Constructing descriptive and discriminative nonlinear features: Rayleigh coefficients in kernel feature spaces

Author

Mika, Sebastian ; Rätsch, Gunnar ; Weston, Jason ; Scholkopf, Bernhard ; Smola, Alex ; Muller, Klaus-Robert

Author_Institution

Fraunhofer FIRST, Berlin, Germany

Volume

25

Issue

5

fYear

2003

fDate

5/1/2003 12:00:00 AM

Firstpage

623

Lastpage

628

Abstract

We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher´s discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.

Keywords

learning (artificial intelligence); learning automata; matrix algebra; principal component analysis; Fisher discriminant; PCA; Rayleigh coefficients; descriptive nonlinear features; discriminative nonlinear features; invariant feature extraction; kernel feature spaces; simulations; support vector kernel functions; support vector machine; Covariance matrix; Data mining; Feature extraction; Kernel; Noise measurement; Principal component analysis; Sufficient conditions; Support vector machines; Symmetric matrices; Tin;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/TPAMI.2003.1195996

Filename

1195996