Multilinear subspace regression: An orthogonal tensor decomposition approach

Qibin Zhao, Cesar F. Caiafa, Danilo P. Mandic, Liqing Zhang, Tonio Ball, Andreas Schulze-Bonhage, Andrzej Cichocki

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

24 Citations (Scopus)

Abstract

A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed approach aims to maximize the correlation between the so derived latent variables and is shown to be suitable for the prediction of multidimensional dependent data from multidimensional independent data, where for the estimation of the latent variables we introduce an algorithm based on Multilinear Singular Value Decomposition (MSVD) on a specially defined cross-covariance tensor. It is next shown that in this way we are also able to unify the existing Partial Least Squares (PLS) and N-way PLS regression algorithms within the same framework. Simulations on benchmark synthetic data confirm the advantages of the proposed approach, in terms of its predictive ability and robustness, especially for small sample sizes. The potential of the proposed technique is further illustrated on a real world task of the decoding of human intracranial electrocorticogram (ECoG) from a simultaneously recorded scalp electroencephalograph (EEG).

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 24
Subtitle of host publication25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
Publication statusPublished - 2011
Externally publishedYes
Event25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011 - Granada, Spain
Duration: 12 Dec 201114 Dec 2011

Publication series

NameAdvances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011

Conference

Conference25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
Country/TerritorySpain
CityGranada
Period12/12/1114/12/11

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