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The Wasserstein Distance as a Dissimilarity Measure for Mass Spectra with Application to Spectral Deconvolution

Authors Szymon Majewski, Michal Aleksander Ciach, Michal Startek, Wanda Niemyska, Blazej Miasojedow, Anna Gambin

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Author Details

Szymon Majewski
  • Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
Michal Aleksander Ciach
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
Michal Startek
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
Wanda Niemyska
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
Blazej Miasojedow
  • Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
Anna Gambin
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

Funding

This work was partially supported by Polish National Science Center grants 2014/12/W/ST5/00592 and UMO-2017/26/D/ST6/00304.

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Szymon Majewski, Michal Aleksander Ciach, Michal Startek, Wanda Niemyska, Blazej Miasojedow, and Anna Gambin. The Wasserstein Distance as a Dissimilarity Measure for Mass Spectra with Application to Spectral Deconvolution. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 25:1-25:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.WABI.2018.25

Abstract

We propose a new approach for the comparison of mass spectra using a metric known in the computer science under the name of Earth Mover's Distance and in mathematics as the Wasserstein distance. We argue that this approach allows for natural and robust solutions to various problems in the analysis of mass spectra. In particular, we show an application to the problem of deconvolution, in which we infer proportions of several overlapping isotopic envelopes of similar compounds. Combined with the previously proposed generator of isotopic envelopes, IsoSpec, our approach works for a wide range of masses and charges in the presence of several types of measurement inaccuracies. To reduce the computational complexity of the solution, we derive an effective implementation of the Interior Point Method as the optimization procedure. The software for mass spectral comparison and deconvolution based on Wasserstein distance is available at https://github.com/mciach/wassersteinms.

Subject Classification

ACM Subject Classification
  • Applied computing → Chemistry
Keywords
  • Mass spectrometry
  • Tandem mass spectrometry
  • Wasserstein distance
  • Earth mover's distance
  • Similarity measure
  • Jaccard score
  • Tanimoto similarity

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