Integration of the Self-Organizing Map and Neural gas with Multidimensional Scaling

In the paper, two combinations (consecutive and integrated) of vector quantization methods (self-orga- nizing map and neural gas) and multidimensional scaling (MDS) have been investigated and compared. The vector quantization is used to reduce the number of dataset items. The dataset with a smaller number of items is analyzed by multidimensional scaling in order to reduce the number of features of data (dimensionality of space) and to map them onto the plane, i.e., to visualize. Some ways of the initialization (at random, on a line, by PCs and by variances) of two- dimensional vectors in MDS have been investigated. Two ways of assignment of two-dimensional vectors in the integ- rated combinations of MDS and vector quantization methods have been examined, too.

[1]  Gintautas Dzemyda,et al.  Conditions for Optimal Efficiency of Relative MDS , 2007, Informatica.

[2]  Gintautas Dzemyda,et al.  Optimal decisions in combining the SOM with nonlinear projection methods , 2006, Eur. J. Oper. Res..

[3]  Olga Kurasova,et al.  Quality of Quantization and Visualization of Vectors Obtained by Neural Gas and Self-Organizing Map , 2011, Informatica.

[4]  Olga Kurasova,et al.  Combination of Vector Quantization and Visualization , 2009, MLDM.

[5]  Georges G. Grinstein,et al.  A survey of visualizations for high-dimensional data mining , 2001 .

[6]  P. Groenen,et al.  Modern multidimensional scaling , 1996 .

[7]  Julius Zilinskas On Dimensionality of Embedding Space in Multidimensional Scaling , 2008, Informatica.

[8]  Gintautas Dzemyda,et al.  Dimension Reduction and Data Visualization Using Neural Networks , 2007, Emerging Artificial Intelligence Applications in Computer Engineering.

[9]  Antanas Zilinskas,et al.  Two level minimization in multidimensional scaling , 2007, J. Glob. Optim..

[10]  Andrej Bugajev,et al.  EFFICIENT VISUALIZATION BY USING PARAVIEW SOFTWARE ON BALTICGRID , 2010 .

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

[12]  Gintautas Dzemyda,et al.  Topology Preservation Measures in the Visualization of Manifold-Type Multidimensional Data , 2009, Informatica.

[13]  Pablo A. Estévez,et al.  Cross-entropy embedding of high-dimensional data using the neural gas model , 2005, Neural Networks.

[14]  Olga Kurasova,et al.  INVESTIGATION OF THE QUALITY OF MAPPING VECTORS OBTAINED BY QUANTIZATION METHODS , 2009 .

[15]  Gintautas Dzemyda,et al.  Heuristic approach for minimizing the projection error in the integrated mapping , 2006, Eur. J. Oper. Res..

[16]  R. Mathar,et al.  On global optimization in two-dimensional scaling , 1993 .