Learning-Augmented $k$-means Clustering
This work addresses the problem of overcoming theoretical performance limits in k-means clustering for researchers and practitioners, representing a novel method for a known bottleneck rather than an incremental advance.
The paper tackles the k-means clustering problem by incorporating a predictor that provides approximate cluster labels, enabling performance improvements that scale with predictor accuracy and breaking computational barriers for worst-case inputs. Results on real datasets show significant quality improvements, though specific numbers are not provided.
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case 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.