Metrics for SiZer map comparison

Abstract

SiZer is a powerful visualization tool for uncovering real structures masked in noisy data. It produces a two-dimensional plot, the so-called SiZer map, to help the data analyst to carry out this task. Since its first proposal, many different extensions and improvements have been developed, including robust SiZer, quantile SiZer, and various SiZers for time series data, just to name a few. Given these many SiZer variants, one important question is, how can one evaluate the quality of a SiZer map produced by any one of these variants? The primary goal of this article aims to answer this question by proposing two metrics for quantifying the discrepancy between any two SiZer maps. With such metrics, one can systematically calculate the distance between a "true" SiZer map and a SiZer map produced by any one of the SiZer variants. Consequently, one can select a "best" SiZer variant for the problem at hand by selecting the variant that produces SiZer maps that are, on average, closest to the "true" SiZer map.