Communications of the ACM
Toward Efficient Agnostic Learning
Machine Learning - Special issue on computational learning theory, COLT'92
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A local search approximation algorithm for k-means clustering
Proceedings of the eighteenth annual symposium on Computational geometry
A discriminative framework for clustering via similarity functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximate clustering without the approximation
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Clustering with or without the approximation
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Clustering under approximation stability
Journal of the ACM (JACM)
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Motivated by the principle of agnostic learning, we present an extension of the model introduced by Balcan, Blum, and Gupta [3] on computing low-error clusterings. The extended model uses a weaker assumption on the target clustering, which captures data clustering in presence of outliers or ill-behaved data points. Unlike the original target clustering property, with our new property it may no longer be the case that all plausible target clusterings are close to each other. Instead, we present algorithms that produce a small list of clusterings with the guarantee that all clusterings satisfying the assumption are close to some clustering in the list, proving both upper and lower bounds on the length of the list needed.