Coresets for minimum enclosing balls over sliding windows

• Main Authors: WANG, Yanhao, LI, Yuchen, TAN, Kian-Lee
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2019
• Subjects: Computer Engineering
• Online Access: https://ink.library.smu.edu.sg/sis_research/4618; https://ink.library.smu.edu.sg/context/sis_research/article/5621/viewcontent/1905.03718.pdf
• Institution: Singapore Management University

Coresets are important tools to generate concise summaries of massive datasets for approximate analysis. A coreset is a small subset of points extracted from the original point set such that certain geometric properties are preserved with provable guarantees. This paper investigates the problem of maintaining a coreset to preserve the minimum enclosing ball (MEB) for a sliding window of points that are continuously updated in a data stream. Although the problem has been extensively studied in batch and append-only streaming settings, no efficient sliding-window solution is available yet. In this work, we first introduce an algorithm, called AOMEB, to build a coreset for MEB in an append-only stream. AOMEB improves the practical performance of the state-of-the-art algorithm while having the same approximation ratio. Furthermore, using AOMEB as a building block, we propose two novel algorithms, namely SWMEB and SWMEB+, to maintain coresets for MEB over the sliding window with constant approximation ratios. The proposed algorithms also support coresets for MEB in a reproducing kernel Hilbert space (RKHS). Finally, extensive experiments on real-world and synthetic datasets demonstrate that SWMEB and SWMEB+ achieve speedups of up to four orders of magnitude over the state-of-the-art batch algorithm while providing coresets for MEB with rather small errors compared to the optimal ones.