Rigorous optimisation of multilinear discriminant analysis with Tucker and PARAFAC structures

BMC Bioinformatics
Laura FrølichMorten Mørup

Abstract

We propose rigorously optimised supervised feature extraction methods for multilinear data based on Multilinear Discriminant Analysis (MDA) and demonstrate their usage on Electroencephalography (EEG) and simulated data. While existing MDA methods use heuristic optimisation procedures based on an ambiguous Tucker structure, we propose a rigorous approach via optimisation on the cross-product of Stiefel manifolds. We also introduce MDA methods with the PARAFAC structure. We compare the proposed approaches to existing MDA methods and unsupervised multilinear decompositions. We find that manifold optimisation substantially improves MDA objective functions relative to existing methods and on simulated data in general improve classification performance. However, we find similar classification performance when applied to the electroencephalography data. Furthermore, supervised approaches substantially outperform unsupervised mulitilinear methods whereas methods with the PARAFAC structure perform similarly to those with Tucker structures. Notably, despite applying the MDA procedures to raw Brain-Computer Interface data, their performances are on par with results employing ample pre-processing and they extract discriminatory patterns si...Continue Reading

References

Sep 1, 1966·Psychometrika·L R Tucker
Jun 11, 2004·IEEE Transactions on Bio-medical Engineering·Gerwin SchalkJonathan R Wolpaw
Jun 24, 2006·IEEE Transactions on Neural Systems and Rehabilitation Engineering : a Publication of the IEEE Engineering in Medicine and Biology Society·Benjamin BlankertzNiels Birbaumer
Aug 11, 2006·IEEE Engineering in Medicine and Biology Magazine : the Quarterly Magazine of the Engineering in Medicine & Biology Society·Zhongming LiuBin He
Sep 26, 2007·Journal of Cognitive Neuroscience·Jeroen J Stekelenburg, Jean Vroomen
Jul 17, 2009·IEEE Transactions on Nanobioscience·Patrick C H Ma, Keith C C Chan
May 20, 2015·International Journal of Neural Systems·Ye LiuLiqing Zhang
Sep 10, 2015·IEEE Transactions on Pattern Analysis and Machine Intelligence·Qun Li, Dan Schonfeld

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Citations

Jun 4, 2021·BMC Bioinformatics·Shiu KumarAlok Sharma

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Methods Mentioned

BETA
MDA
feature extraction

Software Mentioned

PARAFAC2
ManPDA
ManOpt
ManTDA
sr
MDA
nway
DGTDA
HODA
ldots

Related Concepts

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