More Flexible Curve Matching via the Partial Fréchet Similarity

Abstract

We study a modified version of the partial Fréchet similarity that is motivated by real world applications, e.g. the analysis of spectroscopic data in the context of astroinformatics and the analysis of birds’ migration trajectories. In those practical applications of curve matching it is often necessary to ignore outliers while dissimilarities regarding individual directions should be weighted by individual costs. We enable both by computing the partial Fréchet similarity between polygonal curves w.r.t. a non-uniform metric. In particular, we measure distances by a function [Formula: see text] that is induced by a set of weighted vectors. We discuss the approximation quality of [Formula: see text] regarding any [Formula: see text] metric and present a polynomial time algorithm for computing an exact solution of the resulting modified partial Fréchet similarity.