Self Organizing Map and Sammon Mapping for Asymmetric Proximities

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.

[1]  Willem J. Heiser,et al.  Models for asymmetric proximities , 1996 .

[2]  Stephen Grossberg,et al.  Fuzzy ARTMAP: A neural network architecture for incremental supervised learning of analog multidimensional maps , 1992, IEEE Trans. Neural Networks.

[3]  Samuel Kaski,et al.  Dimensionality reduction by random mapping: fast similarity computation for clustering , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[4]  Samuel Kaski,et al.  Self organization of a massive document collection , 2000, IEEE Trans. Neural Networks Learn. Syst..

[5]  Bart Kosko,et al.  Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence , 1991 .

[6]  Alberto Muòoz,et al.  Compound Key Word Generation from Document Databases Using A Hierarchical Clustering ART Model , 1997 .

[7]  Hsinchun Chen,et al.  A Parallel Computing Approach to Creating Engineering Concept Spaces for Semantic Retrieval: The Illinois Digital Library Initiative Project , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Alberto Muñoz,et al.  Creating Term Associations Using a Hierarchical ART Architecture , 1996, ICANN.

[9]  Edgar Schiebel,et al.  Science and Technology Mapping: A New Iteration Model for Representing Multidimensional Relationships , 1998, J. Am. Soc. Inf. Sci..

[10]  Vladimir Cherkassky,et al.  Self-Organization as an Iterative Kernel Smoothing Process , 1995, Neural Computation.

[11]  James C. Bezdek,et al.  An index of topological preservation for feature extraction , 1995, Pattern Recognit..

[12]  M. Rorvig.  Images of Similarity: A Visual Exploration of Optimal Similarity Metrics and Scaling Properties of TREC Topic-Document Sets , 1999, J. Am. Soc. Inf. Sci..

[13]  Hsinchun Chen,et al.  Internet Browsing and Searching: User Evaluations of Category Map and Concept Space Techniques , 1998, J. Am. Soc. Inf. Sci..

[14]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.