Abstract
Recently a robust probabilistic L1-PCA model was introduced in [1] by replacing the conventional Gaussian noise model with the Laplacian L1 model. Due to the heavy tail characteristics of the L1 distribution, the proposed model is more robust against data outliers. In this paper, we generalized the L1-PCA into a mixture of L1-distributions so that the model can be used for possible multiclustering data. For the model learning we use the property that the L1 density can be expanded as a superposition of infinite number of Gaussian densities to include a tractable Bayesian learning and inference based on the variational EM-type algorithm.
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References
Gao, J.: Robust L1 principal component analysis and its bayesian variational inference. Neural Computation (to appear, 2008)
McLachlan, G., Peel, D.: Finite Mixture Models. John Wiley, New York (2000)
Dempster, A., Laird, N., Rubin, D.: Maximum-likelihood from incomplete data via the EM algorithm. J. Royal Statistical Soceity, Ser. B 39, 1–38 (1977)
Tipping, M., Bishop, C.: Mixtures of probabilistic principal component analyzers. Neural Computation 11, 443–482 (1999)
Verbeek, J.: Learning nonlinear image manifolds by global alignment of local linear models. IEEE Trans. on Pattern Analysis and Machine Intelligence 28(8), 1236–1250 (2006)
Bhowmick, D., Davison, A., Goldstein, D., Ruffieux, Y.: A Laplace mixture model for identification of differential expression in microarray experiments. Biostatistics 7, 630–641 (2006)
Jordan, M.: Graphical models. Statistical Science (Special Issue on Bayesian Statistics) 19, 140–155 (2004)
Peel, D., McLachlan, G.: Robust mixture modelling using the t distribution. Statistic and Computing 10, 339–348 (2000)
Ridder, D.D., Franc, V.: Robust subspace mixture models using t-distributions. In: Harvey, R., Bangham, A. (eds.) BMVC 2003. Proceedings of the 14th British Machine Vision Conference, pp. 319–328 (2003)
Archambeau, C.: Probabilistic models in noisy environments and their application to a visual prosthesis for the blind. Doctoral dissertation, Université Catholique de Louvain, Belgium (2005)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B. 58, 267–288 (1996)
Ng, A.: Feature selection, L1 vs. L2 regularization, and rotational invariance. In: Proceedings of Intl Conf. Machine Learning (2004)
Jolliffe, I.: Principal component analysis, 2nd edn. Springer, New York (2002)
Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. Technical report, Statistics Department, Stanford University (2004)
Park, H.J., Lee, T.W.: Modeling nonlinear dependencies in natural images using mixture of laplacian distribution. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems 17, pp. 1041–1048. MIT Press, Cambridge (2005)
Gao, J., Gunn, S., Kandola, J.: Adapting kernels by variational approach in svm. In: McKay, B., Slaney, J.K. (eds.) AI 2002. LNCS (LNAI), vol. 2557, pp. 395–406. Springer, Heidelberg (2002)
Tipping, M., Lawrence, N.: Variational inference for Student-t models: Robust Bayesian interpolation and generalized component analysis. NeuroComputing 69, 123–141 (2005)
Pontil, M., Mukherjee, S., Girosi, F.: On the noise model of support vector machine regression. In: A.I. Memo 1651, AI Laboratory, MIT, Cambridge (1998)
Guo, Y., Gao, J.B., Kwan, P.W.: Kernel Laplacian eigenmaps for visualization of non-vectorial data. In: Sattar, A., Kang, B.-H. (eds.) AI 2006. LNCS (LNAI), vol. 4304, pp. 1179–1183. Springer, Heidelberg (2006)
Guo, Y., Gao, J.B., Kwan, P.W.: Visualization of non-vectorial data using twin kernel embedding. In: Ong, K., Smith-Miles, K., Lee, V., Ng, W. (eds.) AIDM 2006. Proceedings of the International Workshop on Integrating AI and Data Mining, pp. 11–17. IEEE Computer Society Press, Los Alamitos (2006)
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Gao, J., Xu, R.Y. (2007). Mixture of the Robust L1 Distributions and Its Applications. In: Orgun, M.A., Thornton, J. (eds) AI 2007: Advances in Artificial Intelligence. AI 2007. Lecture Notes in Computer Science(), vol 4830. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76928-6_5
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DOI: https://doi.org/10.1007/978-3-540-76928-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76926-2
Online ISBN: 978-3-540-76928-6
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