Expanding Self-Organizing Map for data visualization and cluster analysis

The Self-Organizing Map (SOM) is a powerful tool in the exploratory phase of data mining. It is capable of projecting high-dimensional data onto a regular, usually 2- dimensional grid of neurons with good neighborhood preservation between two spaces. However, due to the dimensional conflict, the neighborhood preservation cannot always lead to perfect topology preservation. In this paper, we establish an Expanding SOM (ESOM) to preserve better topology between the two spaces. Besides the neighborhood relationship, our ESOM can detect and preserve an ordering relationship using an expanding mechanism. The computational complexity of the ESOM is comparable with that of the SOM. Our experiment results demonstrate that the ESOM constructs better mappings than the classic SOM, especially, in terms of the topological error. Furthermore, clustering results generated by the ESOM are more accurate than those obtained by the SOM.

[1]  Esa Alhoniemi,et al.  Clustering of the self-organizing map , 2000, IEEE Trans. Neural Networks Learn. Syst..

[2]  Christopher M. Bishop,et al.  GTM: A Principled Alternative to the Self-Organizing Map , 1996, NIPS.

[3]  Mu-Chun Su,et al.  A new model of self-organizing neural networks and its application in data projection , 2001, IEEE Trans. Neural Networks.

[4]  Juha Vesanto,et al.  SOM-based data visualization methods , 1999, Intell. Data Anal..

[5]  J.A.F. Costa,et al.  A new tree-structured self-organizing map for data analysis , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[6]  Jacek M. Zurada,et al.  A two-stage algorithm for improved topography preservation in self-organizing maps , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[7]  Hujun Yin,et al.  Self-organizing mixture networks for probability density estimation , 2001, IEEE Trans. Neural Networks.

[8]  Holly E. Rushmeier,et al.  A Scalable Parallel Algorithm for Self-Organizing Maps with Applications to Sparse Data Mining Problems , 1999, Data Mining and Knowledge Discovery.

[9]  A. Tenhagen,et al.  On the combination of fuzzy logic and Kohonen nets , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[10]  Juha Vesanto,et al.  Neural Network Tool for Data Mining: SOM Toolbox , 2000 .

[11]  Huidong Jin,et al.  An Integrated Self-Organizing Map for the Traveling Salesman Problem , 2001 .

[12]  Jennie Si,et al.  Weight-Value Convergence of the SOM Algorithm for Discrete Input , 1998, Neural Computation.

[13]  Bernd Michaelis,et al.  Adaptive three-dimensional self-organizing map with a two-dimensional input layer , 1996, 1996 Australian New Zealand Conference on Intelligent Information Systems. Proceedings. ANZIIS 96.

[14]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[15]  Thomas Villmann,et al.  Neural maps and topographic vector quantization , 1999, Neural Networks.

[16]  Yoh-Han Pao,et al.  Visualization and self-organization of multidimensional data through equalized orthogonal mapping , 2000, IEEE Trans. Neural Networks Learn. Syst..

[17]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[18]  Thomas Villmann,et al.  Topology preservation in self-organizing feature maps: exact definition and measurement , 1997, IEEE Trans. Neural Networks.

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