Sage Journals: Discover world-class research

Abstract

This paper made improvements on clustering by fast search and find of density peaks (CFSFDP) algorithm and extended this algorithm to fuzzy numbers (FN-CFSFDP algorithm). Using FN-CFSFDP algorithm, classical information included in the samples are extended to fuzzy sets, and fuzzy samples can be clustered by searching the density peak. Firstly, by means of error analysis, improved Euclidean distance between fuzzy numbers was defined, and some key parameters or operating quantities mainly including cut-off distance and Gaussian Kernel function of fuzzy samples were introduced in detail. Next, 76 random simulations in total were performed on four sets of samples under different conditions with different $t$ -values, different sample sizes, index numbers, cluster numbers and fetching rules. Moreover, Kappa coefficients in above simulations were calculated. Finally, both advantages and disadvantages of the proposed FN-CFSFDP were concluded and some recommendations for improvement were put forward, which can provide insightful guidance for further investigations of fuzzy clustering algorithms on fuzzy sets.

Keywords

Fuzzy clustering on fuzzy sets FN-CFSFDP algorithm fuzzy number improved Euclidean distance Kappa coefficient

Get full access to this article

View all access options for this article.

References

Han

J.W.

Kamber

and Pei

, Clustering analysis, in: Data Mining: Concept and Technique, MK imprint of Elsevier, New York, 2012, pp. 478–490.

Macqueen

, On convergence of K-means and partitions with minimum average variance, Annals of Mathematical Statistics36(3) (1965), 1084–1084.

Kuang

and Zhang

L.C.

, A scheduling algorithm based on CLARA clustering, in: Proceedings of the International Conference on Green Energy and Sustainable Development, 2017, pp. 1–7.

R.T.

and Han

J.W.

, CLARANS: a method for clustering objects for spatial data mining, IEEE Transactions on Knowledge and Data Engineering14(5) (2002), 1003–1016.

Barni

Cappellini

and Mecocci

, A possibilistic approach to clustering-comments, IEEE Transactions on Fuzzy Systems4(3) (1996), 393–396.

Bezdek

J.C.

Ehrlich

and Full

, FCM-The fuzzy c-means clustering-algorithm, Computers & Geosciences10(2-3) (1984), 191–203.

R.N.

Wang

X.L.

and Ding

J.D.

, Multilevel core-sets based aggregation clustering algorithm, Journal of Software24(3) (2013), 490–506.

Guha

Rastogi

and Shim

, Rock: a robust clustering algorithm for categorical attributes, Information Systems25(5) (2000), 345–366.

Wilcox

et al., Simulation tests of galaxy cluster constraints on chameleon gravity, Monthly Notices of the Royal Astronomical Society462(1) (2016), 715–725.

10.

Stratman

et al., Identification of critical inspection samples among railroad wheels by similarity-based agglomerative clustering, Integrated Computer-Aided Engineering18(3) (2011), 203–219.

11.

Lorbeer

et al., Variations on the clustering algorithm BIRCH, Big Data Research11 (2018), 44–53.

12.

Lin

et al., Application of B-KFCM algorithm in the clustering of load in substations, in: Proceedings of the International Conference on Electrical and Electronic Engineering, 2014, pp. 51–56.

13.

Benmouiza

and Cheknane

, Density-based spatial clustering of application with noise algorithm for the classification of solar, in: Proceedings of 2016 8th International Conference on Modelling, Identification & Control, 2016, pp. 279–283.

14.

Kanagala

H.K.

and Krishnaiah

V.V.J.R.

, A comparative study of K-means, DBSCAN and OPTICS, in: Proceedings of 2016 International Conference on Computer Communication and Informatics, 2016.

15.

Terrazas

and Krasnogor

, A genotype-phenotype-fitness assessment protocol for evolutionary self-assembly wang tiles design, Memetic Computing5(1) (2013), 19–33.

16.

Rodriguez

and Laio

, Clustering by fast search and find of density peaks, Science344(6191) (2014), 1492–1496.

17.

Roy

and Mandal

J.K.

, A delaunay triangulation preprocessing based fuzzy-encroachment graph clustering for large scale GIS, in: Proceedings of 2012 International Symposium on Electronic System Design, 2012, pp. 300–305.

18.

et al., CAMAS: a cluster-aware multiagent system for attributed graph clustering, Information Fusion37 (2017), 10–21.

19.

Zaki

M.J.

et al., CLICKS: an effective algorithm for mining subspace clusters in categorical datasets, Data & Knowledge Engineering60(1) (2007), 51–70.

20.

Aghabozorgi

et al., A hybrid algorithm for clustering of time series data based on affinity search technique, Scientific World Journal (2014), 1–12.

21.

Dat

N.D.

et al., Sting algorithm used English sentiment classification in a parallel environment, International Journal of Pattern Recognition and Artificial Intelligence31(7) (2017), 1–30.

22.

