Abstract
In this paper, we initiate a theoretical study of the problem of clustering data under interactive feedback. We introduce a query-based model in which users can provide feedback to a clustering algorithm in a natural way via split and merge requests. We then analyze the “clusterability” of different concept classes in this framework — the ability to cluster correctly with a bounded number of requests under only the assumption that each cluster can be described by a concept in the class — and provide efficient algorithms as well as information-theoretic upper and lower bounds.
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References
Achlioptas, D., McSherry, F.: On spectral learning of mixtures of distributions. In: Proceedings of the 18th Annual Conference on Learning Theory (2005)
Angluin, D.: Queries and concept learning. Machine Learning 2, 319–342 (1998)
Arora, S., Kannan, R.: Learning mixtures of arbitrary gaussians. In: Proceedings of the 33rd ACM Symposium on Theory of Computing (2001)
Balcan, M.-F., Blum, A., Vempala, S.: A Discriminative Framework for Clustering via Similarity Functions. In: Proceedings of the 40th ACM Symposium on Theory of Computing (2008)
Brubaker, S.C., Vempala, S.: Isotropic PCA and affine-invariant clustering. In: Proceedings of the 49th ACM Symposium on Foundations of Computer Science (2008)
Bshouty, N.H., Goldberg, P.W., Goldman, S.A., Mathias, H.D.: Exact learning of discretized geometric concepts. SIAM J. Computing 28(2), 674–699 (1998)
Dasgupta, A., Hopcroft, J., Kleinberg, J., Sandler, M.: On learning mixtures of heavy-tailed distributions. In: 46th IEEE Symposium on Foundations of Computer Science (2005)
Dasgupta, A., Hopcroft, J.E., Kannan, R., Mitra, P.P.: Spectral clustering by recursive partitioning. In: Proceedings of the 14th European Symposium on Algorithms, pp. 256–267 (2006)
Dasgupta, S.: Learning mixtures of gaussians. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science (1999)
Hellerstein, L., Pillaipakkamnatt, K., Raghavan, V.V., Wilkins, D.: How many queries are needed to learn? In: Proceedings of the 27th ACM Symposium on Theory of Computing (1995)
Jackson, J.: An efficient membership-query algorithm for learning dnf with respect to the uniform distribution. Journal of Computer and System Sciences 57(3), 414–440 (1995)
Kannan, R., Salmasian, H., Vempala, S.: The spectral method for general mixture models. In: Proceedings of the 18th Annual Conference on Learning Theory (2005)
Mansour, Y.: Learning boolean functions via the fourier transform. Theoretical Advances in Neural Computation and Learning, 391–424 (1994)
Vempala, S., Wang, G.: A spectral algorithm for learning mixture models. Journal of Computer and System Sciences 68(2), 841–860 (2004)
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Balcan, MF., Blum, A. (2008). Clustering with Interactive Feedback. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2008. Lecture Notes in Computer Science(), vol 5254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87987-9_27
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DOI: https://doi.org/10.1007/978-3-540-87987-9_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87986-2
Online ISBN: 978-3-540-87987-9
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