Individual Preference Stability for Clustering

Saba Ahmadi*, Pranjal Awasthi*, Samir Khuller*, Matthäus Kleindessner*, Jamie Morgenstern*, Pattara Sukprasert, Ali Vakilian*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

Abstract

In this paper, we propose a natural notion of individual preference (IP) stability for clustering, which asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. Our notion can be motivated from several perspectives, including game theory and algorithmic fairness. We study several questions related to our proposed notion. We first show that deciding whether a given data set allows for an IP-stable clustering in general is NP-hard. As a result, we explore the design of efficient algorithms for finding IP-stable clusterings in some restricted metric spaces. We present a polytime algorithm to find a clustering satisfying exact IP-stability on the real line, and an efficient algorithm to find an IP-stable 2-clustering for a tree metric. We also consider relaxing the stability constraint, i.e., every data point should not be too far from its own cluster compared to any other cluster. For this case, we provide polytime algorithms with different guarantees. We evaluate some of our algorithms and several standard clustering approaches on real data sets.

Original languageEnglish (US)
Pages (from-to)197-246
Number of pages50
JournalProceedings of Machine Learning Research
Volume162
StatePublished - 2022
Event39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States
Duration: Jul 17 2022Jul 23 2022

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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