Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Schölkopf, B., Smola, A., & Müller, K. Neural Computation, 10(5):1299–1319, July, 1998.
doi  abstract   bibtex   
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 x 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition. 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 x 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.
@article{scholkopfNonlinearComponentAnalysis1998,
  title = {Nonlinear {{Component Analysis}} as a {{Kernel Eigenvalue Problem}}},
  author = {Sch{\"o}lkopf, Bernhard and Smola, Alexander and M{\"u}ller, Klaus-Robert},
  year = {1998},
  month = jul,
  volume = {10},
  pages = {1299--1319},
  issn = {0899-7667},
  doi = {10.1162/089976698300017467},
  abstract = {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 x 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition. 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 x 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.},
  journal = {Neural Computation},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-3474398,high-impact-publication,mathematics,non-linearity,nonlinear-correlation,pca},
  lccn = {INRMM-MiD:c-3474398},
  number = {5}
}

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