Individual Preference Stability for Clustering

by   Saba Ahmadi, et al.

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.


page 1

page 2

page 3

page 4


A Notion of Individual Fairness for Clustering

A common distinction in fair machine learning, in particular in fair cla...

Clustering Stable Instances of Euclidean k-means

The Euclidean k-means problem is arguably the most widely-studied cluste...

Algorithmic Stability in Fair Allocation of Indivisible Goods Among Two Agents

We propose a notion of algorithmic stability for scenarios where cardina...

On Achieving Fairness and Stability in Many-to-One Matchings

Matching algorithms have been classically studied with the goal of findi...

Clustering without Over-Representation

In this paper we consider clustering problems in which each point is end...

Group Fairness in Committee Selection

In this paper, we study fairness in committee selection problems. We con...

A notion of stability for k-means clustering

In this paper, we define and study a new notion of stability for the k-m...