Abstract
This approach studies 2D object clustering based on Steiner point which is the curvature center for an object. Steiner point can be used as the unique invariable position of a non-symmetric shape body under growth. In contrast to the well known k-means clustering, this technique focuses on calculating Steiner point of an object (or samples of each investitive class) instead of finding center for each class. During clustering iteration, some samples are relabeled according to the distances to all Steiner points which have been updated in the last iteration. The stability analysis of Steiner point is presented based on a 2D data clustering problem. Also, for 2D data clustering this technique is of linear order complexity in calculating Steiner point with respect to the scale of samples. Two groups of experiments are given. The first group includes two representative 2D data sets, and the second is composed of two simple image segmentation problems. Experimental results show that the proposed technique, comparing with the classical k-means clustering and fuzzy c-means clustering, is feasible for 2D object clustering.
Similar content being viewed by others
References
Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31(3):264–323
Duda RO, Hart PE, Stork DG (2004) Pattern classification, 2nd edn. China Machine Press, China
Haykin S (2001) Neural networks: a comprehension foundation, 2nd edn. Prentice Hall, Englewood Cliffs
Guo G, Chen S, Chen L (2011) Soft subspace clustering with an improved feature weight self-adjustment mechanism. Int J Mach Learn Cybern
Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other Kernel-based learning methods. Cambridge University Press, Cambridge
Girolami M, Kernel M (2002) Based clustering in feature space. IEEE Trans Neural Netw 13(3):780–784
Huang GB, Wang DH, Lan Y (2001) Extreme learning machines: a survey. Int J Mach Learn Cybern 2(2):107–122
Liang JZ, Gao JH (2005) Kernel Function Clustering Algorithm with Optimized Parameters. In: The fourth international conference on machine learning and cybernetics, Guangzhou, vol 7, pp 4400–4404
Grunbaum B (2003) Convex polytopes, 2nd edn. Springer, New York
Shephard GC (1968) A uniqueness theorem for the Steiner point of a convex region. J Lond Math Soc 43:439–444
Vetterlein T, Navara M (2006) Defuzzification using Steiner points. Fuzzy Sets Syst 157:1455–1462
Sternberg SR (1986) Grayscale morhpology, computer vision. Graph Image Process 35:333–355
Mondaini R, Freire Mondaini D, Maculan N (1998) The study of Steiner points associated with the vertices of regular tetrahedra joined together at common faces. Invest Opera 6(1–3):103–110
Meyer WJ (1970) Characterization of the Steiner point. Pacif J Math 35(3):717–725
Schneider R (1971) On Steiner points of convex bodies. Israel J Math 9:241–249
Mattioli J (1995) Minkowski operations and vector spaces. Set-valued Anal 3:33–35
Korner R, Nather W (1998) Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least squares estimates. Inform Sci 109:95–118
Schneider R (1993) Convex bodies: the Brunn–Minkowski theory. Cambridge University Press, Cambridge
Chen C (1989) Computing the convex hull of a simple polygon. Pattern Recogn 22(5):561–565
Liang J., Navara M (2007) Implementation of Calculating Steiner Point for 2D Objects. In: Proceedings of the 2007 international conference on intelligent systems and knowledge engineering, Chengdu, 15–16 October 2007, pp 1592–1598
Durocher S, Kirkpatric D (2006) The Steiner centre of a set of points: stability, eccentricity and applications to mobile facility locations. Int J Comput Geom Appl 16(4):345–371
Acknowledgments
This work was supported by CMP laboratory, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University. The author was supported by the Agreement between Czech Ministry of Education and Chinese Ministry of Education. During working in CMP from January 2007 to December 2007, the author cooperated with professor Navara, who is a mathematician, studied on the technical aspects of the use of Steiner point of fuzzy set. So, thanks to professor Navara for his guidance on this topic.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liang, J., Song, W. Clustering based on Steiner points. Int. J. Mach. Learn. & Cyber. 3, 141–148 (2012). https://doi.org/10.1007/s13042-011-0047-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-011-0047-7