Nonlinear Component Analysis as a Kernel Eigenvalue Problem

@article{Schlkopf1998NonlinearCA,
  title={Nonlinear Component Analysis as a Kernel Eigenvalue Problem},
  author={B. Sch{\"o}lkopf and Alex Smola and K. M{\"u}ller},
  journal={Neural Computation},
  year={1998},
  volume={10},
  pages={1299-1319}
}
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 mapfor 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. 
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