Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral co-clustering method that simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor and generalizes to tensors with any number of m...

We are concerned with the tensor equations whose coefficient tensors M-tensors. first propose a Newton method for solving equation positive constant term and establish its global quadratic convergence. Then we extend to solve nonnegative At last, do numerical experiments test proposed methods. The results show that methods quite efficient.

A real symmetric tensor is completely positive (CP) if it a sum of powers nonnegative vectors. We propose dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations Detection tensors and the linear conic optimization with cones can be solved more efficiently by approach.

We investigate the homology representation of symmetric group on rank-selected subposets subword order. show that module for words bounded length, over an alphabet size $n,$ decomposes into a sum tensor powers $S_n$-irreducible $S_{(n-1,1)}$ indexed by partition $(n-1,1),$ recovering, as special case, theorem Bj\"orner and Stanley length at most $k.$ For arbitrary ranks we is integer combinatio...

In this paper, we propose the tensor Noda iteration (NI) and its inexact version for solving eigenvalue problem of a particular class pairs called generalized M-tensor pairs. A pair consists weakly irreducible nonnegative nonsingular within linear combination. It is shown that any admits unique positive with eigenvector. modified (MTNI) developed extending matrix eigenproblems. addition, method...