Abstract
Generative Topographic Mapping is a probabilistic model for data clustering and visualization. It maps points, considered as prototype representatives of data clusters, from a low dimensional latent space onto the observed data space. In semi-supervised settings, class information can be added resulting in a model variation called class-GTM. The number of class-GTM latent points used is usually large for visualization purposes and does not necessarily reflect the class structure of the data. It is therefore convenient to group the clusters further in a two-stage procedure. In this paper, class-GTM is first used to obtain the basic cluster prototypes. Two novel methods are proposed to use this information as prior knowledge for the K-means-based second stage. We evaluate, using an entropy measure, whether these methods retain the class separability capabilities of class-GTM in the two-stage process, and whether the two-stage procedure improves on the direct clustering of the data using K-means.
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References
Figueiredo, M.A.T., Jain, A.K.: Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(3), 381–396 (2002)
Bishop, C.M., Svensén, M., Williams, C.K.I.: The Generative Topographic Mapping. Neural Computation 10(1), 215–234 (1998)
Vellido, A.: Missing data imputation through GTM as a mixture of t-distributions. Neural Networks 19(10), 1624–1635 (2006)
Vellido, A., Lisboa, P.J.G.: Handling outliers in brain tumour MRS data analysis through robust topographic mapping. Computers in Biology and Medicine 36(10), 1049–1063 (2006)
Vellido, A., Lisboa, P.J.G., Vicente, D.: Robust analysis of MRS brain tumour data using t-GTM. Neurocomputing 69(7-9), 754–768 (2006)
Hastie, T., Tibshirani, R.: Discriminant analysis by Gaussian mixtures. Journal of the Royal Statistical Society (B) 58, 155–176 (1996)
Cruz, R., Vellido, A.: On the improvement of brain tumour data clustering using class information. In: STAIRS 2006. Proceedings of the 3rd European Starting AI Researcher Symposium, Riva del Garda, Italy (2006)
Sun, Y., Tiňo, P., Nabney, I.T.: Visualization of incomplete data using class information constraints. In: Winkler, J., Niranjan, M. (eds.) Uncertainty in Geometric Computations, pp. 165–174. Kluwer Academic Publishers, The Netherlands (2002)
Vesanto, J., Alhoniemi, E.: Clustering of the Self-Organizing Map. IEEE Transactions on Neural Networks (2000)
Bishop, C.M., Svensén, M., Williams, C.K.I.: Magnification Factors for the GTM algorithm. In: Proceedings of the IEE fifth International Conference on Artificial Neural Networks, pp. 64–69 (1997)
Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. on Pattern Analysis and Machine Intelligence 1(2), 224–227 (1979)
Bishop, C.M., James, G.D.: Analysis of multiphase flows using dual-energy gamma densitometry and neural networks. Nuclear Instruments and Methods in Physics Research A327, 580–593 (1993)
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Cruz-Barbosa, R., Vellido, A. (2007). On the Initialization of Two-Stage Clustering with Class-GTM. In: Borrajo, D., Castillo, L., Corchado, J.M. (eds) Current Topics in Artificial Intelligence. CAEPIA 2007. Lecture Notes in Computer Science(), vol 4788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75271-4_6
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DOI: https://doi.org/10.1007/978-3-540-75271-4_6
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