Clustering and Curve Fitting by Line Segments

Nonlinear nonparametric statistics (NNS) algorithm offers new tools for curve fitting. 1 A relationship between k-means clustering and NNS regression points is explored with graphics 2 showing a perfect fit in the limit. The goal of this paper is to demonstrate NNS as a form of 3 unsupervised learning, and supply a proof of its limit condition. The procedural similarity NNS 4 shares with vector quantization is also documented, along with identical outputs for NNS and a 5 k nearest neighbours classification algorithm under a specific NNS setting. Fisher’s iris data and 6 artificial data are used. Even though a perfect fit should obviously be reserved for instances of high 7 signal to noise ratios, NNS permits greater flexibility by offering a large spectrum of possible fits 8 from linear to perfect. 9