Skip to main content
SpringerLink
Log in

Decision Theoretic Rough Set-Based Neighborhood for Self-Organizing Map

  • Original Research
  • Published:
SN Computer Science Aims and scope Submit manuscript

Abstract

A decision theoretic rough set-based neighborhood selection process is developed for self-organizing maps. While the neighborhood of the winner neuron is selected based on the probability of its associativity to the winner neuron, the selected neighborhood is updated using a new method which combines the probability of its associativity and the Gaussian function. This approach provides better results as compared to self-organizing map and other clustering algorithms on several real-life datasets. The results are evaluated in terms of DB index, Dunn index, quantization error, ARI, and NMI.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Alon U, Barkai N, Notterman DA, Gish K, Ybarra S, Mack D, Levine AJ. Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc Natl Acad Sci USA. 1999;96:6745–50.

    Article  Google Scholar 

  2. Bednar JA, Kelkar A, Miikkulainen R. Modeling large cortical networks with growing self-organizing maps. Neurocomputing. 2002;44–46:315–21.

    Article  Google Scholar 

  3. Boyle JO, Gümü ZH, Kacker A, Choksi VL, Jennifer M, Zhou XK, Yantiss RK, Hughes DB, Du B, Judson L, Subbaramaiah K, Dannenberg AJ. Effects of cigarette smoke on the human oral mucosal transcriptome. NIH Public Access. 2011;3:266–78.

    Google Scholar 

  4. Braga PH, Bassani HF. A semi-supervised self-organizing map for clustering and classification. In: 2018 international joint conference on neural networks (IJCNN). IEEE; 2018. p. 1–8.

  5. Chiang J-H, Ho S-H. A combination of rough-based feature selection and rbf neural network for classification using gene expression data. IEEE Trans Nanobiosci. 2008;7(1):91–9.

    Article  Google Scholar 

  6. Collignon A. Multi-modality medical image registration by maximization of mutual information. 1998.

  7. Davies DL, Bouldin DW. A cluster separation measure. IEEE Trans Pattern Anal Mach Intell. 1979;1:224–7.

    Article  Google Scholar 

  8. Dunn JC. A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters. J Cybern. 1973;3:32–57.

    Article  MathSciNet  Google Scholar 

  9. Ester M, Kriegel H-P, Sander J, Xu X. A density-based algorithm for discovering clusters a density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the second international conference on knowledge discovery and data mining, KDD’96. AAAI Press; 1996. p. 226–231.

  10. Golub TR, Slonim DK, Tamayo P, Huard C, Gaasenbeek M, Mesirov JP, Coller H, Loh ML, Downing JR, Caligiuri MA, Bloomfield CD, Lander ES. Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science. 1999;286:531–7.

    Article  Google Scholar 

  11. Gorzałczany MB, Rudziński F. Generalized self-organizing maps for automatic determination of the number of clusters and their multiprototypes in cluster analysis. IEEE Trans Neural Netw Learn Syst. 2017;29(7):2833–45.

    MathSciNet  Google Scholar 

  12. Greco S, Matarazzo B, Słowiński R. Parameterized rough set model using rough membership and Bayesian confirmation measures. Int J Approx Reason. 2008;49(2):285–300.

    Article  MathSciNet  Google Scholar 

  13. Hébert P-A, Masson M-H, Denoeux T. Fuzzy multidimensional scaling. Comput Stat Data Anal. 2006;51(1):335–59.

    Article  MathSciNet  Google Scholar 

  14. Kamimura R. Cooperative information maximization with gaussian activation functions for self-organizing maps. IEEE Trans Neural Netw. 2006;17(4):909–18.

    Article  Google Scholar 

  15. Kohonen T. Self-organized formation of topologically correct feature maps. Biol Cybern. 1982;43:59–69.

    Article  MathSciNet  Google Scholar 

  16. Kong EC, Allouche L, Chapot PA, Vranizan K, Moore MS, Wolf FW. Ethanol-regulated genes that contribute to ethanol sensitivity and rapid tolerance in drosophila. NIH Public Access. 2010;34:302–16.

    Google Scholar 

  17. Kostiainen T, Lampinen J. Self-organizing map as a probability density model. In: IJCNN’01. International joint conference on neural networks. Proceedings (Cat. No. 01CH37222), vol. 1. IEEE; 2001. p. 394–399.

  18. Labroche N. New incremental fuzzy c medoids clustering algorithms. In: North American fuzzy information processing society (NAFIPS). 2010. p. 1–6.

  19. Lampinen J, Oja E. Clustering properties of hierarchical self-organizing maps. J Math Imaging Vis. 1992;2:261–72.

    Article  Google Scholar 

  20. Li F, Ye M, Chen X. An extension to rough c-means clustering based on decision-theoretic rough sets model. Int J Approx Reason. 2014;55:116–29.

    Article  MathSciNet  Google Scholar 

  21. Li Y, Fan J-C, Pan J-S, Mao G-H, Wu G-K. A novel rough fuzzy clustering algorithm with a new similarity measurement. J Internet Technol. 2019;20(4):1145–56.

