Consistent k-Median: Simpler, Better and Robust

Xiangyu Guo, Janardhan Kulkarni, Shi Li, Jiayi Xian
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1135-1143, 2021.

Abstract

In this paper we introduce and study the online consistent k-clustering with outliers problem, generalizing the non-outlier version of the problem studied in Lattanzi-Vassilvitskii [18]. We show that a simple local-search based on-line algorithm can give a bicriteria constant approximation for the problem with O(k^2 log^2(nD)) swaps of medians (recourse) in total, where D is the diameter of the metric. When restricted to the problem without outliers, our algorithm is simpler, deterministic and gives better approximation ratio and recourse, compared to that of Lattanzi-Vassilvitskii [18].

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-guo21a, title = { Consistent k-Median: Simpler, Better and Robust }, author = {Guo, Xiangyu and Kulkarni, Janardhan and Li, Shi and Xian, Jiayi}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1135--1143}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/guo21a/guo21a.pdf}, url = {https://proceedings.mlr.press/v130/guo21a.html}, abstract = { In this paper we introduce and study the online consistent k-clustering with outliers problem, generalizing the non-outlier version of the problem studied in Lattanzi-Vassilvitskii [18]. We show that a simple local-search based on-line algorithm can give a bicriteria constant approximation for the problem with O(k^2 log^2(nD)) swaps of medians (recourse) in total, where D is the diameter of the metric. When restricted to the problem without outliers, our algorithm is simpler, deterministic and gives better approximation ratio and recourse, compared to that of Lattanzi-Vassilvitskii [18]. } }
Endnote
%0 Conference Paper %T Consistent k-Median: Simpler, Better and Robust %A Xiangyu Guo %A Janardhan Kulkarni %A Shi Li %A Jiayi Xian %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-guo21a %I PMLR %P 1135--1143 %U https://proceedings.mlr.press/v130/guo21a.html %V 130 %X In this paper we introduce and study the online consistent k-clustering with outliers problem, generalizing the non-outlier version of the problem studied in Lattanzi-Vassilvitskii [18]. We show that a simple local-search based on-line algorithm can give a bicriteria constant approximation for the problem with O(k^2 log^2(nD)) swaps of medians (recourse) in total, where D is the diameter of the metric. When restricted to the problem without outliers, our algorithm is simpler, deterministic and gives better approximation ratio and recourse, compared to that of Lattanzi-Vassilvitskii [18].
APA
Guo, X., Kulkarni, J., Li, S. & Xian, J.. (2021). Consistent k-Median: Simpler, Better and Robust . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1135-1143 Available from https://proceedings.mlr.press/v130/guo21a.html.

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