Clustering via Hedonic Games: New Concepts and Algorithms

Gergely Csáji, Alexander Gundert, Jörg Rothe, Ildikó Schlotter

Keywords: graphical hedonic games, coalition formation, clustering, popularity, community detection

TL;DR: We study a stability notion in coalition formation games, give an efficient algorithm, and show that it is surprisingly good for general clustering tasks too.

Abstract:

We study fundamental connections between coalition formation games and clustering, illustrating the cross-disciplinary relevance of these concepts.
We focus on graphical hedonic games where agents' preferences are compactly represented by a friendship graph and an enemy graph.
In the context of clustering, friendship relations naturally align with data point similarities, whereas enmity corresponds to dissimilarities.
We consider two stability notions based on single-agent deviations: local popularity and local stability.
Exploring these concepts from an algorithmic viewpoint, we
design efficient mechanisms for finding locally stable or locally popular partitions.
Besides gaining theoretical insight into the computational complexity of these problems, we perform simulations that demonstrate how our algorithms can be successfully applied in clustering and community detection.

Our findings highlight the interplay between coalition formation games and data-driven clustering techniques, offering fresh perspectives and applications in both areas.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 17636