Individual Preference Stability for Clustering

Saba Ahmadi, Pranjal Awasthi, Samir Khuller, Matthäus Kleindessner, Jamie Morgenstern, Pattara Sukprasert, Ali Vakilian
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:197-246, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-ahmadi22a, title = {Individual Preference Stability for Clustering}, author = {Ahmadi, Saba and Awasthi, Pranjal and Khuller, Samir and Kleindessner, Matth{\"a}us and Morgenstern, Jamie and Sukprasert, Pattara and Vakilian, Ali}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {197--246}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/ahmadi22a/ahmadi22a.pdf}, url = {https://proceedings.mlr.press/v162/ahmadi22a.html}, 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.} }
Endnote
%0 Conference Paper %T Individual Preference Stability for Clustering %A Saba Ahmadi %A Pranjal Awasthi %A Samir Khuller %A Matthäus Kleindessner %A Jamie Morgenstern %A Pattara Sukprasert %A Ali Vakilian %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-ahmadi22a %I PMLR %P 197--246 %U https://proceedings.mlr.press/v162/ahmadi22a.html %V 162 %X 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.
APA
Ahmadi, S., Awasthi, P., Khuller, S., Kleindessner, M., Morgenstern, J., Sukprasert, P. & Vakilian, A.. (2022). Individual Preference Stability for Clustering. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:197-246 Available from https://proceedings.mlr.press/v162/ahmadi22a.html.

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