Tensor-based data similarity - Tensor-based study of data similarity

From 01-01-2014 to 31-12-2017

Description

Higher-order tensors are the natural generalizations of vectors (first order) and matrices (second order). Blind signal separation consists of the estimation of signals that are observed in mixed form. Blind system identification is the identification of a dynamical system from output observations only. Tensor decompositions have properties that make them proper tools for these generic problems.In this project we make the step from techniques that rely on the decomposition of a single tensor, to the assessment of data similarity, involving two tensors. We work out a technique that allows us to assess whether two tensors have the same components (in different proportions),while avoiding the explicit computation of the latter. Classical linear algebra does not allow such an analysis. We investigate whether complex data may be associated with the behavior of similar dynamical systems, without explicitly identifying the latter. We develop variants for large-scale sparse data. In particular, we develop tensor tools for analyzing and comparing graphs and networks. We develop a comprehensive framework for mapping data to higher-order tensors, facilitating the use of tensor tools in the case of conventional matrix data. We give a proof of concept for electroencephalographic data analysis, where our technique allows us to compare brain states, and magnetic spectroscopy imaging, where sparse versions allow us to compare the composition of samples.

Team

• Johan Suykens, Co-promoter
• Lieven De Lathauwer, Promoter

Financing

Funding: FWO - Research Foundation - Flanders

Program/Grant Type: FWO Research Grant - FWO Research Grant