Power-Law Graph Cuts

TL;DR

This paper introduces a novel power-law graph cut framework that automatically determines the number of clusters and produces clusters with power-law size distributions, addressing limitations of traditional spectral methods.

Contribution

It proposes a new power-law graph cut method using Pitman-Yor processes, enabling flexible cluster sizes and unknown cluster count, with an efficient iterative optimization algorithm.

Findings

Effective in producing power-law distributed clusters

Automatically determines the number of clusters

Outperforms traditional spectral methods in experiments

Abstract

Algorithms based on spectral graph cut objectives such as normalized cuts, ratio cuts and ratio association have become popular in recent years because they are widely applicable and simple to implement via standard eigenvector computations. Despite strong performance for a number of clustering tasks, spectral graph cut algorithms still suffer from several limitations: first, they require the number of clusters to be known in advance, but this information is often unknown a priori; second, they tend to produce clusters with uniform sizes. In some cases, the true clusters exhibit a known size distribution; in image segmentation, for instance, human-segmented images tend to yield segment sizes that follow a power-law distribution. In this paper, we propose a general framework of power-law graph cut algorithms that produce clusters whose sizes are power-law distributed, and also does not fix the number of clusters upfront. To achieve our goals, we treat the Pitman-Yor exchangeable partition probability function (EPPF) as a regularizer to graph cut objectives. Because the resulting objectives cannot be solved by relaxing via eigenvectors, we derive a simple iterative algorithm to locally optimize the objectives. Moreover, we show that our proposed algorithm can be viewed as performing MAP inference on a particular Pitman-Yor mixture model. Our experiments on various data sets show the effectiveness of our algorithms.