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Proceedings of the 2013 SIAM International Conference on Data Mining

k-means–: A unified approach to clustering and outlier detection


We present a unified approach for simultaneously clustering and discovering outliers in data. Our approach is formalized as a generalization of the k-MEANS problem. We prove that the problem is NP-hard and then present a practical polynomial time algorithm, which is guaranteed to converge to a local optimum. Furthermore we extend our approach to all distance measures that can be expressed in the form of a Bregman divergence. Experiments on synthetic and real datasets demonstrate the effectiveness of our approach and the utility of carrying out both clustering and outlier detection in a concurrent manner. In particular on the famous KDD cup network-intrusion dataset, we were able to increase the precision of the outlier detection task by nearly 100% compared to the classical nearest-neighbor approach.

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cover image Proceedings
Proceedings of the 2013 SIAM International Conference on Data Mining
Pages: 189 - 197
Editors: Joydeep Ghosh, University of Texas, Austin, Texas, Zoran Obradovic, Temple University, Philadelphia, Pennsylvania, Jennifer Dy, Northeastern University, Boston, Massachusetts, Zhi-Hua Zhou, Nanjing University, Nanjing, Jiangsu, China, Chandrika Kamath, Lawrence Livermore National Laboratory, Livermore, California, and Srinivasan Parthasarathy, The Ohio State University, Columbus, Ohio
ISBN (Print): 978-1-61197-262-7
ISBN (Online): 978-1-61197-283-2


Published online: 18 December 2013




This work was done while the author was with Yahoo! Research.

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