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arXiv · 2107.08917

Integrated shape-sensitive functional metrics

Sami Helander·Petra Laketa·Pauliina Ilmonen·Stanislav Nagy·Germain Van Bever·Lauri Viitasaari
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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 Fr\'echet 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.

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Sami Helander, Petra Laketa, Pauliina Ilmonen, Stanislav Nagy, Germain Van Bever, Lauri Viitasaari. 2021-06-14. Integrated shape-sensitive functional metrics. https://doi.org/10.1016/j.jmva.2021.104880

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