Sketching semidefinite programs for faster clustering

TL;DR

This paper introduces a sketching technique for semidefinite programs in clustering, demonstrating that higher signal strength simplifies computation and accelerates solutions.

Contribution

It proposes a novel sketching approach for semidefinite relaxations in clustering, linking signal strength to computational efficiency.

Findings

Sketching reduces SDP solving time

Higher signal strength correlates with easier clustering

Supports faster algorithms for planted clustering models

Abstract

Many clustering problems enjoy solutions by semidefinite programming. Theoretical results in this vein frequently consider data with a planted clustering and a notion of signal strength such that the semidefinite program exactly recovers the planted clustering when the signal strength is sufficiently large. In practice, semidefinite programs are notoriously slow, and so speedups are welcome. In this paper, we show how to sketch a popular semidefinite relaxation of a graph clustering problem known as minimum bisection, and our analysis supports a meta-claim that the clustering task is less computationally burdensome when there is more signal.