title: Nonlinear feature extraction using kernel principal component analysis with non-negative pre-image.
abstract: The inherent physical characteristics of many real-life phenomena, including biological and physiological aspects, require adapted nonlinear tools. Moreover, the additive nature in some situations involve solutions expressed as positive combinations of data. In this paper, we propose a nonlinear feature extraction method, with a non-negativity constraint. To this end, the kernel principal component analysis is considered to define the most relevant features in the reproducing kernel Hilbert space. These features are the nonlinear principal components with high-order correlations between input variables. A pre-image technique is required to get back to the input space. With a non-negative constraint, we show that one can solve the pre-image problem efficiently, using a simple iterative scheme. Furthermore, the constrained solution contributes to the stability of the algorithm. Experimental results on event-related potentials (ERP) illustrate the efficiency of the proposed method.
authors.affiliation: Institut Charles Delaunay (UMR CNRS 6279), LM2S, Université de technologie de Troyes, France. maya.kallas@utt.fr
authors.forename: Maya
authors.initials: M
authors.lastname: Kallas
authors.forename: Paul
authors.initials: P
authors.lastname: Honeine
authors.forename: Cedric
authors.initials: C
authors.lastname: Richard
authors.forename: Hassan
authors.initials: H
authors.lastname: Amoud
authors.forename: Clovis
authors.initials: C
authors.lastname: Francis
mesh_terms: D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D004569:Electroencephalography / Q000379:methods*; D005071:Evoked Potentials / Q000502:physiology*; D006801:Humans; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated / Q000379:methods*; D025341:Principal Component Analysis; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity