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2015 | OriginalPaper | Buchkapitel

Variational Learning of Finite Inverted Dirichlet Mixture Models and Applications

verfasst von : Parisa Tirdad, Nizar Bouguila, Djemel Ziou

Erschienen in: Artificial Intelligence Applications in Information and Communication Technologies

Verlag: Springer International Publishing

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Abstract

Statistical modeling provides a useful and well grounded framework to conduct inference from data. This has given rise to the development of varied rich suite of models and techniques. In particular, finite mixture models have received a lot of attention by offering a formal approach to unsupervised learning which allows to discover the latent structure expressed in observed data. In this chapter, we propose a mixture model based on the inverted Dirichlet mixture which provides a natural way of clustering positive data. An EM-style algorithm is developed based upen variational inference for learning the parameters of the mixture model. The proposed statistical framework is applied to the challenging tasks of natural scene categorization and human activity classification.

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Literatur
1.
Zurück zum Zitat Picard, R.W.: Light-years from lena: video and image libraries of the future. In: Proceeding of the IEEE International Conference on Image Processing (ICIP), vol. 1, pp. 310–313 (1995) Picard, R.W.: Light-years from lena: video and image libraries of the future. In: Proceeding of the IEEE International Conference on Image Processing (ICIP), vol. 1, pp. 310–313 (1995)
2.
Zurück zum Zitat Ortega, M., Rui, Y., Chakrabarti, K., Porkaew, K., Mehrotra, S., Huang, T.S.: Supporting ranked boolean similarity queries in mars. IEEE Trans. Knowl. Data Eng. 10(6), 905–925 (1998)CrossRef Ortega, M., Rui, Y., Chakrabarti, K., Porkaew, K., Mehrotra, S., Huang, T.S.: Supporting ranked boolean similarity queries in mars. IEEE Trans. Knowl. Data Eng. 10(6), 905–925 (1998)CrossRef
3.
Zurück zum Zitat Guha, S., Rastogi, R., Shim, K.: Cure: an efficient clustering algorithm for large databases. Inf. Syst. 26(1), 35–58 (2001)CrossRefMATH Guha, S., Rastogi, R., Shim, K.: Cure: an efficient clustering algorithm for large databases. Inf. Syst. 26(1), 35–58 (2001)CrossRefMATH
4.
Zurück zum Zitat Pal, N.R., Biswas, J.: Cluster validation using graph theoretic concepts. Pattern Recognit. 30(6), 847–857 (1997)CrossRef Pal, N.R., Biswas, J.: Cluster validation using graph theoretic concepts. Pattern Recognit. 30(6), 847–857 (1997)CrossRef
5.
Zurück zum Zitat Comaniciu, D., Meer, P.: Distribution free decomposition of multivariate data. Pattern Anal. Appl. 2(1), 22–30 (1999)CrossRef Comaniciu, D., Meer, P.: Distribution free decomposition of multivariate data. Pattern Anal. Appl. 2(1), 22–30 (1999)CrossRef
6.
Zurück zum Zitat Basu, S., Banerjee, A., Mooney, R.J.: Semi-supervised clustering by seeding. In: Proceeding of the Nineteenth International Conference on Machine Learning (ICML), pp. 27–34 (2002) Basu, S., Banerjee, A., Mooney, R.J.: Semi-supervised clustering by seeding. In: Proceeding of the Nineteenth International Conference on Machine Learning (ICML), pp. 27–34 (2002)
7.
Zurück zum Zitat Dougherty, E.R., Brun, M.: A probabilistic theory of clustering. Pattern Recognit. 37, 917–925 (2004)CrossRefMATH Dougherty, E.R., Brun, M.: A probabilistic theory of clustering. Pattern Recognit. 37, 917–925 (2004)CrossRefMATH
8.
Zurück zum Zitat Bagirov, A.M., Ugon, J., Webb, D.: Fast modified global k-means algorithm for incremental cluster construction. Pattern Recognit. 44(4), 866–876 (2011)CrossRefMATH Bagirov, A.M., Ugon, J., Webb, D.: Fast modified global k-means algorithm for incremental cluster construction. Pattern Recognit. 44(4), 866–876 (2011)CrossRefMATH
9.
Zurück zum Zitat Law, M.H.C., Topchy, A.P., Jain, A.K.: Multiobjective data clustering. In: Proceeding of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), vol. 2, pp. II-424–II-430 (2004) Law, M.H.C., Topchy, A.P., Jain, A.K.: Multiobjective data clustering. In: Proceeding of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), vol. 2, pp. II-424–II-430 (2004)
10.
