Preprint Article Version 1 This version not peer reviewed

Clustering and Curve Fitting by Line Segments

Version 1 : Received: 9 January 2018 / Approved: 10 January 2018 / Online: 10 January 2018 (09:48:23 CET)

How to cite: Vinod, H.D.; Viole, F. Clustering and Curve Fitting by Line Segments. Preprints 2018, 2018010090 (doi: 10.20944/preprints201801.0090.v1). Vinod, H.D.; Viole, F. Clustering and Curve Fitting by Line Segments. Preprints 2018, 2018010090 (doi: 10.20944/preprints201801.0090.v1).

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 neighbours 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, NNS permits greater flexibility by offering a large spectrum of possible fits from linear to perfect.

Subject Areas

clustering; curve fitting; nonparametric regression; smoothing data; polynomial approximation

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