Multilinear Low-Rank Tensors on Graphs & Applications

by   Nauman Shahid, et al.
Politecnico di Torino

We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank SVD for matrices and multi-linear SVD for tensors. Then, building on this novel decomposition we construct a general class of convex optimization problems for approximately solving low-rank tensor inverse problems, such as tensor Robust PCA. The whole framework is named as 'Multilinear Low-rank tensors on Graphs (MLRTG)'. Our theoretical analysis shows: 1) MLRTG stands on the notion of approximate stationarity of multi-dimensional signals on graphs and 2) the approximation error depends on the eigen gaps of the graphs. We demonstrate applications for a wide variety of 4 artificial and 12 real tensor datasets, such as EEG, FMRI, BCI, surveillance videos and hyperspectral images. Generalization of the tensor concepts to non-euclidean domain, orders of magnitude speed-up, low-memory requirement and significantly enhanced performance at low SNR are the key aspects of our framework.


page 7

page 8

page 14

page 20

page 22

page 23

page 24

page 25


The low-rank approximation of fourth-order partial-symmetric and conjugate partial-symmetric tensor

We present an orthogonal matrix outer product decomposition for the four...

Tensor Completion via a Low-Rank Approximation Pursuit

This paper considers the completion problem for a tensor (also referred ...

Tensor Convolutional Sparse Coding with Low-Rank activations, an application to EEG analysis

Recently, there has been growing interest in the analysis of spectrogram...

Tensorized Random Projections

We introduce a novel random projection technique for efficiently reducin...

Sparse Sampling for Inverse Problems with Tensors

We consider the problem of designing sparse sampling strategies for mult...

DeepTensor: Low-Rank Tensor Decomposition with Deep Network Priors

DeepTensor is a computationally efficient framework for low-rank decompo...

Stochastic Mirror Descent for Low-Rank Tensor Decomposition Under Non-Euclidean Losses

This work considers low-rank canonical polyadic decomposition (CPD) unde...

Please sign up or login with your details

Forgot password? Click here to reset