Fitting a graph to one-dimensional data

Abstract

Given n data points in R^d, an appropriate edge-weighted graph connecting the data points finds application in solving clustering, classification, and regresssion problems. The graph proposed by Daitch, Kelner and Spielman (ICML 2009) can be computed by quadratic programming and hence in polynomial time. While in practice a more efficient algorithm would be preferable, replacing quadratic programming is challenging even for the special case of points in one dimension. We develop a dynamic programming algorithm for this case that runs in O($n^2$) time. Its practical efficiency is also confirmed in our experimental results.