Sketching semidefinite programs for faster clustering
This work addresses computational bottlenecks in clustering algorithms for practitioners, but it is incremental as it builds on existing semidefinite programming methods.
The paper tackles the slow speed of semidefinite programs for clustering by sketching a relaxation of the minimum bisection problem, showing that clustering becomes computationally easier with stronger signal.
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.