Dimension Reduction and Data Visualization Using Neural Networks

The problem of visual presentation of multidimensional data is discussed. The projection methods for dimension reduction are reviewed. The chapter deals with the artificial neural networks that may be used for reducing dimension and data visualization, too. The stress is put on combining the selforganizing map (SOM) and Sammon mapping and on the neural network for Sammon's mapping SAMANN. Large scale applications are discussed: environmental data analysis, statistical analysis of curricula, comparison of schools, analysis of the economic and social conditions of countries, analysis of data on the fundus of eyes and analysis of physiological data on men's health.

[1]  A. E. Maxwell,et al.  Factor Analysis as a Statistical Method. , 1964 .

[2]  Robert P. W. Duin,et al.  Sammon's mapping using neural networks: A comparison , 1997, Pattern Recognit. Lett..

[3]  Gintautas Dzemyda,et al.  Optimization of the Local Search in the Training for SAMANN Neural Network , 2006, J. Glob. Optim..

[4]  J. Douglas Carroll,et al.  14 Multidimensional scaling and its applications , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[5]  Pirjo Hellemaa,et al.  The development of coastal dunes and their vegetation in Finland , 1998 .

[6]  Eric R Ziegel,et al.  Encyclopedia of Environmetrics Vols. 1-4 , 2002, Technometrics.

[7]  Gintautas Dzemyda,et al.  Dimensionality Problem in the Visualization of Correlation-Based Data , 2007, ICANNGA.

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

[9]  Aimo Törn,et al.  Models and Algorithms for Global Optimization , 2007 .

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

[11]  M. Kramer.  Nonlinear principal component analysis using autoassociative neural networks , 1991 .

[12]  D. Ruppert,et al.  Trimmed Least Squares Estimation in the Linear Model , 1980 .

[13]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[14]  Manuel Rubio,et al.  Visual Analysis of Self-Organizing Maps , 2002 .

[15]  Enrico Tronci.  1997 , 1997, Les 25 ans de l’OMC: Une rétrospective en photos.

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

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

[18]  Gintautas Dzemyda,et al.  The use of information technologies for diagnosis in ophthalmology , 2006, Journal of telemedicine and telecare.

[19]  Gautam Biswas,et al.  Evaluation of Projection Algorithms , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  J. Rubner,et al.  A Self-Organizing Network for Principal-Component Analysis , 1989 .

[21]  Gintautas Dzemyda,et al.  The Problem of Visual Analysis of Multidimensional Medical Data , 2007 .

[22]  Norma Banas,et al.  Visualization , 1968, Machine-mediated learning.

[23]  L. N. Kanal,et al.  Theory of Multidimensional Scaling , 2005 .

[24]  G. V. Kass,et al.  Location of Several Outliers in Multiple-Regression Data Using Elemental Sets , 1984 .

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

[26]  Willem J. Heiser,et al.  13 Theory of multidimensional scaling , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[27]  Gintautas Dzemyda,et al.  Forecasting Models in the State Education System , 2003, Informatics Educ..

[28]  Walter A. Kosters,et al.  Nonmetric multidimensional scaling: Neural networks versus traditional techniques , 2004, Intell. Data Anal..

[29]  David J. Hand,et al.  Intelligent Data Analysis: An Introduction , 2005 .

[30]  Erkki Oja,et al.  Principal components, minor components, and linear neural networks , 1992, Neural Networks.

[31]  T. Hastie,et al.  Principal Curves , 2007 .

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

[33]  David Lowe,et al.  Radial basis function networks , 1998 .

[34]  Michael E. Tipping,et al.  Feed-forward neural networks and topographic mappings for exploratory data analysis , 1996, Neural Computing & Applications.

[35]  Anil K. Jain,et al.  Artificial neural networks for feature extraction and multivariate data projection , 1995, IEEE Trans. Neural Networks.

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

[37]  Arthur Flexer,et al.  Limitations of Self-organizing Maps for Vector Quantization and Multidimensional Scaling , 1996, NIPS.

[38]  Gintautas Dzemyda,et al.  Visualization of a set of parameters characterized by their correlation matrix , 2001 .

[39]  Gintautas Dzemyda,et al.  Visualisation of Multidimensional Objects and the Socio-Economical Impact to Activity in EC RTD Databases , 2001, Informatica.

[40]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[41]  Martin Charlton,et al.  An Investigation of Methods for Visualising Highly Multivariate Datasets , 1998 .

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

[43]  Kurt Hornik,et al.  Neural networks and principal component analysis: Learning from examples without local minima , 1989, Neural Networks.

[44]  Gintautas Dzemyda,et al.  Visualization of correlation‐based environmental data , 2004 .

[45]  Jeanny Hérault,et al.  Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets , 1997, IEEE Trans. Neural Networks.

[46]  Gintautas Dzemyda,et al.  Multidimensional data visualization in the statistical analysis of curricula , 2005, Comput. Stat. Data Anal..

[47]  Christopher A. Badurek,et al.  Review of Information visualization in data mining and knowledge discovery by Usama Fayyad, Georges G. Grinstein, and Andreas Wierse. Morgan Kaufmann 2002 , 2003 .

[48]  Gintautas Dzemyda,et al.  Quantitative Forecasting and Assessment Models in the State Education System , 2002, Informatica.

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

[50]  Michael E. Tipping.  Topographic mappings and feed-forward neural networks , 1996 .

[51]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[52]  P. Groenen,et al.  Modern Multidimensional Scaling: Theory and Applications , 1999 .

[53]  Gintautas Dzemyda,et al.  Parallel Realizations of the SAMANN Algorithm , 2007, ICANNGA.

[54]  Richard C. T. Lee,et al.  A Triangulation Method for the Sequential Mapping of Points from N-Space to Two-Space , 1977, IEEE Transactions on Computers.