Sketch-and-solve approaches to k-means clustering by semidefinite programming
Machine Learning
2022-11-30 v1 Data Structures and Algorithms
Information Theory
math.IT
Optimization and Control
Statistics Theory
Machine Learning
Statistics Theory
Abstract
We introduce a sketch-and-solve approach to speed up the Peng-Wei semidefinite relaxation of k-means clustering. When the data is appropriately separated we identify the k-means optimal clustering. Otherwise, our approach provides a high-confidence lower bound on the optimal k-means value. This lower bound is data-driven; it does not make any assumption on the data nor how it is generated. We provide code and an extensive set of numerical experiments where we use this approach to certify approximate optimality of clustering solutions obtained by k-means++.
Cite
@article{arxiv.2211.15744,
title = {Sketch-and-solve approaches to k-means clustering by semidefinite programming},
author = {Charles Clum and Dustin G. Mixon and Soledad Villar and Kaiying Xie},
journal= {arXiv preprint arXiv:2211.15744},
year = {2022}
}