Zurück zum Zitat Hastie, T., Tibshirani, R.: Discriminant analysis by gaussian mixtures. J. Roy. Stat. Soc. Ser. B 58(1), 155–176 (1996)MathSciNetMATH Hastie, T., Tibshirani, R.: Discriminant analysis by gaussian mixtures. J. Roy. Stat. Soc. Ser. B 58(1), 155–176 (1996)MathSciNetMATH
11.
Zurück zum Zitat Garcia, V., Nielsen, F., Nock, R.: Levels of details for gaussian mixture models. In: Zha, H., Taniguchi, R., Maybank, S.J. (eds.) ACCV (2), volume 5995 of Lecture Notes in Computer Science, pp. 514–525. Springer (2009) Garcia, V., Nielsen, F., Nock, R.: Levels of details for gaussian mixture models. In: Zha, H., Taniguchi, R., Maybank, S.J. (eds.) ACCV (2), volume 5995 of Lecture Notes in Computer Science, pp. 514–525. Springer (2009)
12.
Zurück zum Zitat Dixit, M., Rasiwasia, N., Vasconcelos, N.: Adapted gaussian models for image classification. In: Proceeding of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 937–943 (2011) Dixit, M., Rasiwasia, N., Vasconcelos, N.: Adapted gaussian models for image classification. In: Proceeding of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 937–943 (2011)
13.
Zurück zum Zitat Elgammal, A.M., Harwood, D., Davis, L.S.: Non-parametric model for background subtraction. In: Vernon, D. (ed.) Computer Vision - ECCV 2000, 6th European Conference on Computer Vision, Dublin, Ireland, 26 June– 1 July 2000. Proceedings, Part II, volume 1843 of Lecture Notes in Computer Science, pp. 751–767. Springer (2000) Elgammal, A.M., Harwood, D., Davis, L.S.: Non-parametric model for background subtraction. In: Vernon, D. (ed.) Computer Vision - ECCV 2000, 6th European Conference on Computer Vision, Dublin, Ireland, 26 June– 1 July 2000. Proceedings, Part II, volume 1843 of Lecture Notes in Computer Science, pp. 751–767. Springer (2000)
14.
Zurück zum Zitat Liu, L., Fan, G.: Combined key-frame extraction and object-based video segmentation. IEEE Trans. Circ. Syst. Video Technol. 15(7), 869–884 (2005)CrossRef Liu, L., Fan, G.: Combined key-frame extraction and object-based video segmentation. IEEE Trans. Circ. Syst. Video Technol. 15(7), 869–884 (2005)CrossRef
15.
Zurück zum Zitat Song, X., Fan, G.: Joint key-frame extraction and object segmentation for content-based video analysis. IEEE Trans. Circ. Syst. Video Technol. 16(7), 904–914 (2006)MathSciNetCrossRef Song, X., Fan, G.: Joint key-frame extraction and object segmentation for content-based video analysis. IEEE Trans. Circ. Syst. Video Technol. 16(7), 904–914 (2006)MathSciNetCrossRef
16.
Zurück zum Zitat Allili, M.S., Bouguila, N., Ziou, D.: Finite generalized gaussian mixture modeling and applications to image and video foreground segmentation. In: Proceeding of the Fourth Canadian Conference on Computer and Robot Vision (CRV), pp. 183–190 (2007) Allili, M.S., Bouguila, N., Ziou, D.: Finite generalized gaussian mixture modeling and applications to image and video foreground segmentation. In: Proceeding of the Fourth Canadian Conference on Computer and Robot Vision (CRV), pp. 183–190 (2007)
17.
Zurück zum Zitat Bouguila, N.: Spatial color image databases summarization. In: Proceeding of the IEEE International Conference on Acoustics, Speech, and Signal Processing, (ICASSP), pp. 953–956 (2007) Bouguila, N.: Spatial color image databases summarization. In: Proceeding of the IEEE International Conference on Acoustics, Speech, and Signal Processing, (ICASSP), pp. 953–956 (2007)
18.
Zurück zum Zitat Bouguila, N., Ziou, D.: Online clustering via finite mixtures of dirichlet and minimum message length. Eng. Appl. Artif. Intell. 19(4), 371–379 (2006)CrossRef Bouguila, N., Ziou, D.: Online clustering via finite mixtures of dirichlet and minimum message length. Eng. Appl. Artif. Intell. 19(4), 371–379 (2006)CrossRef
19.
