Skip to main content

Gödel Number Based Encoding Technique for Effective Clustering

  • Conference paper
  • First Online:
Pattern Recognition and Machine Intelligence (PReMI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14301))

  • 631 Accesses

Abstract

In this paper, a Gödel number-based encoding technique is proposed to encode each object of a dataset before applying any clustering algorithm. This encoding technique converts the objects into a decimal string while maintaining the properties of the features. The results of all standard existing clustering algorithms after applying this encoding are evaluated based on benchmark metrics like, Silhouette Score, Davis Bouldin, Calinski Harabasz and Dunn Index. In comparison to the existing clustering algorithms if one uses Gödel number-based encoding over the dataset, it gives better performance.

This work is partially supported by Start-up Research Grant (File number: SRG/2022/002098), SERB, Govt. of India.

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 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
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. UCI Machine Learning Repository, Center for Machine Learning and Intelligent Systems (2007). http://archive.ics.uci.edu/ml/index.php. Accessed January 2023

  2. Abhishek, S., Dharwish, M., Das, A., Bhattacharjee, K.: A cellular automata based clustering technique for high-dimensional data. In: Das, S., Martinez, G.J. (eds.) ASCAT 2023. AISC, vol. 1443, pp. 37–51. Springer, Singapore (2023). https://doi.org/10.1007/978-981-99-0688-8_4

    Chapter  Google Scholar 

  3. Caliński, T., Harabasz, J.A.: A dendrite method for cluster analysis. Commun. Stat. - Theory Methods 3, 1–27 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  4. Comaniciu, D., Meer, P.: Mean shift: a robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24(5), 603–619 (2002)

    Article  Google Scholar 

  5. Dunn, J.C.: Well separated clusters and fuzzy partitions. J. Cybern. 4, 95–104 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ester, M., Kriegel, H.-P., Sander, J., Xu, X.: 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 1996, pp. 226–231. AAAI Press (1996)

    Google Scholar 

  7. Ester, M., Kriegel, H.-P., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Knowledge Discovery and Data Mining (1996)

    Google Scholar 

  8. Hartigan, J.A., Wong, M.A.: Algorithm AS 136: a K-Means clustering algorithm. Appl. Stat. 28(1), 100–108 (1979)

    Article  MATH  Google Scholar 

  9. Martín-Fernández, F., Caballero-Gil, P.: Analysis of the new standard hash function. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2013. LNCS, vol. 8111, pp. 142–149. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-53856-8_18

    Chapter  Google Scholar 

  10. Rousseeuw, P.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)

    Article  MATH  Google Scholar 

  11. Zepeda-Mendoza, M.L., Resendis-Antonio, O.: Hierarchical agglomerative clustering. In: Dubitzky, W., Wolkenhauer, O., Cho, K.H., Yokota, H. (eds.) Encyclopedia of Systems Biology, pp. 886–887. Springer, New York (2013). https://doi.org/10.1007/978-1-4419-9863-7_1371

    Chapter  Google Scholar 

  12. Zhang, T., Ramakrishnan, R., Livny, M.: BIRCH: a new data clustering algorithm and its applications. Data Min. Knowl. Disc. 1(2), 141–182 (1997)

    Article  Google Scholar 

Download references

Acknowledgment

The authors are grateful to Prof. Sukanta Das for his valuable comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kamalika Bhattacharjee .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Narodia Parth, P., Bhattacharjee, K. (2023). Gödel Number Based Encoding Technique for Effective Clustering. In: Maji, P., Huang, T., Pal, N.R., Chaudhury, S., De, R.K. (eds) Pattern Recognition and Machine Intelligence. PReMI 2023. Lecture Notes in Computer Science, vol 14301. Springer, Cham. https://doi.org/10.1007/978-3-031-45170-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-45170-6_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45169-0

  • Online ISBN: 978-3-031-45170-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics