Clustering and Curve Fitting by Line Segments

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