Deep Clustering via Probabilistic Ratio-Cut Optimization

TL;DR

This paper introduces PRCut, a probabilistic method for graph ratio-cut optimization that improves clustering performance by modeling binary assignments as random variables and leveraging online learning, outperforming traditional methods.

Contribution

It presents a novel probabilistic framework for graph ratio-cut optimization that enables online learning and improves clustering accuracy over existing relaxation methods.

Findings

PRCut outperforms traditional ratio-cut relaxations and online extensions.

The probabilistic approach aligns well with similarity measures.

PRCut can match supervised classifiers when using label-based similarities.

Abstract

We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables. We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the parameters of the assignment variables in an online setting. The clustering resulting from our probabilistic approach (PRCut) outperforms the Rayleigh quotient relaxation of the combinatorial problem, its online learning extensions, and several widely used methods. We demonstrate that the PRCut clustering closely aligns with the similarity measure and can perform as well as a supervised classifier when label-based similarities are provided. This novel approach can leverage out-of-the-box self-supervised representations to achieve competitive performance and serve as an evaluation method for the quality of these representations.