Zurück zum Zitat Bdiri, T., Bouguila, N.: Learning inverted dirichlet mixtures for positive data clustering. In: Kuznetsov, S.O., Slezak, D., Hepting, D.H., Mirkin, B. (eds.) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing - 13th International Conference, RSFDGrC 2011, Moscow, Russia, 25–27 June 2011. Proceedings, volume 6743 of Lecture Notes in Computer Science, pp. 265–272. Springer (2011) Bdiri, T., Bouguila, N.: Learning inverted dirichlet mixtures for positive data clustering. In: Kuznetsov, S.O., Slezak, D., Hepting, D.H., Mirkin, B. (eds.) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing - 13th International Conference, RSFDGrC 2011, Moscow, Russia, 25–27 June 2011. Proceedings, volume 6743 of Lecture Notes in Computer Science, pp. 265–272. Springer (2011)
20.
Zurück zum Zitat Bdiri, T., Bouguila, N.: Positive vectors clustering using inverted dirichlet finite mixture models. Expert Syst. Appl. 39(2), 1869–1882 (2012)CrossRef Bdiri, T., Bouguila, N.: Positive vectors clustering using inverted dirichlet finite mixture models. Expert Syst. Appl. 39(2), 1869–1882 (2012)CrossRef
21.
Zurück zum Zitat Bdiri, T., Bouguila, N.: Bayesian learning of inverted dirichlet mixtures for SVM kernels generation. Neural Comput. Appl. 23(5), 1443–1458 (2013)CrossRef Bdiri, T., Bouguila, N.: Bayesian learning of inverted dirichlet mixtures for SVM kernels generation. Neural Comput. Appl. 23(5), 1443–1458 (2013)CrossRef
22.
Zurück zum Zitat Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the em algorithm. J. Roy. Stat. Soc. Ser. B 39, 1–38 (1977)MathSciNetMATH Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the em algorithm. J. Roy. Stat. Soc. Ser. B 39, 1–38 (1977)MathSciNetMATH
23.
Zurück zum Zitat Bouguila, N., Ziou, D., Hammoud, R.I.: On bayesian analysis of a finite generalized dirichlet mixture via a metropolis-within-gibbs sampling. Pattern Anal. Appl. 12(2), 151–166 (2009)MathSciNetCrossRef Bouguila, N., Ziou, D., Hammoud, R.I.: On bayesian analysis of a finite generalized dirichlet mixture via a metropolis-within-gibbs sampling. Pattern Anal. Appl. 12(2), 151–166 (2009)MathSciNetCrossRef
24.
Zurück zum Zitat Ghahramani, Z., Beal, M.J.: Variational inference for bayesian mixtures of factor analysers. In: Advances in Neural Information Processing Systems (NIPS), pp. 449–455 (1999) Ghahramani, Z., Beal, M.J.: Variational inference for bayesian mixtures of factor analysers. In: Advances in Neural Information Processing Systems (NIPS), pp. 449–455 (1999)
25.
Zurück zum Zitat Archambeau, C., Opper, M., Shen, Y., Cornford, D., Shawe-Taylor, J.: Variational inference for diffusion processes. In: Advances in Neural Information Processing Systems (NIPS) (2007) Archambeau, C., Opper, M., Shen, Y., Cornford, D., Shawe-Taylor, J.: Variational inference for diffusion processes. In: Advances in Neural Information Processing Systems (NIPS) (2007)
26.
Zurück zum Zitat Opper, M., Sanguinetti, G.: Variational inference for markov jump processes. In: Advances in Neural Information Processing Systems (NIPS) (2007) Opper, M., Sanguinetti, G.: Variational inference for markov jump processes. In: Advances in Neural Information Processing Systems (NIPS) (2007)
27.
Zurück zum Zitat Tiao, G.G., Cuttman, I.: The inverted dirichlet distribution with applications. J. Am. Stat. Assoc. 60(311), 793–805 (1965)MathSciNetCrossRefMATH Tiao, G.G., Cuttman, I.: The inverted dirichlet distribution with applications. J. Am. Stat. Assoc. 60(311), 793–805 (1965)MathSciNetCrossRefMATH
28.
29.
30.
Zurück zum Zitat Corduneanu, A., Bishop, C.M.: Variational Bayesian model selection for mixture distributions. In: Proceeding of the International Conference on Artificial Intelligence and Statistics (AISTAT), pp. 27–34 (2001) Corduneanu, A., Bishop, C.M.: Variational Bayesian model selection for mixture distributions. In: Proceeding of the International Conference on Artificial Intelligence and Statistics (AISTAT), pp. 27–34 (2001)
31.
