Center based clustering and averaging aggregation functions
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2017), pp. 70-77 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We propose a new clustering method for partitioning of finite sets from $R^n$, which is based on the application of averaging aggregating functions and an iterative re-weighing method for searching cluster centers.
Keywords: aggregation function, M-average, K-means, clustering.
@article{VKAM_2017_3_a6,
     author = {Z. M. Shibzukhov},
     title = {Center based clustering and averaging aggregation functions},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {70--77},
     year = {2017},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2017_3_a6/}
}
TY  - JOUR
AU  - Z. M. Shibzukhov
TI  - Center based clustering and averaging aggregation functions
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2017
SP  - 70
EP  - 77
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VKAM_2017_3_a6/
LA  - ru
ID  - VKAM_2017_3_a6
ER  - 
%0 Journal Article
%A Z. M. Shibzukhov
%T Center based clustering and averaging aggregation functions
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2017
%P 70-77
%N 3
%U http://geodesic.mathdoc.fr/item/VKAM_2017_3_a6/
%G ru
%F VKAM_2017_3_a6
Z. M. Shibzukhov. Center based clustering and averaging aggregation functions. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2017), pp. 70-77. http://geodesic.mathdoc.fr/item/VKAM_2017_3_a6/

[1] Teboulle M., “A Unified Continuous Optimization Framework for Center-Based Clustering Method”, Journal of Machine Learning Research, 2007, no. 8, 65–102 | MR | Zbl

[2] Mesiar R., Komornikova M., Kolesarova A., Calvo T., Aggregation functions: A revision. In H. Bustince, F. Herrera, J. Montero, editors, Fuzzy Sets and Their Extensions: Representation, Aggregation and Models., Springer, Berlin, Heidelberg, 2008 | MR

[3] Grabich M., Marichal J.-L., Pap E., Aggregation Functions. Series: Encyclopedia of Mathematics and its Applications, v. 127, Cambridge University Press, 2009 | MR

[4] Shibzukhov Z.M., “O printsipe minimizatsii empiricheskogo riska na osnove usrednyayushchikh agregiruyushchikh funktsiy.”, Doklady RAN, 476:5 (2017)

[5] Calvo T., Beliakov G., “Aggregation functions based on penalties”, Fuzzy Sets and Systems, 161:10 (2010), 1420–1436 | DOI | MR | Zbl

[6] Beliakov G., Sola H., Calvo T., A Practical Guide to Averaging Functions, Springer, 2016 | MR

[7] Bezdek J.C., Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981 | MR | Zbl

[8] Duda R.O., Hart P.E., Stork D.G., Pattern Classification., John Wiley Sons, Inc., 2-nd edition, 2001. | MR

[9] Rose K., Gurewitz E., Fox C.G., “A deterministic annealing approach to clustering”, Pattern Recognition Letters, 11:9 (1990), 589–594 | DOI | Zbl

[10] Banerjee A., Merugu S., Dhillon I.S., Ghosh J., “Clustering with Bregman Divergences”, Journal of Machine Learning Research, 2005, no. 6, 1705–1749 | MR | Zbl