Properties of Standard and Sketched Kernel Fisher Discriminant

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Original languageEnglish
Number of pages8
Journal / PublicationIEEE Transactions on Pattern Analysis and Machine Intelligence
Online published6 Feb 2023
Publication statusOnline published - 6 Feb 2023


Kernel Fisher discriminant (KFD) is a popular tool as a nonlinear extension of Fisher's linear discriminant, based on the use of the kernel trick. However, its asymptotic properties are still rarely studied. We first present an operator-theoretical formulation of KFD which elucidates the population target of the estimation problem. Convergence of the KFD solution to its population target is then established. However, the complexity of finding the solution poses significant challenges when n is large and we further propose a sketched estimation approach based on a m x sketching matrix which possesses the same asymptotic properties (in terms of convergence rate) even when m
is much smaller than n. Some numerical results are presented to illustrate the performances of the sketched estimator. © 2023  IEEE.

Research Area(s)

  • Convergence, Eigenvalues and eigenfunctions, Estimation, Kernel, Kernel method, random projection, reproducing kernel Hilbert space, Sociology, Standards, Urban areas, variance operator