NEW ALGORITHMS FOR THE LEARNING-AUGMENTED k-MEANS PROBLEM

In this paper, we study the clustering problems in the learning-augmented setting, where predicted labels for a d-dimensional dataset with size m are given by an oracle to serve as auxiliary information to enhance the clustering performance. Following the prior work, the given oracle is parameterized by some error rate α, which captures the accuracy of the oracle such that there are at most α fraction of false positives and false negatives in each predicted cluster. In this setting, the goal is to design fast and practical algorithms that can break the computational barriers of inapproximability for clustering problems. The current state-of-the-art learning-augmented k-means algorithm relies on sorting strategies to find coordinates approximation, where a (1 + O(α))-approximation can be achieved with near-linear running time in the data size. However, the sorting process may limit the scalability of the algorithm for handling large-scale datasets. To address this issue, in this paper, we propose new algorithms that can identify good coordinates approximation using sampling-based strategies, where (1 + O(α))-approximation can be achieved with linear running time in the data size. To obtain a more practical algorithm for the problem with better clustering quality and running time, we propose a sampling-based heuristic which can directly find center approximations for each cluster. Empirical experiments show that our proposed methods are faster than the state-of-the-art learning-augmented k-means algorithms with comparable performances on clustering quality.