A Global Optimization Algorithm for K-Center Clustering of One Billion Samples

• URL: http://arxiv.org/abs/2301.00061v1
• Date: Fri, 30 Dec 2022 21:53:08 GMT
• Title: A Global Optimization Algorithm for K-Center Clustering of One Billion Samples
• Authors: Jiayang Ren, Ningning You, Kaixun Hua, Chaojie Ji, Yankai Cao
• Abstract summary: This paper presents a practical global optimization algorithm for the K-center clustering problem. It aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. Our algorithm can averagely reduce the objective function by 25.8% on all the synthetic and real-world datasets.
• Score: 3.4998703934432682
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a reduced-space branch and bound scheme and guarantees convergence to the global optimum in a finite number of steps by only branching on the regions of centers. To improve efficiency, we have designed a two-stage decomposable lower bound, the solution of which can be derived in a closed form. In addition, we also propose several acceleration techniques to narrow down the region of centers, including bounds tightening, sample reduction, and parallelization. Extensive studies on synthetic and real-world datasets have demonstrated that our algorithm can solve the K-center problems to global optimal within 4 hours for ten million samples in the serial mode and one billion samples in the parallel mode. Moreover, compared with the state-of-the-art heuristic methods, the global optimum obtained by our algorithm can averagely reduce the objective function by 25.8% on all the synthetic and real-world datasets.

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