Abstract
Self Organizing Maps (SOM) and Sammon Mapping (SM) are two information visualization techniques widely used in the data mining community. These techniques assume that the similarity matrix for the data set under consideration is symmetric. However there are many interesting problems where asymmetric proximities arise, like text mining problems are. In this work we propose modified versions of SOM and SM to deal with data where the proximity matrix is asymmetric. The algorithms are tested using a real document database, and performance is reported using appropriate measures. As a result, the asymmetric algorithms proposed outperform their symmetric counterparts.
Financial support from DGICYT grant BEC2000-0167 (Spain) is gratefully appreciated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. Baeza-Yates and B. Ribeiro-Neto. Modern Information Retrieval. Addison Wesley, 1999.
J. C. Bezdek and N. R. Pal. ”An Index of Topological Preservation for Feature Extraction”, Pattern Recognition, 28(3):381–391, 1995.
G.A. Carpenter and S. Grossberg and N. Markuzon and J.H. Reynolds and D.B. Rosen. Fuzzy ARTMAP: A neural network architecture for incremental supervised learning of analog multidimensional maps. IEEE Transactions on Neural Networks, 3(5):698–713, 1992.
H. Chen, B. Schatz, T. Ng, J. Martinez, A. Kirchhoff and C. Lin. A Paralell Computing Approach to Creating Engineering Concept Spaces for Semantic Retrieval: The Illinois Digital Library Initiative Project. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(8):775–782, August 1996.
H. Chen and A. L. Houston. Internet Browsing and Searching: User Evaluations of Category Map and Concept Space Techniques. Journal of the American Society for Information Science, 49(7):582–603, 1998.
T. F. Cox and M. A. A. Cox, Multidimensional Scaling, Chapman and Hall/CRC, 2nd ed., USA, 2001.
I. Dagan, L. Lee and F. C. N. Pereira. Similarity-Based Models of Word Coocurrence Probabilities. Machine Learning, 34:48–69, 1999.
S. Kaski. Dimensionality Reduction by Random Mapping: Fast Similarity Computation for Clustering. 1:413–418, Proceedings of IJCNN’98.
T. Kohonen, S. Kaski, K. Lagus, J. Salojarvi, J. Honkela, V. Paatero and A. Saarela. Organization of a Massive Document Collection. IEEE Transactions on Neural Networks, 11(3):574–585, May 2000.
A. Kopcsa and E. Schievel. Science and Technology Mapping: A New Iteration Model for Representing Multidimensional Relationships. Journal of the American Society for Information Science, 49(1): 7–17, 1998.
B. Kosko. Neural Networks and Fuzzy Systems: A Dynamical Approach to Machine Intelligence. Prentice Hall, Englewood Cliffs, New Jersey, 1991.
David D. Lewis. The Reuters-21578, Distribution 1.0 test collection. AT&T Labs. Available at http://www.research.att.comĺewis
F. Mulier and V. Cherkassky. Self-Organization as an Iterative Kernel Smoothing Process. Neural Computation, 7:1165–1177, 1995.
A. Muñoz. Extracting term associations from a text database using a hierarchical ART architecture. Proceedings of the ICANN 96, LNCS 866:376–385, Springer-Verlag.
A. Muñoz. Compound key word generation from document databases using a hierarchical clustering ART model. Journal of Intelligent Data Analysis, 1(1), 1997.
M. Rorvig. Images of Similarity: A Visual Exploration of Optimal Similarity Metrics and Scaling Properties of TREC Topic-Document Sets. Journal of the American Society for Information Science. 50(8):639–651, 1999.
J.W. Sammon. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, 18(5):401–409, 1969.
B. Zielman and W.J. Heiser. Models for asymmetric proximities. British Journal of Mathematical and Statistical Psychology, 49:127–146, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Martin-Merino, M., Muñoz, A. (2001). Self Organizing Map and Sammon Mapping for Asymmetric Proximities. In: Dorffner, G., Bischof, H., Hornik, K. (eds) Artificial Neural Networks — ICANN 2001. ICANN 2001. Lecture Notes in Computer Science, vol 2130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44668-0_60
Download citation
DOI: https://doi.org/10.1007/3-540-44668-0_60
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42486-4
Online ISBN: 978-3-540-44668-2
eBook Packages: Springer Book Archive