Tensor gauge condition and tensor field decomposition

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 ...

Randomized CP Tensor Decomposition

The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought since many high-dimensional tensors have low intrinsic rank relative to the dimension of the ambient measurement space. However, the emergence of ‘big data’ poses significant computational challenges for computing this fundamental tensor decomp...