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Poster
Coresets for Clustering in Graphs of Bounded Treewidth
Daniel Baker · Vladimir Braverman · Lingxiao Huang · Shaofeng H.-C. Jiang · Robert Krauthgamer · Xuan Wu

Wed Jul 15 08:00 AM -- 08:45 AM & Wed Jul 15 08:00 PM -- 08:45 PM (PDT) @
in Poster Session 22 »
We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path metric of edge-weighted graphs. Such clustering problems are essential to data analysis and used for example in road networks and data visualization. A coreset is a compact summary of the data that approximately preserves the clustering objective for every possible center set, and it offers significant efficiency improvements in terms of running time, storage, and communication, including in streaming and distributed settings. Our main result is a near-linear time construction of a coreset for k-Median in a general graph $G$, with size $O_{\epsilon, k}(\mathrm{tw}(G))$ where $\mathrm{tw}(G)$ is the treewidth of $G$, and we complement the construction with a nearly-tight size lower bound. The construction is based on the framework of Feldman and Langberg [STOC 2011], and our main technical contribution, as required by this framework, is a uniform bound of $O(\mathrm{tw}(G))$ on the shattering dimension under any point weights. We validate our coreset on real-world road networks, and our scalable algorithm constructs tiny coresets with high accuracy, which translates to a massive speedup of existing approximation algorithms such as local search for graph k-Median.
Keywords: Clustering · Large Scale Learning and Big Data · Unsupervised and Semi-supervised Learning

Author Information

Daniel Baker (Johns Hopkins University)
Vladimir Braverman (Johns Hopkins University)
Lingxiao Huang (Yale University)
Shaofeng H.-C. Jiang (Weizmann Institute of Science)
Robert Krauthgamer (Weizmann Institute of Science)
Xuan Wu (Johns Hopkins University)

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