Sheikholeslami

Chatterjee

and Zhang

A.D.

, WaveCluster: a wavelet-based clustering approach for spatial data in very large databases, VLDB Journal8(3-4) (2000), 289–304.

23.

Chrobak

Durr

and Nilsson

B.J.

, Competitive strategies for online CLIQUE clustering, in: Proceedings of 9th International Conference of Algorithms and Complexity, 2015, pp. 101–113.

24.

Holmes

and Pfahringer

, Clustering large datasets using Cobweb and K-means in tandem, in: Proceedings of 17th Annual Australian Conference on Artificial Intelligence, 2004, pp. 368–379.

25.

Zander

Nguyen

and Armitage

, Automated traffic classification and application identification using machine learning, in: Proceedings of the 2005 IEEE Conference on Local Computer Networks, 2005.

26.

Kohonen

, Self-organized formation of topologically correct feature maps, Biological Cybernetics43(1) (1982), 59–69.

27.

and Wunsch

, Survey of clustering algorithms, IEEE Transactions on Neural Networks16(3) (2005), 645–678.

28.

Zhang

X.C.

, Data Clustering, Science Press, Beijing, 2017, 1–388.

29.

Zadeh

L.A.

, Fuzzy sets, Information and Control8(3) (1965), 338–353.

30.

Chen

S.L.

J.G.

and Wang

X.G.

, in: Fuzzy sets and membership function, in: The Theory of Fuzzy Sets and Its Application, Science Press, Beijing, 2005, pp. 1–3.

31.

Ruspini

E.H.

, A new approach to clustering, Information and Control15(1) (1969), 22–32.

32.

Dunn

J.C.

, A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, Journal of Cybernetics3(3) (1974), 32–57.

33.

Bezdek

J.C.

, Cluster validity, in: Pattern Recognition With Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981, pp. 95–154.

34.

Krishnapuram

and Keller

J.M.

, A possibilistic means algorithms, IEEE Trans on Fuzzy Systems1(2) (1993), 98–110.

35.

Pal

N.R.

et al., A possibilistic fuzzy c-means clustering algorithm, Journal of Cybernetics3(3) (1974), 32–57.

36.

Yang

M.S.

and Wu

K.L.

, Unsupervised possibilistic clustering, Pattern Recognition39(1) (2006), 5–21.

37.

Zhang

J.S.

and Leung

Y.W.

, Improved possibilistic C-means clustering algorithms, IEEE Trans on Fuzzy Systems12(2) (2004), 209–217.

38.

Kriegel

H.P.

and Pfeifle

, Density-based clustering of uncertain data, in: Proceedings of the 11th ACM SIGKDD international Conference on Knowledge Discovery in Data Mining, 2005, pp. 672–677.

39.

Tepwankul

and Maneewongwattana

, U-DBSCAN: a density-based clustering algorithm for uncertain objects, in: Proceedings of 2010 IEEE 26th International Conference on Data Engineering Workshops, 2010, pp. 209–217.

40.

Erdem

and Gundem

T.I.

, M-FDBSCAN: A multicore density-based uncertain data clustering algorithm, Turkish Journal of Electrical Engineering and Computer Sciences22(1) (2014), 143–154.

41.

Smiti

and Elouedi

, DBSCAN-GM: an improved clustering method based on Gaussian means and DBSCAN techniques, in: Proceedings of the 16th International Conference on Intelligent Engineering Systems, 2012, pp. 573–578.

42.

Tran

T.N.

Drab

and Daszykowski

, Revised DBSCAN algorithm to cluster data with dense adjacent clusters, Chemometrics and Intelligent Laboratory Systems120(2) (2013), 92–96.

43.

C.L.

et al., Research on important places identification method based on improved CFSFDP algorithm, Application Research of Computers34(1) (2017), 136–140.

44.

Jiang

L.Q.

et al., Optimization of clustering by fast search and find of density peaks, Application Research of Computers33(11) (2016), 3251–3254.

45.

Wang

Han

and Li

, Fixed point theorems of fuzzy integer value mappings and optimization management to balance problem, International Journal of Fuzzy Systems19(3) (2017), 829–837.

46.

Zhu

J.Y.

, Fuzzy distance and fuzzy degree, in: Non-classical Mathematics for Intelligent Systems, Huazhong University of Science and Technology Press, Wuhan, 2001, pp. 75–81.

47.

Al-Shammary

et al., Fractal self-similarity measurements based clustering technique for SOAP web messages, Journal of Parallel and Distributed Computing73(5) (2013), 664–676.

48.

Cohen

, A coefficient of agreement for nominal scales, Educational and Psychological Measurement20(1) (1960), 37–46.

49.

Landis

J.R.

and Koch

G.G.

, The measurement of observer agreement for categorical data, Biometrics33(1) (1977), 159–174.

A clustering algorithm for fuzzy numbers based on fast search and find of density peaks

Abstract

Keywords

Get full access to this article

References