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Kernel principal component analysis : ウィキペディア英語版 | Kernel principal component analysis In the field of multivariate statistics, kernel principal component analysis (kernel PCA) 〔(Nonlinear Component Analysis as a Kernel Eigenvalue Problem )〕 is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are done in a reproducing kernel Hilbert space with a non-linear mapping. ==Background: Linear PCA==
Recall that conventional PCA operates on zero-centered data; that is, :. It operates by diagonalizing the covariance matrix, : in other words, it gives an eigendecomposition of the covariance matrix: : which can be rewritten as :.〔(Nonlinear Component Analysis as a Kernel Eigenvalue Problem (Technical Report) )〕 (See also: Covariance matrix as a linear operator)
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