The Delaunay Density Diagnostic
Andrew Gillette, Eugene Kur

TL;DR
This paper introduces a computational geometric method to determine if input data density is sufficient to capture the true variation of a function, aiding in accurate approximation and analysis.
Contribution
It presents a novel deterministic interpolation-based algorithm to detect the geometric scale of functions from data, applicable in moderate dimensions.
Findings
The method can identify feature scale in scalar data.
It estimates uncertainty in feature scale.
It assesses sampling density effectiveness.
Abstract
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is \textit{sufficient} to identify the relevant variations in outputs -- i.e., the ``geometric scale'' of the function -- despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this paper, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2-10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will…
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Taxonomy
TopicsAnomaly Detection Techniques and Applications · Advanced Statistical Methods and Models · Hydrology and Drought Analysis
