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A linear transportation Lp distance for pattern recognition
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Crook, Oliver, Cucuringu, Mihai, Hurst, Tim, Schoenlieb, Carola-Bibiane, Thorpe, Matthew and Zygalakis, Konstantinos (2024) A linear transportation Lp distance for pattern recognition. Pattern Recognition, 147 . 110080. doi:10.1016/j.patcog.2023.110080 ISSN 0031-3203.
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Official URL: https://doi.org/10.1016/j.patcog.2023.110080
Abstract
The transportation Lp distance, denoted TLp, has been proposed as a generalisation of Wasserstein Wp distances motivated by the property that it can be applied directly to colour or multi-channelled images, as well as multivariate time-series without normalisation or mass constraints. These distances, as with Wp, are powerful tools in modelling data with spatial or temporal perturbations. However, their computational cost can make them infeasible to apply to even moderate pattern recognition tasks. We propose linear versions of these distances and show that the linear TLp distance significantly improves over the linear Wp distance on signal processing tasks, whilst being several orders of magnitude faster to compute than the TLp distance.
Item Type: | Journal Article | |||||||||||||||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Transportation problems (Programming), Geometry, Riemannian, Measure theory, Mathematical optimization, Machine learning | |||||||||||||||||||||||||||||||||
Journal or Publication Title: | Pattern Recognition | |||||||||||||||||||||||||||||||||
Publisher: | Elsevier | |||||||||||||||||||||||||||||||||
ISSN: | 0031-3203 | |||||||||||||||||||||||||||||||||
Official Date: | March 2024 | |||||||||||||||||||||||||||||||||
Dates: |
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Volume: | 147 | |||||||||||||||||||||||||||||||||
Article Number: | 110080 | |||||||||||||||||||||||||||||||||
DOI: | 10.1016/j.patcog.2023.110080 | |||||||||||||||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||||||||||||||
Date of first compliant deposit: | 7 May 2024 | |||||||||||||||||||||||||||||||||
Date of first compliant Open Access: | 7 May 2024 | |||||||||||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
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