Integrated shape-sensitive functional metrics

Sami Helander; Petra Laketa; Pauliina Ilmonen; Stanislav Nagy; Germain Van Bever; Lauri Viitasaari

doi:10.1016/j.jmva.2021.104880

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 Lp distance in general function spaces. Selecting d as the Hausdorff or Fréchet 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.

Original language	English
Article number	104880
Number of pages	14
Journal	Journal of Multivariate Analysis
Volume	189
Early online date	2021
DOIs	https://doi.org/10.1016/j.jmva.2021.104880
Publication status	Published - May 2022
MoE publication type	A1 Journal article-refereed

Keywords

Fréchet distance
Functional data analysis
Hausdorff distance
Pseudometric

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10.1016/j.jmva.2021.104880

https://arxiv.org/abs/2107.08917

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title = "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 Lp distance in general function spaces. Selecting d as the Hausdorff or Fr{\'e}chet 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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author = "Sami Helander and Petra Laketa and Pauliina Ilmonen and Stanislav Nagy and {Van Bever}, Germain and Lauri Viitasaari",

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AU - Helander, Sami

AU - Laketa, Petra

AU - Ilmonen, Pauliina

AU - Nagy, Stanislav

AU - Van Bever, Germain

AU - Viitasaari, Lauri

PY - 2022/5

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AB - This paper develops a new integrated ball (pseudo)metric which provides an intermediary between a chosen starting (pseudo)metric d and the Lp distance in general function spaces. Selecting d as the Hausdorff or Fréchet 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.

KW - Fréchet distance

KW - Functional data analysis

KW - Hausdorff distance

KW - Pseudometric

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JF - Journal of Multivariate Analysis

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ER -

Integrated shape-sensitive functional metrics

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Keywords

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