Zurück zum Zitat Saul, L., Jordan, M.I.: Exploiting tractable substructures in intractable networks. In: Advances in Neural Information Processing Systems 8, pp. 486–492. MIT Press, Cambridge (1995) Saul, L., Jordan, M.I.: Exploiting tractable substructures in intractable networks. In: Advances in Neural Information Processing Systems 8, pp. 486–492. MIT Press, Cambridge (1995)
32.
Zurück zum Zitat Jaakkola, T.S., Jordan, M.I.: Computing upper and lower bounds on likelihoods in intractable networks. In: Proceeding of the Twelfth International Conference on Uncertainty in Artificial Intelligence, UAI’96, pp. 340–348, Morgan Kaufmann Publishers Inc, San Francisco, CA, USA (1996) Jaakkola, T.S., Jordan, M.I.: Computing upper and lower bounds on likelihoods in intractable networks. In: Proceeding of the Twelfth International Conference on Uncertainty in Artificial Intelligence, UAI’96, pp. 340–348, Morgan Kaufmann Publishers Inc, San Francisco, CA, USA (1996)
33.
Zurück zum Zitat Attias, H.: A variational bayesian framework for graphical models. In: Advances in Neural Information Processing Systems 12, pp. 209–215. MIT Press, Cambridge (2000) Attias, H.: A variational bayesian framework for graphical models. In: Advances in Neural Information Processing Systems 12, pp. 209–215. MIT Press, Cambridge (2000)
34.
Zurück zum Zitat Fei-Fei, L., Perona, P.: A bayesian hierarchical model for learning natural scene categories. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005. CVPR 2005. vol. 2, pp. 524–531 (2005) Fei-Fei, L., Perona, P.: A bayesian hierarchical model for learning natural scene categories. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005. CVPR 2005. vol. 2, pp. 524–531 (2005)
35.
Zurück zum Zitat Bosch, A., Zisserman, A., Munoz, X.: Scene classification via plsa. In: Proceeding of the 9th European Conference on Computer Vision - Volume Part IV, ECCV’06, pp. 517–530, Springer, Berlin, (2006) Bosch, A., Zisserman, A., Munoz, X.: Scene classification via plsa. In: Proceeding of the 9th European Conference on Computer Vision - Volume Part IV, ECCV’06, pp. 517–530, Springer, Berlin, (2006)
36.
Zurück zum Zitat Yang, J., Jiang, Y.G., Hauptmann, A.G., Ngo, C.W.: Evaluating bag-of-visual-words representations in scene classification. In: Proceeding of the International Workshop on Workshop on Multimedia Information Retrieval, pp. 197–206, ACM, New York, USA, 2007 Yang, J., Jiang, Y.G., Hauptmann, A.G., Ngo, C.W.: Evaluating bag-of-visual-words representations in scene classification. In: Proceeding of the International Workshop on Workshop on Multimedia Information Retrieval, pp. 197–206, ACM, New York, USA, 2007
37.
Zurück zum Zitat Nilsback, M.E., Zisserman, A.: A visual vocabulary for flower classification. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 1447–1454 (2006) Nilsback, M.E., Zisserman, A.: A visual vocabulary for flower classification. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 1447–1454 (2006)
38.
Zurück zum Zitat Lowe, D.G.: Object recognition from local scale-invariant features. In: Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2, ICCV ’99, pp. 1150-1157, IEEE Computer Society, Washington, DC, USA (1999) Lowe, D.G.: Object recognition from local scale-invariant features. In: Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2, ICCV ’99, pp. 1150-1157, IEEE Computer Society, Washington, DC, USA (1999)
39.
Zurück zum Zitat Oliva, A., Torralba, A.: Modeling the shape of the scene: a holistic representation of the spatial envelope. Int. J. Comput. Vision 42(3), 145–175 (2001)CrossRefMATH Oliva, A., Torralba, A.: Modeling the shape of the scene: a holistic representation of the spatial envelope. Int. J. Comput. Vision 42(3), 145–175 (2001)CrossRefMATH
40.
Zurück zum Zitat Aggarwal, J.K., Ryoo, M.S.: Human activity analysis: a review. ACM Comput. Surv. 43(3):16:1–16:43 (2011) Aggarwal, J.K., Ryoo, M.S.: Human activity analysis: a review. ACM Comput. Surv. 43(3):16:1–16:43 (2011)
41.
Zurück zum Zitat Luo, J., Wang, W., Qi, H.: Feature extraction and representation for distributed multi-view human action recognition. IEEE J. Emerg. Sel. Top. Circ. Syst. 3(2), 145–154 (2013)CrossRefMATH Luo, J., Wang, W., Qi, H.: Feature extraction and representation for distributed multi-view human action recognition. IEEE J. Emerg. Sel. Top. Circ. Syst. 3(2), 145–154 (2013)CrossRefMATH
42.
