Elkan's k-Means for Graphs

TL;DR

This paper adapts Elkan's k-means algorithm to graph data, using subgradient methods for centroid computation and triangle inequality to accelerate clustering, demonstrating faster performance on structured graph datasets.

Contribution

It introduces an accelerated k-means algorithm for graphs that combines subgradient centroid computation with triangle inequality-based speed-ups.

Findings

Accelerated k-means outperforms standard k-means on graph data with cluster structure.

The method reduces unnecessary graph distance calculations, improving efficiency.

Experimental results confirm faster convergence on structured graph datasets.

Abstract

This paper extends k-means algorithms from the Euclidean domain to the domain of graphs. To recompute the centroids, we apply subgradient methods for solving the optimization-based formulation of the sample mean of graphs. To accelerate the k-means algorithm for graphs without trading computational time against solution quality, we avoid unnecessary graph distance calculations by exploiting the triangle inequality of the underlying distance metric following Elkan's k-means algorithm proposed in \cite{Elkan03}. In experiments we show that the accelerated k-means algorithm are faster than the standard k-means algorithm for graphs provided there is a cluster structure in the data.