Abstract
A number of mixture models of local Principal Component Analysis (PCA) have been developed to analyze data distributed in space. Most of these models require the users to determine the number of the local PCA models, i.e., the number of clusters for clustering analysis. This is not a reasonable requirement in practical applications. This paper proposes an automatic clustering algorithm to analyze data based on a competition model of probabilistic PCA. Without identifying the number of clusters in advance, the algorithm automatically evolves to partition a given data set into some small clusters in terms of the empirical rule of Gaussian distribution. It is shown the algorithm will not only group data but also can explore the hierarchical structure of a given data.
This work was supported by Specialized Research Fund for the Doctoral Program of Higher Education under Grant 2010081110053.
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References
Honda, K., Ichihashi, H.: Regularized Linear fuzzy clustering and probabilistic PCA mixture models. IEEE Transactions on Fuzzy Systems 13(4), 508–516 (2005)
Lv, J.C., Yi, Z., Zhou, J.: Subspace Learning of Neural Networks. CRC Press, Taylor & Francis Group (2011)
Lv, J.C., Tan, K.K., Yi, Z., Huang, S.: A family of fuzzy learning algorithms for robust principal component analysis neural networks. IEEE Transactions on Fuzzy Systems 18(1), 217–226 (2010)
Lv, J.C., Tan, K.K., Yi, Z., Huang, S.: Convergence Analysis of Hyvärinen and Oja’s ICA Learning Algorithms with Constant Learning Rates. IEEE Transactions on Signal Processing 57(5), 1811–1824 (2009)
Xu, R., Wunsch II, D.: Survery of clustering algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)
Zhao, J., Jian, Q.: Probabilistic PCA for t distribution. Neurocomputing 69, 2217–2226 (2006)
Bruneau, P., Gelgon, M., Picarougne, F.: Parsimonious reduction of gaussian mixture models with a variational-bayes approach. Pattern Recognition 43(3), 850–858 (2010)
Archambeau, C., Delannay, N., Verleysen, M.: Mixtures of robust probabilistic principal component analysizers. Neurocomputing 71, 1274–1282 (2008)
Kambhatla, N., Leen, T.K.: Dimension reduction by local principal component analysis. Neural Computation 9(7), 1493–1516 (1997)
Möller, R., Hoffmann, H.: An extension of neural gas to local PCA. Neurocomputing 62, 305–326 (2004)
Tipping, M.E., Bishop, C.M.: Probabilistic principal component analyzers. J. Roy. Statist. Soc. Ser. B. 63, 611–622 (1999)
Tipping, M.E., Bishop, C.M.: Mixtures of probabilistic principal component analyzers. Neural Computation 11, 443–482 (1999)
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Li, Y., Lv, J.C., Li, X. (2015). An Automatic Clustering Algorithm Based on a Competition Model of Probabilistic PCA. In: Handa, H., Ishibuchi, H., Ong, YS., Tan, K. (eds) Proceedings of the 18th Asia Pacific Symposium on Intelligent and Evolutionary Systems, Volume 1. Proceedings in Adaptation, Learning and Optimization, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-13359-1_6
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DOI: https://doi.org/10.1007/978-3-319-13359-1_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13358-4
Online ISBN: 978-3-319-13359-1
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