Convergence of a Steepest Descent Algorithm for Ratio Cut Clustering

TL;DR

This paper introduces a gradient flow algorithm for ratio cut clustering, demonstrating convergence to critical points and efficiency on a synthetic dataset, advancing methods for high-dimensional, noisy data clustering.

Contribution

It proposes an explicit-implicit gradient flow scheme for the relaxed ratio cut problem with proven convergence, improving clustering techniques for complex data.

Findings

Algorithm converges to a critical point of the energy.

Demonstrates efficiency on the two moons dataset.

Provides theoretical guarantees for the clustering method.

Abstract

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove that the algorithm converges to a critical point of the energy. We also show the efficiency of the proposed algorithm on the two moons dataset.