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On Robustness of Kernel Clustering
Bowei Yan · Purnamrita Sarkar

Mon Dec 05 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #3

Clustering is an important unsupervised learning problem in machine learning and statistics. Among many existing algorithms, kernel \km has drawn much research attention due to its ability to find non-linear cluster boundaries and its inherent simplicity. There are two main approaches for kernel k-means: SVD of the kernel matrix and convex relaxations. Despite the attention kernel clustering has received both from theoretical and applied quarters, not much is known about robustness of the methods. In this paper we first introduce a semidefinite programming relaxation for the kernel clustering problem, then prove that under a suitable model specification, both K-SVD and SDP approaches are consistent in the limit, albeit SDP is strongly consistent, i.e. achieves exact recovery, whereas K-SVD is weakly consistent, i.e. the fraction of misclassified nodes vanish. Also the error bounds suggest that SDP is more resilient towards outliers, which we also demonstrate with experiments.

Author Information

Bowei Yan (University of Texas at Austin)
Purnamrita Sarkar (U.C. Berkeley)

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