Fitting a Graph to One-Dimensional Data

TL;DR

This paper introduces a dynamic programming algorithm for fitting a graph to one-dimensional data points, providing an efficient alternative to quadratic programming with a quadratic time complexity.

Contribution

It presents the first polynomial-time dynamic programming method specifically designed for graph fitting in one-dimensional data, improving computational efficiency.

Findings

The algorithm runs in O(n^2) time for 1D data.

It offers a more efficient solution than quadratic programming.

Applicable to clustering, classification, and regression tasks.

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 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.