Additive Tensor Decomposition Considering Structural Data Information

Decomposition of Additive CA

We consider finite additive cellular automata with fixed and periodic boundary conditions as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. We determine the generalized eigenspace decomposition, and describe relevant cyclic subspaces in terms of symmetries. As an application, we calc...

From Tensor to Coupled Matrix/Tensor Decomposition

Decompositions of higher-order tensors are becoming more and more important in signal processing, data analysis, machine learning, scientific computing, optimization and many other fields. A new trend is the study of coupled matrix/tensor decompositions (i.e., decompositions of multiple matrices and/or tensors that are linked in one or several ways). Applications can be found in various fields ...

Tensor Decomposition with Smoothness

Tensor Ring Decomposition

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the complicated tensor networks. However, the TT decomposition highly depends on permutations of tensor dimensions, due to its strictly sequential multilinear products ...

Legendre Tensor Decomposition

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and alwaysminimizes the KL divergence from an input tensor. We empirically show that Legendre decomposition can more accurately ...