Abstract
We propose an unsupervised algorithm for learning the optimal number of clusters in a finite Libby-Novick Beta mixture model. In unsupervised learning, it is crucial to determine the number of clusters that best describes the data. By extending the minimum message length (MML) principle, we are able to determine the number of clusters in Libby-Novick Beta mixtures. Our model has been evaluated on three publicly available and real-world medical datasets.
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References
Bouguila, N.: Hybrid generative/discriminative approaches for proportional data modeling and classification. IEEE Trans. Knowl. Data Eng. 24(12), 2184–2202 (2012)
Bouguila, N., Fan, W.: Mixture Models and Applications. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-23876-6
Bouguila, N.: A model-based approach for discrete data clustering and feature weighting using map and stochastic complexity. IEEE Trans. Knowl. Data Eng. 21(12), 1649–1664 (2009)
Boutemedjet, S., Ziou, D., Bouguila, N.: Unsupervised feature selection for accurate recommendation of high-dimensional image data. In: Advances in Neural Information Processing Systems, pp. 177–184. Curran Associates Inc. (2007)
Bouguila, N.: Spatial color image databases summarization. In: 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP 2007, vol. 1, pp. I-953–I-956 (2007)
Hu, C., Fan, W., Du, J., Bouguila, N.: A novel statistical approach for clustering positive data based on finite inverted beta-liouville mixture models. Neurocomputing 333, 110–123 (2019)
Oboh, B.S., Bouguila, N.: Unsupervised learning of finite mixtures using scaled dirichlet distribution and its application to software modules categorization. In: IEEE International Conference on Industrial Technology (ICIT) 2017, pp. 1085–1090 (2017)
Bouguila, N., Elguebaly, T.: A fully Bayesian model based on reversible jump MCMC and finite beta mixtures for clustering. Expert Syst. Appl. 39(5), 5946–5959 (2012)
Wallace, C.S., Boulton, D.: An Information Measure for Classification. Comput. J. 11(2), 185–194 (1968)
Bezdek, James C..: Selected applications in classifier design. In: Pattern Recognition with Fuzzy Objective Function Algorithms. AAPR, pp. 203–239. Springer, Boston, MA (1981). https://doi.org/10.1007/978-1-4757-0450-1_6
Gath, I., Geva, A.B.: Unsupervised optimal fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 773–780 (1989)
Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)
Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)
Figueiredo, M., Jain, A.: Unsupervised learning of finite mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 24(3), 381–396 (2002)
Bouguila, N., Ziou, D.: Unsupervised selection of a finite dirichlet mixture model: an mml-based approach. IEEE Trans. Knowl. Data Eng. 18(8), 993–1009 (2006)
Roberts, S.J., Husmeier, D., Rezek, I., Penny, W.D.: Bayesian approaches to gaussian mixture modeling. IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1133–1142 (1998)
Baxter, R.A., Oliver, J.J.: Finding overlapping components with mml. Stat. Comput. 10(1), 5–16 (2000)
Bouguila, N., Ziou, D.: MML-based approach for finite dirichlet mixture estimation and selection. In: Perner, P., Imiya, A. (eds.) MLDM 2005. LNCS (LNAI), vol. 3587, pp. 42–51. Springer, Heidelberg (2005). https://doi.org/10.1007/11510888_5
Bouguila, N., Ziou, D.: On fitting finite dirichlet mixture using ECM and MML. In: Singh, S., Singh, M., Apte, C., Perner, P. (eds.) ICAPR 2005. LNCS, vol. 3686, pp. 172–182. Springer, Heidelberg (2005). https://doi.org/10.1007/11551188_19
Bouguila, N., Ziou, D.: Mml-based approach for high-dimensional unsupervised learning using the generalized dirichlet mixture. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR Workshops 2005, San Diego, CA, USA, 21–23 September, 2005, p. 53. IEEE Computer Society (2005)
Samiee, N., Manouchehri, N., Bouguila, N.: Maximum likelihood-based estimation of finite multivariate Libby-Novick beta mixture models in medical applications. In: IEEE International Conference on Industrial Technology (ICIT) 2023, 1–6 (2023)
Ketabchi, K., Manouchehri, N., Bouguila, N.: Fully Bayesian Libby-Novick beta mixture model with feature selection. In: IEEE International Conference on Industrial Technology, ICIT 2022, Shanghai, China, 22–25 August 2022, pp. 1–6. IEEE (2022)
Cordeiro, G., Santana, L., Ortega, E., Pescim, R.: A new family of distributions: Libby-Novick beta. Int. J. Stat. Probability 3, 63–80 (2014)
Autzen, B.: Bayesian Ockham’s razor and nested models. Econ. Philos. 35(2), 321–338 (2019)
Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision 60(2), 91–110 (2004)
Rao, L.J., Neelakanteswar, P., Ramkumar, M., Krishna, A., Basha, C.Z.: An effective bone fracture detection using bag-of-visual-words with the features extracted from sift. In: International Conference on Electronics and Sustainable Communication Systems (ICESC) 2020, pp. 6–10 (2020)
Tangpukdee, N., Duangdee, C., Wilairatana, P., Krudsood, S.: Malaria diagnosis: a brief review. Korean J. Parasitol. 47, 93–102 (2009)
https://www.kaggle.com/paultimothymooney/breast-histopathology-images
https://www.cancer.org/cancer/lung-cancer/causes-risks-prevention/risk-factors.html
Lung dataset (2018). https://www.kaggle.com/andrewmvd/lung-and-colon-cancer-histopathological-images
Acknowledgment
The completion of this research was made possible thanks to the Natural Sciences and Engineering Research Council of Canada (NSERC).
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Samiee, N., Manouchehri, N., Bouguila, N. (2023). Finite Libby-Novick Beta Mixture Model: An MML-Based Approach. In: Nguyen, N.T., et al. Intelligent Information and Database Systems. ACIIDS 2023. Lecture Notes in Computer Science(), vol 13995. Springer, Singapore. https://doi.org/10.1007/978-981-99-5834-4_30
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DOI: https://doi.org/10.1007/978-981-99-5834-4_30
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