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9 - Universal Clustering

Published online by Cambridge University Press:  22 March 2021

By
Ravi Kiran Raman  and
Lav R. Varshney
Edited by
Miguel R. D. Rodrigues  and
Yonina C. Eldar
Miguel R. D. Rodrigues
Affiliation:
University College London
Yonina C. Eldar
Affiliation:
Weizmann Institute of Science, Israel
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Summary

Clustering is a general term for techniques that, given a set of objects, aim to select those that are closer to one another than to the rest, according to a chosen notion of closeness. It is an unsupervised-learning problem since objects are not externally labeled by category. Much effort has been expended on finding natural mathematical definitions of closeness and then developing/evaluating algorithms in these terms. Many have argued that there is no domain-independent mathematical notion of similarity but that it is context-dependent; categories are perhaps natural in that people can evaluate them when they see them. Some have dismissed the problem of unsupervised learning in favor of supervised learning, saying it is not a powerful natural phenomenon. Yet, most learning is unsupervised. We largely learn how to think through categories by observing the world in its unlabeled state. Drawing on universal information theory, we ask whether there are universal approaches to unsupervised clustering. In particular, we consider instances wherein the ground-truth clusters are defined by the unknown statistics governing the data to be clustered.

Keywords

supervised learningunsupervised learningclusteringuniversal clustering
Type
Chapter
Information
Information-Theoretic Methods in Data Science , pp. 263 - 301
Publisher: Cambridge University Press
Print publication year: 2021

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