DOI: 10.1162/089976698300017467 ISSN:

Nonlinear Component Analysis as a Kernel Eigenvalue Problem

Bernhard Schölkopf, Alexander Smola, Klaus-Robert Müller
  • Cognitive Neuroscience
  • Arts and Humanities (miscellaneous)

A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in high-dimensional feature spaces, related to input space by some nonlinear map—for instance, the space of all possible five-pixel products in 16 × 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.