Greedy Strategy Works for $k$-Center Clustering with Outliers and Coreset Construction
This work addresses a challenging clustering problem with outliers, offering an efficient and easy-to-implement solution, though it is incremental as it builds on a known greedy strategy.
The paper tackles the problem of k-center clustering with outliers by adapting Gonzalez's greedy algorithm, achieving near-optimal solutions with lower running times compared to existing methods.
We study the problem of $k$-center clustering with outliers in arbitrary metrics and Euclidean space. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem. Our idea is inspired by the greedy method, Gonzalez's algorithm, for solving the problem of ordinary $k$-center clustering. Based on some novel observations, we show that this greedy strategy actually can handle $k$-center clustering with outliers efficiently, in terms of clustering quality and time complexity. We further show that the greedy approach yields small coreset for the problem in doubling metrics, so as to reduce the time complexity significantly. Our algorithms are easy to implement in practice. We test our method on both synthetic and real datasets. The experimental results suggest that our algorithms can achieve near optimal solutions and yield lower running times comparing with existing methods.