title: A kernel-based framework to tensorial data analysis.
abstract: Tensor-based techniques for learning allow one to exploit the structure of carefully chosen representations of data. This is a desirable feature in particular when the number of training patterns is small which is often the case in areas such as biosignal processing and chemometrics. However, the class of tensor-based models is somewhat restricted and might suffer from limited discriminative power. On a different track, kernel methods lead to flexible nonlinear models that have been proven successful in many different contexts. Nonetheless, a naïve application of kernel methods does not exploit structural properties possessed by the given tensorial representations. The goal of this work is to go beyond this limitation by introducing non-parametric tensor-based models. The proposed framework aims at improving the discriminative power of supervised tensor-based models while still exploiting the structural information embodied in the data. We begin by introducing a feature space formed by multilinear functionals. The latter can be considered as the infinite dimensional analogue of tensors. Successively we show how to implicitly map input patterns in such a feature space by means of kernels that exploit the algebraic structure of data tensors. The proposed tensorial kernel links to the MLSVD and features an interesting invariance property; the approach leads to convex optimization and fits into the same primal-dual framework underlying SVM-like algorithms.
authors.affiliation: Katholieke Universiteit Leuven, ESAT-SCD/SISTA Kasteelpark Arenberg 10, B-3001 Leuven, Belgium. marco.signoretto@esat.kuleuven.be
authors.forename: Marco
authors.initials: M
authors.lastname: Signoretto
authors.forename: Lieven
authors.initials: L
authors.lastname: De Lathauwer
authors.forename: Johan A K
authors.initials: JA
authors.lastname: Suykens
mesh_terms: D019540:Area Under Curve; D001185:Artificial Intelligence; D003627:Data Interpretation, Statistical; D016208:Databases, Factual; D020342:Finite Element Analysis; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D016011:Normal Distribution; D015203:Reproducibility of Results; D012813:Sign Language; D012815:Signal Processing, Computer-Assisted; D012984:Software; D060388:Support Vector Machine