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

Sebastian Mika; Gunnar Rätsch; Jason Weston; Bernhard Schölkopf; Alex Smola; Klaus Robert Müller

doi:10.1109/TPAMI.2003.1195996

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

Sebastian Mika^*, Gunnar Rätsch, Jason Weston, Bernhard Schölkopf, Alex Smola, Klaus Robert Müller

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

178 Citations (Scopus)

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 Raylelgh 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.

Original language	English
Pages (from-to)	623-628
Number of pages	6
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	25
Issue number	5
DOIs	https://doi.org/10.1109/TPAMI.2003.1195996
Publication status	Published - 2003 May
Externally published	Yes

Bibliographical note

Funding Information:
This work was partially supported by the DFG (JA 379/9-2, MU 987/1-1, AS 62/1-1), and EU BLISS (IST-1999-14190).

Keywords

Fisher's discriminant
Kernel functions
Nonlinear feature extraction
Oriented PCA
Raylelgh coefficient
Support vector machine

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/TPAMI.2003.1195996

Cite this

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title = "Constructing descriptive and discriminative nonlinear features: Rayleigh coefficients in Kernel feature spaces",

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 Raylelgh 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 = "Fisher's discriminant, Kernel functions, Nonlinear feature extraction, Oriented PCA, Raylelgh coefficient, Support vector machine",

author = "Sebastian Mika and Gunnar R{\"a}tsch and Jason Weston and Bernhard Sch{\"o}lkopf and Alex Smola and M{\"u}ller, \{Klaus Robert\}",

note = "Funding Information: This work was partially supported by the DFG (JA 379/9-2, MU 987/1-1, AS 62/1-1), and EU BLISS (IST-1999-14190).",

year = "2003",

month = may,

doi = "10.1109/TPAMI.2003.1195996",

language = "English",

volume = "25",

pages = "623--628",

journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",

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TY - JOUR

T1 - Constructing descriptive and discriminative nonlinear features

T2 - Rayleigh coefficients in Kernel feature spaces

AU - Mika, Sebastian

AU - Rätsch, Gunnar

AU - Weston, Jason

AU - Schölkopf, Bernhard

AU - Smola, Alex

AU - Müller, Klaus Robert

N1 - Funding Information: This work was partially supported by the DFG (JA 379/9-2, MU 987/1-1, AS 62/1-1), and EU BLISS (IST-1999-14190).

PY - 2003/5

Y1 - 2003/5

N2 - 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 Raylelgh 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.

AB - 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 Raylelgh 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.

KW - Fisher's discriminant

KW - Kernel functions

KW - Nonlinear feature extraction

KW - Oriented PCA

KW - Raylelgh coefficient

KW - Support vector machine

UR - https://www.scopus.com/pages/publications/0038633559

U2 - 10.1109/TPAMI.2003.1195996

DO - 10.1109/TPAMI.2003.1195996

M3 - Article

AN - SCOPUS:0038633559

SN - 0162-8828

VL - 25

SP - 623

EP - 628

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

IS - 5

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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