Clustering and Curve Fitting by Line Segments

29 Pages Posted: 31 Oct 2016 Last revised: 15 Aug 2017

See all articles by Hrishikesh D. Vinod

Hrishikesh D. Vinod

Fordham University - Department of Economics

Fred Viole

OVVO Financial Systems; Fordham University

Date Written: August 12, 2017

Abstract

Nonlinear nonparametric statistics (NNS) algorithm offers new tools for curve fitting. A relationship between k-means clustering and NNS regression points is explored with graphics showing a perfect fit in the limit. The goal of this paper is to demonstrate NNS as a form of unsupervised learning, and supply a proof of its limit condition. The procedural similarity NNS shares with vector quantization is also documented, along with identical outputs for NNS and a k nearest neighbors (kNN) classification algorithm under a specific NNS setting. Fisher's iris data and artificial data are used. Even though a perfect fit should obviously be reserved for instances of high signal to noise ratios, it permits greater flexibility by offering a large spectrum of possible fits from linear to perfect.

Keywords: Nonparametric regression, smoothing, iris data, polynomial approximation

JEL Classification: C14, C38, C40

Suggested Citation

Vinod, Hrishikesh D. and Viole, Fred, Clustering and Curve Fitting by Line Segments (August 12, 2017). Available at SSRN: https://ssrn.com/abstract=2861339 or http://dx.doi.org/10.2139/ssrn.2861339

Hrishikesh D. Vinod

Fordham University - Department of Economics ( email )

Dealy Hall
Bronx, NY 10458
United States
718-817-4065 (Phone)
718-817-3518 (Fax)

Fred Viole (Contact Author)

OVVO Financial Systems ( email )

NJ
United States

Fordham University ( email )

113 West 60th Street
New York, NY 10023
United States

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