ≥ 3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, grap...