ClusterFuG: Clustering Fully connected Graphs by Multicut

TL;DR

This paper introduces ClusterFuG, a novel graph clustering method based on multicut that operates on complete graphs with weighted costs, offering improved efficiency and scalability for large dense graphs, demonstrated on image segmentation and clustering tasks.

Contribution

It presents a simplified, dense multicut formulation that handles complete graphs with weighted costs, enabling scalable and efficient clustering algorithms for large datasets.

Findings

Scales to graphs with tens of thousands of nodes.

Effective on instance segmentation and image clustering tasks.

Outperforms traditional sparse multicut methods.

Abstract

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.