LearningAugmented $k$means Clustering
Abstract
$k$means clustering is a wellstudied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$means problem on worstcase inputs. To overcome this barrier, we consider a scenario where "advice" is provided to help perform clustering. Specifically, we consider the $k$means problem augmented with a predictor that, given any point, returns its cluster label in an approximately optimal clustering up to some, possibly adversarial, error. We present an algorithm whose performance improves along with the accuracy of the predictor, even though naïvely following the accurate predictor can still lead to a high clustering cost. Thus if the predictor is sufficiently accurate, we can retrieve a close to optimal clustering with nearly optimal runtime, breaking known computational barriers for algorithms that do not have access to such advice. We evaluate our algorithms on real datasets and show significant improvements in the quality of clustering.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.14094
 Bibcode:
 2021arXiv211014094E
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Data Structures and Algorithms