Replicator Graph Clustering

Motivation Data clustering, which aims at identifying a varying number of clusters and unique cluster assignments in a fully unsupervised manner, is an important topic in machine learning and computer vision. Many of the available methods in this field such as k-means or mean shift are based on a Euclidean assumption. In this work we overcome the shortcomings of such an assumption by considering the underlying similarity manifold using diffusion processes, which allows to handle non-metric data. Core idea of our novel approach is to combine an effective diffusion process, based on iteratively approaching evolutionary stable strategies from the field of game theory, with a provably optimal clustering step that analyzes a specific graph structure, that we denote as Replicator Graph. Our clustering method (Replicator Graph Clustering) belongs to the field of pairwise or proximity-based based clustering approaches assuming that the input is an N×N affinity matrix A = ( ai j ) , where each entry ai j measures the similarity between two specific data points-to-beclustered i and j. The goal of clustering is to uniquely assign each of the N data points to one of a set of clusters C = (C1,C2, . . .CC), where C is an automatically found number of clusters. Our method mainly consists of three subsequent steps (a) diffusing affinities by finding personalized evolutionary stable strategies of non-cooperative games (b) building a mutual k-nearest neighbor graph representing the underlying manifold and (c) applying a graph based clustering strategy which identifies the final clusters. Individual steps have low computational complexity which leads to an efficient clustering method, scaling well with an increasing number of data points.