Nonparametric density estimation of streaming data using orthogonal series

2009 ◽  
Vol 53 (12) ◽  
pp. 3980-3986 ◽  
Author(s):  
Kyle A. Caudle ◽  
Edward Wegman
Keyword(s):  
Density Estimation ◽  
Orthogonal Series ◽  
Nonparametric Density Estimation ◽  
Streaming Data

Orthogonal Series Density Estimation and the Kernel Eigenvalue Problem

2002 ◽  
Vol 14 (3) ◽  
pp. 669-688 ◽  
Author(s):  
Mark Girolami
Keyword(s):  
Principal Component Analysis ◽  
Density Estimation ◽  
Orthogonal Series ◽  
Principal Component ◽  
Component Analysis ◽  
Nonparametric Density Estimation ◽  
Kernel Principal Component Analysis ◽  
Eigenvalue Decomposition ◽  
Density Estimator ◽  
Nonlinear Features

Kernel principal component analysis has been introduced as a method of extracting a set of orthonormal nonlinear features from multivariate data, and many impressive applications are being reported within the literature. This article presents the view that the eigenvalue decomposition of a kernel matrix can also provide the discrete expansion coefficients required for a nonparametric orthogonal series density estimator. In addition to providing novel insights into nonparametric density estimation, this article provides an intuitively appealing interpretation for the nonlinear features extracted from data using kernel principal component analysis.

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