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Nonlinear Component Analysis as a Kernel Eigenvalue Problem




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.

Author(s): Schölkopf, B. and Smola, AJ. and Müller, K-R.
Journal: Neural Computation
Volume: 10
Number (issue): 5
Pages: 1299-1319
Year: 1998
Month: July
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1162/089976698300017467
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web


  title = {Nonlinear Component Analysis as a Kernel Eigenvalue Problem},
  author = {Sch{\"o}lkopf, B. and Smola, AJ. and M{\"u}ller, K-R.},
  journal = {Neural Computation},
  volume = {10},
  number = {5},
  pages = {1299-1319},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = jul,
  year = {1998},
  month_numeric = {7}