A0459
Title: Comparing curves with the discrete Frechet distance via the family of exponentiated generalized distributions
Authors: Mireya Diaz - Case Western Reserve University (United States) [presenting]
Abstract: The discrete Frechet distance is widely used in applications assessing the similarity between curves in areas including pattern recognition, map routing, protein structure alignment, and time series clustering. It is defined as the minimum among the maxima of a series of feasible paths along the curves under comparison connecting the first and last differences between these curves. Despite its use in diverse problems and profuse computational developments, little is known about its distributional properties and, thus, its power in statistical inference. A simulation study allowed the assessment of such distributional properties empirically under null and alternative scenarios for four families of functions: linear, quadratic, sinusoidal, and exponential. A parallel analytic work using extreme value theory under dependence identified its distribution. The discrete Frechet distance belongs to the family of exponentiated generalized distributions. One of these corresponds to the Kumaraswamy distribution, a beta-type distribution. Under conditions of exchangeability of the random variables, the distribution of the discrete Frechet distance is bounded by the conventional cumulative distribution function of the minimum. The empirical side confirmed this by the 2- and 4-parameter beta distributions, which fit most of the histograms adequately for both null and alternative scenarios. These findings allow the application of the Frechet distance under an inferential framework.