Zurück zum Zitat Ballan, L., Bertini, M., Del Bimbo, A., Seidenari, L., Serra, G.: Effective codebooks for human action representation and classification in unconstrained videos. IEEE Trans. Multimedia 14(4), 1234–1245 (2012)CrossRef Ballan, L., Bertini, M., Del Bimbo, A., Seidenari, L., Serra, G.: Effective codebooks for human action representation and classification in unconstrained videos. IEEE Trans. Multimedia 14(4), 1234–1245 (2012)CrossRef
43.
Zurück zum Zitat Ballan, L., Bertini, M., Del Bimbo, A., Seidenari, L., Serra, G.: Effective codebooks for human action representation and classification in unconstrained videos. IEEE Trans. Multimedia 14(4), 1234–1245 (2012)CrossRef Ballan, L., Bertini, M., Del Bimbo, A., Seidenari, L., Serra, G.: Effective codebooks for human action representation and classification in unconstrained videos. IEEE Trans. Multimedia 14(4), 1234–1245 (2012)CrossRef
44.
Zurück zum Zitat Laptev, I., Marszalek, M., Schmid, C., Rozenfeld, B.: Learning realistic human actions from movies. In: 2013 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2008) Laptev, I., Marszalek, M., Schmid, C., Rozenfeld, B.: Learning realistic human actions from movies. In: 2013 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2008)
45.
Zurück zum Zitat Horn, B.K.P., Schunck, B.G.: Determining optical flow. Technical report, Massachusetts Institute of Technology, Cambridge, MA, USA (1980) Horn, B.K.P., Schunck, B.G.: Determining optical flow. Technical report, Massachusetts Institute of Technology, Cambridge, MA, USA (1980)
46.
Zurück zum Zitat Peng, H., Long, F., Ding, C.: Feature selection based on mutual information: criteria of max-dependency, max-relevance and min-redundancy. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1226–1238 (2005)CrossRef Peng, H., Long, F., Ding, C.: Feature selection based on mutual information: criteria of max-dependency, max-relevance and min-redundancy. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1226–1238 (2005)CrossRef
47.
Zurück zum Zitat Peng, H., Long, F., Ding, C.: Feature selection based on mutual information: criteria of max-dependency, max-relevance and min-redundancy. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1226–1238 (2005)CrossRef Peng, H., Long, F., Ding, C.: Feature selection based on mutual information: criteria of max-dependency, max-relevance and min-redundancy. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1226–1238 (2005)CrossRef
48.
Zurück zum Zitat Bouguila, N.: A model-based discriminative framework for sets of positive vectors classification: Application to object categorization. In: 2014 1st International Conference on Advanced Technologies for Signal and Image Processing (ATSIP), pp. 277–282 (2014) Bouguila, N.: A model-based discriminative framework for sets of positive vectors classification: Application to object categorization. In: 2014 1st International Conference on Advanced Technologies for Signal and Image Processing (ATSIP), pp. 277–282 (2014)
49.
Zurück zum Zitat Ma, Z., Leijon, A.: Bayesian estimation of beta mixture models with variational inference. IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2160–2173 (2011)CrossRef Ma, Z., Leijon, A.: Bayesian estimation of beta mixture models with variational inference. IEEE Trans. Pattern Anal. Mach. Intell. 33(11), 2160–2173 (2011)CrossRef
50.
Zurück zum Zitat Woolrich, M.W., Behrens, T.E.: Variational bayes inference of spatial mixture models for segmentation. IEEE Trans. Med. Imaging 25(10), 1380–1391 (2006)CrossRef Woolrich, M.W., Behrens, T.E.: Variational bayes inference of spatial mixture models for segmentation. IEEE Trans. Med. Imaging 25(10), 1380–1391 (2006)CrossRef
51.
Zurück zum Zitat Jordan, M.I., Ghahramani, Z., Jaakkola, T.S., Saul, L.K.: An introduction to variational methods for graphical models. Mach. Learn. 37(2), 183–233 (1999)CrossRefMATH Jordan, M.I., Ghahramani, Z., Jaakkola, T.S., Saul, L.K.: An introduction to variational methods for graphical models. Mach. Learn. 37(2), 183–233 (1999)CrossRefMATH
Metadaten
Titel
Variational Learning of Finite Inverted Dirichlet Mixture Models and Applications
verfasst von
Parisa Tirdad
Nizar Bouguila
Djemel Ziou
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-19833-0_6