NDLI: A Radial Basis Function Algorithm with Automatic Model Order Determination

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kirby, Michael J. Jamshidi, Arta A.
Copyright Year	2015
Abstract	We present a new radial basis function (RBF) algorithm for constructing nonlinear models from data that may be sparsely scattered in high dimensions. We propose a simplified method for identifying function locations that is based on an approximation to the autocorrelation function. Local regions are now defined based on zero crossings of the modified autocorrelation contribution. The resulting local spatiotemporal data appear to capture increased structure as evidenced by the reduced number of basis functions required to achieve algorithm convergence and the fact that the resulting approximations have significantly improved accuracy. We prove a zero crossing lemma and convergence of the algorithm in the norm for continuous functions over a compact domain. Further, we show that several hypotheses tests can be used to detect this convergence. The model parameters and the number of basis functions are determined automatically from the given data. The only user parameter is the confidence level of the hypotheses tests which we fix at 95% . We apply the algorithm to modeling data on manifolds and the prediction of a chaotic time series using compactly supported skew RBFs in the setting of the overdetermined data fitting problem.
Starting Page	A1319
Ending Page	A1341
Page Count	23
File Format	PDF
ISSN	10648275
DOI	10.1137/130948252
e-ISSN	10957197
Issue Number	3
Volume Number	37
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-05-19
Access Restriction	Subscribed
Subject Keyword	Algorithms for functional approximation convergence analysis Smoothing, curve fitting low order models nonlinear function approximation Time series, auto-correlation, regression, etc. Signal theory radial basis functions scattered data data driven modeling
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in