Skip to main content

Finite Libby-Novick Beta Mixture Model: An MML-Based Approach

  • Conference paper
  • First Online:
Intelligent Information and Database Systems (ACIIDS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13995))

Included in the following conference series:

  • 285 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bouguila, N.: Hybrid generative/discriminative approaches for proportional data modeling and classification. IEEE Trans. Knowl. Data Eng. 24(12), 2184–2202 (2012)

    Article  Google Scholar 

  2. Bouguila, N., Fan, W.: Mixture Models and Applications. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-23876-6

    Book  MATH  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. 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)

    Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Wallace, C.S., Boulton, D.: An Information Measure for Classification. Comput. J. 11(2), 185–194 (1968)

    Article  MATH  Google Scholar 

  10. 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

    Chapter  MATH  Google Scholar 

  11. Gath, I., Geva, A.B.: Unsupervised optimal fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 773–780 (1989)

    Article  MATH  Google Scholar 

  12. Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)

    Article  MATH  Google Scholar 

  14. Figueiredo, M., Jain, A.: Unsupervised learning of finite mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 24(3), 381–396 (2002)

    Article  Google Scholar 

  15. 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)

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Baxter, R.A., Oliver, J.J.: Finding overlapping components with mml. Stat. Comput. 10(1), 5–16 (2000)

    Article  Google Scholar 

  18. 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

    Chapter  Google Scholar 

  19. 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

    Chapter  MATH  Google Scholar 

  20. 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)

    Google Scholar 

  21. 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)

    Google Scholar 

  22. 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)

    Google Scholar 

  23. Cordeiro, G., Santana, L., Ortega, E., Pescim, R.: A new family of distributions: Libby-Novick beta. Int. J. Stat. Probability 3, 63–80 (2014)

    Article  Google Scholar 

  24. Autzen, B.: Bayesian Ockham’s razor and nested models. Econ. Philos. 35(2), 321–338 (2019)

    Article  Google Scholar 

  25. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision 60(2), 91–110 (2004)

    Article  Google Scholar 

  26. 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)

    Google Scholar 

  27. https://ceb.nlm.nih.gov/repositories/malaria-datasets

  28. Tangpukdee, N., Duangdee, C., Wilairatana, P., Krudsood, S.: Malaria diagnosis: a brief review. Korean J. Parasitol. 47, 93–102 (2009)

    Article  Google Scholar 

  29. https://www.cancer.gov/types/breast

  30. https://www.kaggle.com/paultimothymooney/breast-histopathology-images

  31. https://www.cancer.org/cancer/lung-cancer/causes-risks-prevention/risk-factors.html

  32. Lung dataset (2018). https://www.kaggle.com/andrewmvd/lung-and-colon-cancer-histopathological-images

Download references

Acknowledgment

The completion of this research was made possible thanks to the Natural Sciences and Engineering Research Council of Canada (NSERC).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Niloufar Samiee .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-5834-4_30

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-5833-7

  • Online ISBN: 978-981-99-5834-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics