Advanced visualization of Self-Organizing Maps with vector fields

Self-Organizing Maps have been applied in various industrial applications and have proven to be a valuable data mining tool. In order to fully benefit from their potential, advanced visualization techniques assist the user in analyzing and interpreting the maps. We propose two new methods for depicting the SOM based on vector fields, namely the Gradient Field and Borderline visualization techniques, to show the clustering structure at various levels of detail. We explain how this method can be used on aggregated parts of the SOM that show which factors contribute to the clustering structure, and show how to use it for finding correlations and dependencies in the underlying data. We provide examples on several artificial and real-world data sets to point out the strengths of our technique, specifically as a means to combine different types of visualizations offering effective multidimensional information visualization of SOMs.

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

[2]  A. Skupin,et al.  A picture from a thousand words [information visualization] , 2004, Comput. Sci. Eng..

[3]  T. Kohonen,et al.  Bibliography of Self-Organizing Map SOM) Papers: 1998-2001 Addendum , 2003 .

[4]  Bernd Fritzke,et al.  Growing cell structures--A self-organizing network for unsupervised and supervised learning , 1994, Neural Networks.

[5]  Esa Alhoniemi,et al.  Publication 6 SelfOrganizing Map in Matlab: the SOM Toolbox , 1999 .

[6]  Gunter Zangl,et al.  Data Mining: Applications in the Petroleum Industry , 2003 .

[7]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.

[8]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[9]  Andreas Rauber,et al.  Gradient visualization of grouped component planes on the SOM lattice , 2005 .

[10]  Urska Cvek,et al.  High-Dimensional Visualizations , 2002 .

[11]  A. Ultsch.  Maps for the Visualization of high-dimensional Data Spaces , 2003 .

[12]  Johan Himberg,et al.  Enhancing SOM-based data visualization by linking different data projections , 1998 .

[13]  Teuvo Kohonen,et al.  Self-Organizing Maps, Third Edition , 2001, Springer Series in Information Sciences.

[14]  Alfred Ultsch,et al.  Data Mining and Knowledge Discovery with Emergent Self-Organizing Feature Maps for Multivariate Time Series , 1999 .

[15]  Michel Verleysen,et al.  Nonlinear projection with curvilinear distances: Isomap versus curvilinear distance analysis , 2004, Neurocomputing.

[16]  Samuel Kaski,et al.  Methods for Exploratory Cluster Analysis , 2003, Intelligent Exploration of the Web.

[17]  Charu C. Aggarwal,et al.  Towards systematic design of distance functions for data mining applications , 2003, KDD '03.

[18]  Maurice K. Wong,et al.  Algorithm AS136: A k-means clustering algorithm. , 1979 .

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

[20]  Alan F. Murray,et al.  Synaptic Rewiring for Topographic Map Formation , 2008, ICANN.

[21]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[22]  Erkki Oja,et al.  Kohonen Maps , 1999, Encyclopedia of Machine Learning.

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

[24]  Juha Vesanto,et al.  Hunting for Correlations in Data Using the Self-Organizing Map , 1999 .

[25]  Andreas Rauber,et al.  Uncovering hierarchical structure in data using the growing hierarchical self-organizing map , 2002, Neurocomputing.

[26]  Alfred Ultsch,et al.  U *-Matrix : a Tool to visualize Clusters in high dimensional Data , 2004 .

[27]  Hujun Yin,et al.  ViSOM - a novel method for multivariate data projection and structure visualization , 2002, IEEE Trans. Neural Networks.

[28]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[29]  Elias Pampalk,et al.  Using Smoothed Data Histograms for Cluster Visualization in Self-Organizing Maps , 2002, ICANN.

[30]  Samuel Kaski,et al.  Bibliography of Self-Organizing Map (SOM) Papers: 1981-1997 , 1998 .

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

[32]  Christopher K. I. Williams,et al.  Magnification factors for the GTM algorithm , 1997 .

[33]  Tao Xiong,et al.  A combined SVM and LDA approach for classification , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[34]  Andreas Rauber,et al.  Advanced Visualization Techniques for Self-organizing Maps with Graph-Based Methods , 2005, ISNN.

[35]  Christopher M. Bishop,et al.  GTM: The Generative Topographic Mapping , 1998, Neural Computation.

[36]  G. Polzlbauer,et al.  A visualization technique for self-organizing maps with vector fields to obtain the cluster structure at desired levels of detail , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[37]  Peter Tiño,et al.  Using Directional Curvatures to Visualize Folding Patterns of the GTM Projection Manifolds , 2001, ICANN.

[38]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[39]  W. Torgerson.  Multidimensional scaling: I. Theory and method , 1952 .