Community Research and Development Information Service - CORDIS


BIOTENSORS Report Summary

Project ID: 339804
Funded under: FP7-IDEAS-ERC
Country: Belgium

Mid-Term Report Summary - BIOTENSORS (Biomedical Data Fusion using Tensor based Blind Source Separation)

Summary: the quest for a general functional tensor framework for blind source separation

Our overall objective is the development of a general functional framework for solving tensor based blind source separation (BSS) problems in biomedical data fusion, using tensor decompositions (TDs) as basic core. We claim that TDs will allow the extraction of fairly complicated sources of biomedical activity from fairly complicated sets of uni- and multimodal data.
Significant progress is made on the development of algebraically and numerically well-founded tensor techniques for BSS, including the Canonical Polyadic Decomposition (CPD) and Block Term Decomposition (BTD) and their extensions involving block terms, various constraints, source models and heterogeneous coupled data sets. In particular:

• Relaxed uniqueness conditions have been proven for several tensor decompositions, including block terms, constraints and coupling.
• New signal separation techniques, positioned in a tensor framework, including exponential polynomials, rational functions and Kronecker-product structured sources, have been presented. The corresponding structured tensor algorithms (CPD, Tensor Train, Hankel, Löwner...) have been optimized in speed and data storage, i.e., without the need to expand a structured tensor to a full tensor.
• Many new constraints and their corresponding constrained tensor decompositions have been implemented including non-negativity, orthogonality and Vandermonde structure, Kronecker and Khatri-Rao structure, exponential or Cauchy structured columns and finite differences.
• Randomized block sampling enables the decomposition of very large-scale tensors (e.g. 10e+18 entries) by sampling very few entries (e.g. 10e+5).
• New ways of tensorisation are presented, among which segmentation is especially useful for both large-scale (instantaneous) blind source separation and large-scale (convolutive) blind system identification.
• By formulating linear systems with a Kronecker product structure on the solution as a multilinear system, a new high-performing algorithm has been developed, outperforming ad-hoc solutions in many application domains which do not recognize the multilinear structure.
• Computationally efficient algorithms for tensor-based convolutive signal separation have been developed.
These extensions have been efficiently implemented in Tensorlab 3.0. Its user friendliness has improved significantly by simplifying model construction and adding visualization routines, documentation and demos.These powerful improvements allow to face current grand challenges in biomedical data fusion. The following outcomes are mentioned:
• A reliable CPD/BTD framework for tensor-based blind source separation of epileptic EEG and fMRI data, including new constraints and coupling strategies, has been developed. Its added value in epileptic seizure zone localization has been demonstrated.
• Using structured CPD/BTD, novel tensor-based classifiers for mobile Brain-Computer Interfacing (BCI) have been developed without subject-specific calibration phase: the latter showing a major benefit over traditional supervised methods at comparable accuracy.
• Using constrained non-negative CPD, a new class of tensor-based unsupervised classifiers has been developed for brain tissue type differentiation from Magnetic Resonance (MR) Spectroscopic Imaging or multiparametric MR Imaging data, which outperforms the existing matrix-based counterparts.

More information on the research, publications and software is available on the project website

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