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Global and Local Views of the Hilbert Space Associated to Gaussian KernelGlobal and Local Views of the Hilbert Space Associated to Gaussian Kernel
- Other Titles
- Global and Local Views of the Hilbert Space Associated to Gaussian Kernel
- Authors
- 허명회
- Issue Date
- 2014
- Publisher
- 한국통계학회
- Keywords
- Data visualization; Hilbert space; Gaussian kernel; principal component analysis
- Citation
- Communications for Statistical Applications and Methods, v.21, no.4, pp.317 - 325
- Indexed
- KCI
- Volume
- 21
- Number
- 4
- Start Page
- 317
- End Page
- 325
- ISSN
- 2287-7843
- Abstract
- Consider a nonlinear transform Φ(x) of x in Rp to Hilbert space H and assume that the dot product betweenΦ(x) and Φ(x′) in H is given by < Φ(x);Φ(x′) >= K(x; x′). The aim of this paper is to propose a mathematicaltechnique to take screen shots of the multivariate dataset mapped to Hilbert space H, particularly suited to Gaussiankernel K(· ; ·), which is defined by K(x; x′) = exp(− ∥ x − x′∥2); > 0. Several numerical examples are given.
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