利用背景知识进行高效受限 k 中心聚类

ArXiv Pub Date : 2024-03-24 DOI:10.48550/arXiv.2401.12533
Longkun Guo, Chaoqi Jia, Kewen Liao, Zhigang Lu, Minhui Xue
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引用次数: 0

摘要

基于中心的聚类在理论和实践方面都引起了极大的研究兴趣。在许多实际应用中,输入数据往往包含可用于改善聚类结果的背景知识。在这项工作中,我们以广泛采用的 k 中心聚类为基础,将其输入背景知识建模为必须链接(ML)和不能链接(CL)约束集。然而,包括 k 中心在内的大多数聚类问题本质上都是 NP 难的,而众所周知,更复杂的约束变体会遭遇更严重的近似和计算障碍,从而大大限制了其适用性。通过采用反向支配集、线性规划(LP)积分多面体和 LP 对偶性等一系列技术,我们首次为受限 k 中心问题提出了高效的近似算法,其最佳比率为 2。我们还构建了具有竞争力的基准算法,并在各种真实数据集上对我们的近似算法进行了实证评估。结果验证了我们的理论发现,并证明了我们的算法在聚类成本、聚类质量和运行时间方面的巨大优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient Constrained k-Center Clustering with Background Knowledge
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted k-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including k-center are inherently NP-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained k-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.
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