    Google Scholar 

  22. Maji P, Pal S. Rough set based generalized fuzzy c-means algorithm and quantitative indices. IEEE Trans Syst Man Cybern Part B. 2007;37:1529–40.

    Article  Google Scholar 

  23. Maji P, Paul S. Robust rough-fuzzy c-means algorithm: design and applications in coding and non-coding rna expression data clustering. Fundam Inform. 2013;124:153–74.

    Article  MathSciNet  Google Scholar 

  24. Na S,  Xumin L,  Yong G. Research on k-means clustering algorithm: an improved k-means clustering algorithm. In: Intelligent information technology and security informatics (IITSI). 2010. p. 63–67.

  25. Papliński AP, Gustafsson L. Multimodal feedforward self-organizing maps. Berlin: Springer; 2005. p. 81–88.

  26. Pawlak Z. Rough set theory and its applications. J Telecommun Inf Technol. 1998;29:7–10.

    MATH  Google Scholar 

  27. Ramos AD, López-Rubio E, Palomo EJ. The forbidden region self-organizing map neural network. IEEE Trans Neural Netw Learn Syst. 2019;31(1):201–11.

    Article  Google Scholar 

  28. Ray SS, Ganivada A, Pal S. A granular self-organizing map for clustering and gene selection in microarray data. IEEE Trans Neural Netw (online). 2015. p. 1–17.

  29. Ray SS, Misra S. A supervised weighted similarity measure for gene expressions using biological knowledge. Gene. 2016;595(2):150–60.

    Article  Google Scholar 

  30. Rokach L,  Maimon O. Clustering methods. Springer US; 2005. p. 321–352.

  31. Sarkar M, Yegnanarayana B. Fuzzy-rough membership functions. IEEE Int Conf Syst Man Cybern. 1998;2:2028–33.

    Google Scholar 

  32. Singh D, Febbo PG, Ross K, Jackson DG, Manola J, Ladd C, Tamayo P, Renshaw AA, D’Amico AV, Richie JP, Lander ES, Loda M, Kantoff PW, Golub TR, Sellers WR. Gene expression correlates of clinical prostate cancer behaviour. Cancer Cell. 2002;1:203–9.

    Article  Google Scholar 

  33. Sun Y. On quantization error of self-organizing map network. Neurocomputing. 2000;34(1–4):169–93.

    Article  Google Scholar 

  34. Wu X, Wang JJ, Cui XX, Maianu LL, Rhees BB, Rosinski JJ, So WVWV, Willi SMSM, Osier MV, Hill HS, Page GP, Allison DB, Martin M, Garvey WT. The effect of insulin on expression of genes and biochemical pathways in human skeletal muscle. Endocrine. 2007;31(1):5–17.

    Article  Google Scholar 

  35. Xu R, Wunsch D. Survey of clustering algorithms for manet. IEEE Trans Neural Netw. 2005;16:645–78.

    Article  Google Scholar 

  36. Yao Y. Decision-theoretic rough set models. Proc Rough Sets Knowl Technol. 2007;4481:1–12.

    Article  Google Scholar 

  37. Yao Y. Probabilistic rough set approximations. Int J Approx Reason. 2008;49:255–71.

    Article  Google Scholar 

  38. Yao YY. Probabilistic approaches to rough sets. Expert Syst. 2003;20:287–97.

    Article  Google Scholar 

  39. Yeung KY, Ruzzo WL. Details of the adjusted rand index and clustering algorithms, supplement to the paper an empirical study on principal component analysis for clustering gene expression data. Bioinformatics. 2001;17(9):763–74.

    Article  Google Scholar 

  40. Zadeh A. Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 1997;90:111–27.

    Article  MathSciNet  Google Scholar 

  41. Zhang S, Ge S. User power interaction behavior clustering analysis that is based on the self-organizing-center k-means algorithm. IEEE Access. 2019;7:175879–888.

    Article  Google Scholar 

  42. Ziarko W. Variable precision rough set model. J Comput Syst Sci. 1993;46:39–59.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Sudip Ghosh acknowledges the financial assistance provided by Department of Science and Technology.

Author information

Authors and Affiliations

  1. Machine Intelligence Unit, Center for Soft Computing Research, Kolkata, India

    Shubhra Sankar Ray

  2. Center for Soft Computing Research, Kolkata, India

    Sresht Agrawal

  3. Machine Intelligence Unit, Kolkata, India

    Sudip Ghosh

Authors
  1. Shubhra Sankar Ray
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sresht Agrawal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sudip Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sudip Ghosh.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ray, S.S., Agrawal, S. & Ghosh, S. Decision Theoretic Rough Set-Based Neighborhood for Self-Organizing Map. SN COMPUT. SCI. 2, 102 (2021). https://doi.org/10.1007/s42979-021-00490-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42979-021-00490-2

Keywords

Search

Navigation