Determining Cluster Boundaries Using Particle Swarm Optimization

Self-organizing map (SOM) is a well known data reduction technique used in data mining. Data visualization can reveal structure in data sets that is otherwise hard to detect from raw data alone. However, interpretation through visual inspection is prone to errors and can be very tedious. There are several techniques for the automatic detection of clusters of code vectors found by SOMs, but they generally do not take into account the distribution of code vectors; this may lead to unsatisfactory clustering and poor definition of cluster boundaries, particularly where the density of data points is low. In this paper, we propose the use of a generic particle swarm optimization (PSO) algorithm for finding cluster boundaries directly from the code vectors obtained from SOMs. The application of our method to unlabeled call data for a mobile phone operator demonstrates its feasibility. PSO algorithm utilizes U-matrix of SOMs to determine cluster boundaries; the results of this novel automatic method correspond well to boundary detection through visual inspection of code vectors and k-means algorithm.

• Anurag Sharma
• Christian W. Omlin

• Particle swarm optimization
• self-organizing maps
• clustering
• data mining.

[1] A. Rauber and D. Merkl, "Automatic Labelling of Self-Organizing
Maps: Making a Treasure Maps Reveal Its Secrets," in Proc. 4th Pacific-
Asia Conference on Knowledge Discovery and Data Mining,
PAKDD99. Beijing, China, (1999).
[2] A. Carlistle, and G. Dozier. (1998). Adapting Particle Swarm
Optimization to Dynamic Environments [Online]. Available:
http://www.CartistleA.edu
[3] J. Vesanto, and E. Alhoniemi, "Clustering of the Self-Organizing Map,"
IEEE transaction on neural network, Vol. 11, No. 3, May 2000.
[4] J. Vesanto, and M. Sulkava, "Distance matrix based clustering of the
self-organizing map," in Proc. International Conference on Artificial
Neural Networks - ICANN 2002, Lecture Notes in Computer Science,
No. 2415, pages 951-956. Springer-Verlag, 2002.
[5] T. Kohonen, Self-Organizing Maps. Springer-Verlag, Berlin, Germany,
2001.
[6] B. Jiang, and L. Harrie, "Selection of streets form a network using self-
Organizing maps," Transactions in GIS, Vol 8(3), pages 335-350, 2004.
[7] O. Abidogun, "Data Mining, Fraud Detection and Mobile
Telecommunication: Call pattern Analysis with Unsupervised Neural
Networks," M.Sc. thesis, University of the Western Cape, Bellville,
Cape Town, South Africa, 2004.
[8] J. Vesanto, and E. Alhoniemi, "Clustering of the Self-Organizing Map,"
IEEE Transaction on Neural Neetworks, Volume 11, Number 3, pages
586-600, 2000.
[9] J. Hollmén, "Process Modelling using the Self-Organizing Map," M.Sc.
thesis, Dept. Computer Science, Helsinki Univ. of Technology, Finland,
1996.
[10] J. Vesanto, J. Himberg, E. Alhoniemi, and J. Parhankangas, "SOM
Toolbox for Matlab 5," ISBN 951-22-4951-0, ISSN 1456-2243, Espoo,
Finland, 2000.
[11] J. Kennedy, and R. C. Eberhart, "The particle swarm: social adaptation
in information processing systems," In Corne, D., Dorigo, M., and
Glover, F., Eds., New Ideas in Optimization. London: McGraw-Hill, pp.
379-387, 1999.
[12] M. Kantardzic, "Cluster Analysis," Data Mining - concepts, models,
methods, and algrorithms. Wiley InterScience, pp 129-132, 2003.