Minimal Spanning Tree based Fuzzy Clustering
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32769
Minimal Spanning Tree based Fuzzy Clustering

Authors: Ágnes Vathy-Fogarassy, Balázs Feil, János Abonyi

Abstract:

Most of fuzzy clustering algorithms have some discrepancies, e.g. they are not able to detect clusters with convex shapes, the number of the clusters should be a priori known, they suffer from numerical problems, like sensitiveness to the initialization, etc. This paper studies the synergistic combination of the hierarchical and graph theoretic minimal spanning tree based clustering algorithm with the partitional Gath-Geva fuzzy clustering algorithm. The aim of this hybridization is to increase the robustness and consistency of the clustering results and to decrease the number of the heuristically defined parameters of these algorithms to decrease the influence of the user on the clustering results. For the analysis of the resulted fuzzy clusters a new fuzzy similarity measure based tool has been presented. The calculated similarities of the clusters can be used for the hierarchical clustering of the resulted fuzzy clusters, which information is useful for cluster merging and for the visualization of the clustering results. As the examples used for the illustration of the operation of the new algorithm will show, the proposed algorithm can detect clusters from data with arbitrary shape and does not suffer from the numerical problems of the classical Gath-Geva fuzzy clustering algorithm.

Keywords: Clustering, fuzzy clustering, minimal spanning tree, cluster validity, fuzzy similarity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1055914

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2338

References:


[1] Augustson J.G., Minker J., "An analysis of some graph theoretical clustering techniques", J. ACM Vol.17, 4, pp. 571-588., 1970.
[2] Backer F.B., Hubert L.J., "A graph-theoretic approach to goodness-of-fit in complete-link hierarchical clustering" J. Am. Stat. Assoc. Vol. 71, pp. 870-878., 1976.
[3] Barrow, J.D., Bhavsar, S.P., Sonoda, D.H., "Minimal spanning trees, filaments and galaxy clustering" In Monthly Notices of the Royal Astronomical Society, 216:17-35., 1985.
[4] Bezdek, J.C, Ehrlich, R., Full, W., "FCM:Fuzzy C-Means Algorithm", Computers and Geoscience, 1984.
[5] Bezdek, J.C., Clarke, L.P., Silbiger, M.L., Arrington, J.A., Bensaid, A.M., Hall, L.O., Murtagh, R.F., "Validity-guided (re)clustering with applications to image segmentation" IEEE Transactions on Fuzzy Systems, 4:112-123., 1996.
[6] Dunn, J.C., "Well separated clusters and optimal fuzzy partitions", Journal Cybernetics, 4: 95-104., 1974.
[7] Forina, M., Oliveros, C., Concepcin M., Casolino, C., Casale, M., "Minimum spanning tree: ordering edges to identify clustering structure" In Analytica Chimica Acta, 515: 43-53., 2004.
[8] Gath I., Geva, A.B. "Unsupervised optimal fuzzy clustering", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11(7), 1989.
[9] Gonzales-Barrios, J.M., Quiroz, A.J., "A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree" In Statistics & Probability Letter, 62: 23-34., 2003.
[10] Gower J.C., Ross G.J.S., "Minimal Spanning Trees and Single Linkage Cluster Analysis", Applied Statistics, Vol. 18, pp. 54-64., 1969.
[11] Jain, A.K., Dubes, R.C., "Algorithms for Clustering Data", Prentice- Hall advanced reference series, Prentice-Hall, Inc., Upper Saddle River, NJ., 1988.
[12] Kruskal, J.B., "On the shortest spanning subtree of a graph and the traveling salesman problem" In American Mathematical Society, 7: 48- 50., 1956.
[13] Päivinen, N., "Clustering with a minimum spanning tree of scale-freelike structure", In Pattern Recognition Letters, 26(7): 921-930., 2005.
[14] Prim, R., "Shortest connection networks and some generalizations" Bell System Technical Journal, Vol. 36, pp. 1389-1401., 1957.
[15] Raghavan V.V., YU C.T., "A comparison of the stability characteristics of some graph theoretic clustering methods", IEEE Trans. Pattern Anal. Mach. Intell. 3, pp. 3-402., 1981.
[16] Varma, S., Simon, R., "Iterative class discovery and feature selection using Minimal Spanning Trees" BMC Bioinformatics, Vol. 5, pp. 126- 134., 2004.
[17] Zahn, C.T., "Graph-theoretical methods for detecting and describing gestalt clusters" IEEE Transaction on Computers, C20: 68-86., 1971.