Geodesic
The cluster algorithms for solving problems with asymmetric proximity measures
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 2, pp. 127-138 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The cluster analysis is used in various fundamental and applied fields and is a current topic of research. Unlike conventional methods, the proposed algorithms are used for clustering objects represented by vectors in space with the non-observance of the axiom of symmetry. In this case, the feature of solving the clustering problem is the use of an asymmetric proximity measures. The first one among the proposed clustering algorithms sequentially forms clusters with a simultaneous generalization to clustered objects from previously created clusters to a current cluster if this reduces the quality criterion. This approach to the formation of clusters allows reducing the computational costs as compared with existing non-hierarchical cluster algorithms. The second algorithm is a modified version of the first algorithm. The second algorithm allows reassigning the main objects of clusters to further reduce the proposed quality criterion. 
@article{SJVM_2018_21_2_a0,
     author = {A. R. Aydinyan and O. L. Tsvetkova},
     title = {The cluster algorithms for solving problems with asymmetric proximity measures},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {127--138},
     year = {2018},
     volume = {21},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a0/}
}
TY  - JOUR
AU  - A. R. Aydinyan
AU  - O. L. Tsvetkova
TI  - The cluster algorithms for solving problems with asymmetric proximity measures
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2018
SP  - 127
EP  - 138
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a0/
LA  - ru
ID  - SJVM_2018_21_2_a0
ER  - 
%0 Journal Article
%A A. R. Aydinyan
%A O. L. Tsvetkova
%T The cluster algorithms for solving problems with asymmetric proximity measures
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2018
%P 127-138
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a0/
%G ru
%F SJVM_2018_21_2_a0
A. R. Aydinyan; O. L. Tsvetkova. The cluster algorithms for solving problems with asymmetric proximity measures. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 2, pp. 127-138. http://geodesic.mathdoc.fr/item/SJVM_2018_21_2_a0/

[1] Tryon R. C., Cluster analysis, Ann Arbor Edwards Bros, London, 1939

[2] Madhulatha T. S., “An overview on clustering methods”, IOSR J. of Engineering, 2:4 (2012), 719–725 | DOI

[3] Hartigan J. A., Clustering Algorithms, Probability Mathematical Statistics, John Wiley Sons Inc, New York–London–Sydney–Toronto, 1975 | MR | Zbl

[4] Sörensen T., “A method of establishing groups of equal amplitude in plant sociology based on similarity of species content”, Kongelige Danske Videnskabernes Selskab. Biol. Skrifter., 5:4 (1948), 1–34

[5] Safari K. M., Tive M., Babania A., Hesan M., “Analyzing the applications of customer lifetime value (CLV) based on benefit segmentation for the banking sector”, Procedia – Social and Behavioral Sciences, 109, 2nd World Conference on Business, Economics and Management (2014), 590–594 | DOI

[6] Srihadi D. T. F., Hartoyo, Sukandar D., Soehadi A. W., “Segmentation of the tourism market for Jakarta: Classification of foreign visitors' lifestyle typologies”, Tourism Management Perspectives, 19:1 (2016), 32–39 | DOI

[7] Beh A., Bruyere B. L., “Segmentation by visitor motivation in three Kenyan national reserves”, Tourism Management, 28 (2007), 1464–1471 | DOI

[8] Kel'manov A. V., Khamidullin S. A., “An approximation polynomial-time algorithm for a sequence BI-clustering problem”, Computational Mathematics and Mathematical Physics, 55:6 (2015), 1068–1076 | DOI | DOI | MR | Zbl

[9] Kelmanov A. V., Romanchenko S. M., Khamidullin S. A., “Tochnye psevdopolinomialnye algoritmy dlya nekotorykh trudnoreshaemykh zadach poiska podposledovatelnosti vektorov”, Zhurn. vychisl. matem. i mat. fiziki, 53:1 (2013), 143–153 | DOI | Zbl

[10] Kel'manov A. V., Jeon B. A., “Posteriori joint detection and discrimination of pulses in a quasiperiodic pulse train”, IEEE Trans. on Signal Proc., 52:3 (2004), 645–656 | DOI | MR | Zbl

[11] Aidinyan A. R., Tsvetkova O. L., “Geneticheskie algoritmy raspredeleniya rabot”, Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta, 11:5(56) (2011), 723–729

[12] Shalymov D. S., “Algoritmy ustoichivoi klasterizatsii na osnove indeksnykh funktsii i funktsii ustoichivosti”, Stokhasticheskaya optimizatsiya v informatike (SPb.), 2008, no. 4, 236–248

[13] Jain A. K., Murty M. N., Flynn P. J., “Data clustering: a review”, ACM Computing Surveys, 31:3 (1999), 264–323 | DOI

[14] Soni N., Ganatra A., “Categorization of several clustering algorithms from different perspective: a review”, Int. J. of Advanced Research in Computer Science and Software Engineering, 2:8 (2012), 63–68

[15] Mao J., Jain A. K., “A self-organizing network for hyperellipsoidal clustering (HEC”, IEEE Trans. Neural Netw., 7 (1996), 16–29 | DOI

[16] Huttenlocher D. P., Klanderman G. A., Rucklidge W. J., “Comparing images using the Hausdorff distance”, IEEE Trans. Pattern Anal. Mach. Intell., 15:9 (1993), 850–863 | DOI

[17] Dubuisson M. P., Jain A. K., “A modified Hausdorff distance for objec matching”, Proc. of the International Conference on Pattern Recognition (ICPR'94), 1994, 566–568 | DOI

[18] Van der Lann M. J., Pollard K. S., Bryan J., “A new partitioning around medoids algorithm”, J. of Statistical Computation and Simulation, 5:8 (2003), 575–584 | MR