To meet the need of extracting cluster boundary from mixed attribute data in the field of data analysis, we propose a cluster boundary detection algorithm for mixed attribute data sets in this research, named CHASM (Cluster Boundary Detection Algorithm based on Shadowed Set). Based on the structure of clusters, the CHASM defines a new objective function according to the data set which is categorized into three collections, i.e. core, exclusion and shadow. Then CHASM updates the centroid information of clusters based on the variance of contribution degree among these collections to the clusters centroids. Finally, in an iterative optimization process, the CHASM can extract its shadow sets from each cluster to form the boundary of clusters. The experimental results, on both the synthetic data and real data with mixed attributes, numerical attributes and categorical attributes, show that CHASM can effectively detect cluster boundary with higher or similar accuracy to its rival methods. Furthermore, the CHASM can eliminate noise effectively.
JainA.K., MurtyM.N. and FlynnP.J., Data clustering: A review, ACM Computing Surveys (CSUR)3 (1999), 264-323.
2.
ChuanjunM., SifengL. et al., Study on commerical bank off-site regulation based on GSOM clustering method, Management Science and Engineering, International Conference on IEEE, (2006), 1580-1583.
3.
YinghuaL., TinghuaiM., ChanghongY. et al., Implementation of the fuzzy c-means clustering algorithm in meteorological data, International Journal of Database Theory and Application6 (2013), 1-18.
4.
ChouC.A., ChaoW.A. et al., Capacitated clustering problem in computational biology: Combinatorial and statistical approach for sibling reconstruction, Computers & Operations Research3 (2012), 609-619.
5.
CasagrandeD., SassanoM. and AstolfiA., Hamiltonian-based clustering: Algorithm for static and dynamic clustering in data mining and image processing, Control System, IEEE4 (2012), 74-91.
6.
BharathiG. and VenkatesanD., Study of ontology or thesaurus based document clustering and information retrieval, Journal of Engineering and Applied Sciences4 (2012), 342-347.
7.
XiaC.Y., HsuW., LeeM.L. et al., BORDER: An efficient computation of boundary points, Knowledge and Data Engineering, IEEE Transactions3 (2006), 289-303.
8.
M.Ester, KriegelH.P., SanderJ. et al., A density-based algorithm for discovering clusters in large spatial databases with noise, KDD, (1996), 226-231.
9.
NosovskiyG.V., LiuD. and SourinaO., Automatic clustering and boundary detection algorithm based on adaptive influence function, Pattern Recognition9 (2008), 2757-2776.
10.
QiuB.Z., YueF. and ShenJ.Y., BRIM: An efficient boundary points detecting algorithm, Advances in Knowledge Discovery and Data Mining, (2007), 761-768.
11.
XieL.X. and QiuB.Z., Boundary points detection algorithm based on coefficient of variation, Pattern Recognition and Artificial Intelligence5 (2009), 799-802.
12.
QiuB.Z., YangY. and DuX.W., BRINK: An algorithm of boundary points of clusters detection based on local qualitative factors, Journal of Zhengzhou University (Engineering Science)3 (2012), 117-121.
13.
QiuB.Z. and CaoH.L., An efficient boundary points detecting algorithm based on joint entropy, Control and Decision1 (2011), 71-74.
14.
QiuB.Z. and WangB., Cluster boundary detection technology for categorical data, Journal of Computer Applications6 (2012), 1654-1656.
15.
ZhouJ., PedryczW. and MiaoD., Shadowed sets in the characterization of rough-fuzzy clustering, Pattern Recognition8 (2011), 1738-1749.
16.
TanP.N., Introduction to Data Mining, Pearson Education India, 2007.
17.
MitraS., PedryczW. and BarmanB., Shadowed c-means: Integrating fuzzy and rough clustering, Pattern Recognition4 (2010), 1282-1291.
18.
DesoerC.A., Slowly varying system x = A(t)x, IEEE Trans on Automatic Control6 (1969), 780-781.
19.
AnkerstM., BreunigM.M., KriegelH.P. et al., Optics: Ordering points to identify the clustering structure, ACM SIGMOD Record, (1999), 49-60.
20.
HalkidiM., BatistakisY. and VazirgiannisM., Cluster validity methods: Part 1, ACM SIGMOD Record2 (2002), 40-45.
21.
HalkidiM., BatistakisY. and VazirgiannisM., Clustering validity checking methods: Part 2, ACM SIGMOD Record3 (2002), 19-27.
22.
WangD., MaoZ.Y. and WuM.D., Outlier detection algorithm on shadowed sets clustering, Journal of Frontiers of Computer Science and Technology11 (2012), 985-993.
23.
PedryczW., Interpretation of clusters in the framework of shadowed sets, Pattern Recognition Letters15 (2005), 2439-2449.
24.
PedryczW., Shadowed sets: representing and processing fuzzy sets, Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions1 (1998), 103-109.
25.
LiuD., NosovskiyG.V. and SourinaO., Effective clustering and boundary detection algorithm based on Delaunay triangulation, Pattern Recognition Letters9 (2008), 1261-1273.
26.
HanJ., KamberM. and PeiJ., Data Mining: Concepts and Techniques, Morgan kaufmann, 2006.
27.
QiuB.Z. and XuM., Research on nonparametric clustering boundary detection algorithm, Computer Engineering15 (2011), 133-137.
28.
HuangZ., Extensions to the k-means algorithm for clustering large data sets with categorical values, Data Mining and Knowledge Discovery3 (1998), 283-304.
29.
MajiP. and PalS.K., RFCM: A hybrid clustering algorithm using rough and fuzzy sets, Fundamenta Informaticae4 (2007), 475-496.
30.
PalS.K. and MajumderD.D., Fuzzy sets and decision making approaches in vowel and speaker recognition, IEEE Trans Syst, Man, Cybern8 (1977), 625-629.
31.
PetersG., Some refinements of rough k-means clustering, Pattern Recognition8 (2006), 1481-1491.
