Properties of Standard and Sketched Kernel Fisher Discriminant
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Number of pages | 8 |
| Journal / Publication | IEEE Transactions on Pattern Analysis and Machine Intelligence |
| Online published | 6 Feb 2023 |
| Publication status | Online published - 6 Feb 2023 |
Link(s)
Abstract
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 n 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.
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
Citation Format(s)
Properties of Standard and Sketched Kernel Fisher Discriminant. / Liu, Jiamin; Xu, Wangli; Zhang, Fode et al.
In: IEEE Transactions on Pattern Analysis and Machine Intelligence, 06.02.2023.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
