Integrated shape-sensitive functional metrics

Abstract

This paper develops a new integrated ball (pseudo)metric which provides an intermediary between a chosen starting (pseudo)metric d and the L-p distance in general function spaces. Selecting d as the Hausdorff or Frechet distances, we introduce integrated shape sensitive versions of these supremum-based metrics.

The new metrics allow for finer analyses in functional settings, not attainable applying the non-integrated versions directly. Moreover, convergent discrete approximations make computations feasible in practice. (C) 2021 Elsevier Inc.

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Keywords

• Frechet distance
• Functional data analysis
• Hausdorff distance
• Pseudometric