The Permutable k-means for the Bi-Partial Criterion

Abstract

The here applied objective function for clustering consists of two parts, where the first one takes into account intra-cluster relations, and the second – inter-cluster ones. In the case of k-means algorithm, such bi-partial objective function combines cluster dispersions with inter-cluster similarity, to be jointly minimized. The first part only of such objective function provides the “standard” quality of clustering based on distances between objects (the well-known classical k-means). To improve the clustering quality based on the bi-partial objective function, we need to develop the permutable version of k-means algorithm. This paper shows the permutable k-means that appears to be a new type of clustering procedure.

Author Biographies

Serge D. Dvoenko, Tula State University

Institute of Applied Mathematics and Computer Sciences (IAMCS)Prof.

Jan W Owsinski, Systems Research Institute, Polish Academy of Sciences

Deputy Director for Research

References

Jan W. Owsinski (2012). On the optimal division of an empirical distribution (and some related prob-lems). Przegląd Statystyczny, special issue, 1, 109-122.

Jan W. Owsinski (2013). On dividing an empirical distribution into optimal segments. Retrieved June 3, 2017 from http://new.sis-statistica.org/wp-content/uploads/2013/09/RS12-On-Dividing-an-Empirical-Distribution-into.pdf

Jan W. Owsinski (2011). The bi-partial approach in clustering and ordering: the model and the algo-rithms. Statistica & Applicazioni. Special Issue, 43–59.

Sergey D. Dvoenko (2009). Clustering and separat-ing of a set of members in terms of mutual distances and similarities. Transactions on MLDM. IBaI Pub-lishing 2, 2 (Oct. 2009), 80-99.

Sergey Dvoenko (2014). Meanless k-means as k-meanless clustering with the bi-partial approach. In Proceedings of 12th Int. Conf. on Pattern Recogni-tion and Image Processing (PRIP’2014). UIIP NASB, Minsk, Belarus, 50-54.

W.S. Torgerson (1958). Theory and Methods of Scaling. Wiley, New York, NY.

Ronald A. Fisher (1936). The use of multiple mea-surements in taxonomic problems. Ann. Eugenics. 7, 2 (Sept. 1936), 179-188. DOI:http://dx.doi.org/10.1111/j.1469-1809.1936.tb02137.x

Sergey D. Dvoenko, and Denis O. Pshenichny (2016). A recovering of violated metric in machine learning. In Proceedings of 8th Int. Symposium on Information and Communication Technology (SoICT’2016). ACM NY, 15-21. DOI:http://dx.doi.org/10.1145/3011077.3011084

Authors

  • Serge D. Dvoenko Tula State University
  • Jan W Owsinski Systems Research Institute, Polish Academy of Sciences

DOI:

https://doi.org/10.31449/inf.v43i2.2090

Downloads

Published

06/15/2019

How to Cite

Dvoenko, S. D., & Owsinski, J. W. (2019). The Permutable k-means for the Bi-Partial Criterion. Informatica, 43(2). https://doi.org/10.31449/inf.v43i2.2090

Issue

Vol. 43 No. 2 (2019)

Section

Regular papers

License

Authors retain copyright in their work. By submitting to and publishing with Informatica, authors grant the publisher (Slovene Society Informatika) the non-exclusive right to publish, reproduce, and distribute the article and to identify itself as the original publisher.

All articles are published under the Creative Commons Attribution license CC BY 3.0. Under this license, others may share and adapt the work for any purpose, provided appropriate credit is given and changes (if any) are indicated.

Authors may deposit and share the submitted version, accepted manuscript, and published version, provided the original publication in Informatica is properly cited.