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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)
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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