Abstract
Considering data processing problems from a geometric point of view, previous work has shown that the intrinsic dimension of the data could have some semantics. In this paper, we start from the consideration of this inherent topology property and propose the usage of such a semantic criterion for clustering. The corresponding learning algorithms are provided. Theoretical justification and analysis of the algorithms are shown. Promising results are reported by the experiments that generally fail with conventional clustering algorithms.
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References
Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Dietterich, T.G., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems 14, pp. 585–591. MIT Press, Cambridge (2002)
Blimes, J.A.: A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. International Computer Science Institute, UC Berkeley (1998)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Scociety B 39, 1–39 (1977)
Donoho, D.L., Grimes, C.: Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. In: Proceedings of the National Academy of Arts and Sciences (2003)
Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)
Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Computing Surveys 31(3), 263–323 (1999)
Levina, E., Bickel, P.J.: Maximum likelihood estimation of intrinsic dimension. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems 17, pp. 777–784. MIT Press, Cambridge (2005)
Michael, K., Yishay, M., Andrew, N.: An information-theoretic analysis of hard and soft assignment methods for clustering. In: Proceedings of the 13th Annual Conference on Uncertainty in Artificial Intelligence (UAI 1997), pp. 282–293. Morgan Kaufmann Publishers, San Francisco (1997)
Pettis, K.W., Bailey, T.A., Jain, A.K., Dubes, R.C.: An intrinsic dimensionality estimator from near-neighbor information. IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 25–37 (1979)
Roweis, S., Smola, A.J.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)
Seung, H.S., Lee, D.D.: The manifold ways of perception. Science 290, 2268–2269 (2000)
Tenenbaum, J.B., de Silva, V., Landford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2313–2323 (2000)
Verveer, R., Duin, R.: An evaluation of intrinsic dimensionality estimators. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(1), 81–86 (1995)
Xu, L., Krzyzak, A., Oja, E.: Rival penalized competitive learning for clustering analysis, RBF net, and curve detection. IEEE Transactions on Neural Networks 4 (1993)
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Li, W., Lee, KH., Leung, KS. (2006). Clustering with a Semantic Criterion Based on Dimensionality Analysis. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893257_88
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DOI: https://doi.org/10.1007/11893257_88
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46481-5
Online ISBN: 978-3-540-46482-2
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