Pattern Clustering using Cooperative Game Theory

TL;DR

This paper introduces a novel clustering algorithm called DRAC that leverages cooperative game theory concepts like Nucleolus and Shapley value, demonstrating their equivalence and effectiveness through extensive experiments.

Contribution

The paper formulates clustering as a characteristic form game and develops DRAC, a new density-restricted agglomerative clustering algorithm based on cooperative game theory.

Findings

Nucleolus, Shapley value, Gately point, and τ-value coincide in the clustering game.

DRAC outperforms some existing clustering algorithms on standard datasets.

The cooperative game theory approach provides a strong theoretical foundation for clustering.

Abstract

In this paper, we approach the classical problem of clustering using solution concepts from cooperative game theory such as Nucleolus and Shapley value. We formulate the problem of clustering as a characteristic form game and develop a novel algorithm DRAC (Density-Restricted Agglomerative Clustering) for clustering. With extensive experimentation on standard data sets, we compare the performance of DRAC with that of well known algorithms. We show an interesting result that four prominent solution concepts, Nucleolus, Shapley value, Gately point and \tau-value coincide for the defined characteristic form game. This vindicates the choice of the characteristic function of the clustering game and also provides strong intuitive foundation for our approach.