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Type Book Chapter
Scope Discipline-based scholarship
Title Wasserstein t-SNE
Organization Unit
  • Contribution from another University/Organization than University of Zurich
Authors
  • Fynn Bachmann
  • Philipp Hennig
  • Dmitry Kobak
Editors
  • Massih-Reza Amini
  • Stéphane Canu
  • Asja Fischer
  • Tias Guns
  • Grigorios Tsoumakas
  • Petra Kralj Novak
Item Subtype Original Work
Refereed Yes
Status Published in final form
Language
  • English
Booktitle Machine Learning and Knowledge Discovery in Databases
Series Name Lecture Notes in Computer Science
ISBN 978-3-031-26386-6
ISSN 0302-9743
Number 13713
Place of Publication Switzerland
Publisher Springer
Page Range 104 - 120
Date 2023-03-16
Abstract Text Scientific datasets often have hierarchical structure: for example, in surveys, individual participants (samples) might be grouped at a higher level (units) such as their geographical region. In these settings, the interest is often in exploring the structure on the unit level rather than on the sample level. Units can be compared based on the distance between their means, however this ignores the within-unit distribution of samples. Here we develop an approach for exploratory analysis of hierarchical datasets using the Wasserstein distance metric that takes into account the shapes of within-unit distributions. We use t-SNE to construct 2D embeddings of the units, based on the matrix of pairwise Wasserstein distances between them. The distance matrix can be efficiently computed by approximating each unit with a Gaussian distribution, but we also provide a scalable method to compute exact Wasserstein distances. We use synthetic data to demonstrate the effectiveness of our Wasserstein t-SNE, and apply it to data from the 2017 German parliamentary election, considering polling stations as samples and voting districts as units. The resulting embedding uncovers meaningful structure in the data.
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Digital Object Identifier 10.1007/978-3-031-26387-3_7
Other Identification Number merlin-id:22706; arXiv: 10.48550/arXiv.2205.07531 (DOI); eISBN 978-3-031-26387-3
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Additional Information European Conference, ECML PKDD 2022, Grenoble, France, September 19–23, 2022, Proceedings // Also part of the book sub series: Lecture Notes in Artificial Intelligence (LNAI)