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  • 2206.08858v1

    Submitted manuscript, 1.04 MB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

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Distances for Comparing Multisets and Sequences

Research output: Working paper › Preprint

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Distances for Comparing Multisets and Sequences. / Bolt, George; Lunagómez, Simón; Nemeth, Christopher.
Arxiv, 2022.

Research output: Working paper › Preprint

Harvard

Bolt, G, Lunagómez, S & Nemeth, C 2022 'Distances for Comparing Multisets and Sequences' Arxiv. <http://arxiv.org/abs/2206.08858v1>

APA

Bolt, G., Lunagómez, S., & Nemeth, C. (2022). Distances for Comparing Multisets and Sequences. Arxiv. http://arxiv.org/abs/2206.08858v1

Vancouver

Bolt G, Lunagómez S, Nemeth C. Distances for Comparing Multisets and Sequences. Arxiv. 2022 Jun 17.

Author

Bolt, George ; Lunagómez, Simón ; Nemeth, Christopher. / Distances for Comparing Multisets and Sequences. Arxiv, 2022.

Bibtex

@techreport{5a169fe2a6714faea7c9dd23e72f4c8c,
title = "Distances for Comparing Multisets and Sequences",
abstract = "Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of structured data for which standard distance measures are inapplicable. In this paper, we consider the problem of measuring the distance between sequences and multisets of points lying within a metric space, motivated by the analysis of an in-play football data set. Drawing on the wider literature, including that of time series analysis and optimal transport, we discuss various distances which are available in such an instance. For each distance, we state and prove theoretical properties, proposing possible extensions where they fail. Finally, via an example analysis of the in-play football data, we illustrate the usefulness of these distances in practice.",
keywords = "stat.ME",
author = "George Bolt and Sim{\'o}n Lunag{\'o}mez and Christopher Nemeth",
year = "2022",
month = jun,
day = "17",
language = "English",
publisher = "Arxiv",
type = "WorkingPaper",
institution = "Arxiv",

}

RIS

TY - UNPB

T1 - Distances for Comparing Multisets and Sequences

AU - Bolt, George

AU - Lunagómez, Simón

AU - Nemeth, Christopher

PY - 2022/6/17

Y1 - 2022/6/17

N2 - Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of structured data for which standard distance measures are inapplicable. In this paper, we consider the problem of measuring the distance between sequences and multisets of points lying within a metric space, motivated by the analysis of an in-play football data set. Drawing on the wider literature, including that of time series analysis and optimal transport, we discuss various distances which are available in such an instance. For each distance, we state and prove theoretical properties, proposing possible extensions where they fail. Finally, via an example analysis of the in-play football data, we illustrate the usefulness of these distances in practice.

AB - Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of structured data for which standard distance measures are inapplicable. In this paper, we consider the problem of measuring the distance between sequences and multisets of points lying within a metric space, motivated by the analysis of an in-play football data set. Drawing on the wider literature, including that of time series analysis and optimal transport, we discuss various distances which are available in such an instance. For each distance, we state and prove theoretical properties, proposing possible extensions where they fail. Finally, via an example analysis of the in-play football data, we illustrate the usefulness of these distances in practice.

KW - stat.ME

M3 - Preprint

BT - Distances for Comparing Multisets and Sequences

PB - Arxiv

ER -