TY - JOUR
T1 - A Linear Transportation Lp Distance for Pattern Recognition
AU - Crook, Oliver M.
AU - Cucuringu, Mihai
AU - Hurst, Tim
AU - Schönlieb, Carola-Bibiane
AU - Thorpe, Matthew
AU - Zygalakis, Konstantinos C
N1 - Funding Information:
This work was supported by The Alan Turing Institute, UK under EPSRC grant EP/N510129/1. In addition the authors are grateful for discussions with Elizabeth Soilleux, whose interest in machine learning methods for diagnosing coeliac disease motivated this work, and Dejan Slepčev. OMC is a Wellcome Trust Mathematical Genomics and Medicine student and is grateful for generous funding from the Cambridge school of clinical medicine, UK. TDH was supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the EPSRC (grant EP/L016508/01), the SFC, Heriot-Watt University and the University of Edinburgh. CBS acknowledges support from the Leverhulme Trust project on ‘Breaking the non-convexity barrier’, UK, the Philip Leverhulme Prize, UK, the Royal Society Wolfson Fellowship, UK, the EPSRC, UK grants EP/S026045/1 and EP/T003553/1, the EPSRC Centre Nr. EP/N014588/1, the Wellcome Innovator Award, UK RG98755, European Union Horizon 2020 research and innovation programmes under the Marie Skodowska-Curie grant agreement No. 777826 (NoMADS) and No. 691070 (CHiPS) and the Cantab Capital Institute for the Mathematics of Information, UK. MT is grateful for the support of the Cantab Capital Institute for the Mathematics of Information (CCIMI), UK and Cambridge Image Analysis (CIA), UK groups at the University of Cambridge, and is supported by the European Research Council under the European Union's Horizon 2020 research and innovation programme grant agreement No. 777826 (NoMADS) and grant agreement No. 647812.
Funding Information:
This work was supported by The Alan Turing Institute, UK under EPSRC grant EP/N510129/1 . In addition the authors are grateful for discussions with Elizabeth Soilleux, whose interest in machine learning methods for diagnosing coeliac disease motivated this work, and Dejan Slepčev. OMC is a Wellcome Trust Mathematical Genomics and Medicine student and is grateful for generous funding from the Cambridge school of clinical medicine, UK . TDH was supported by The Maxwell Institute Graduate School in Analysis and its Applications , a Centre for Doctoral Training funded by the EPSRC (grant EP/L016508/01 ), the SFC, Heriot-Watt University and the University of Edinburgh. CBS acknowledges support from the Leverhulme Trust project on ‘Breaking the non-convexity barrier’, UK , the Philip Leverhulme Prize, UK , the Royal Society Wolfson Fellowship, UK , the EPSRC, UK grants EP/S026045/1 and EP/T003553/1 , the EPSRC Centre Nr. EP/N014588/1 , the Wellcome Innovator Award, UK RG98755 , European Union Horizon 2020 research and innovation programmes under the Marie Skodowska-Curie grant agreement No. 777826 (NoMADS) and No. 691070 (CHiPS) and the Cantab Capital Institute for the Mathematics of Information, UK . MT is grateful for the support of the Cantab Capital Institute for the Mathematics of Information (CCIMI), UK and Cambridge Image Analysis (CIA), UK groups at the University of Cambridge, and is supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme grant agreement No. 777826 (NoMADS) and grant agreement No. 647812 .
Publisher Copyright:
© 2023 The Author(s)
PY - 2024/3/31
Y1 - 2024/3/31
N2 - 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 nor- malisation or mass constraints. These distances, as with , 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 distance significantly improves over the linear distance on signal processing tasks, whilst being several orders of magnitude faster to compute than the distance.
AB - 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 nor- malisation or mass constraints. These distances, as with , 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 distance significantly improves over the linear distance on signal processing tasks, whilst being several orders of magnitude faster to compute than the distance.
U2 - 10.1016/j.patcog.2023.110080
DO - 10.1016/j.patcog.2023.110080
M3 - Article
SN - 0031-3203
VL - 147
JO - Pattern Recognition
JF - Pattern Recognition
M1 - 110080
ER -