Kaski, S., Data exploration using self-organizing maps. Acta Polytechnica Scandinavica, Mathematics, Computing and Management in Engineering Series No. 82, Espoo 1997, 57 pp. Published by the Finnish Academy of Technology. ISBN 952-5148-13-0. ISSN 1238-9803. UDC 681.327.12:159.95:519.2

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Keywords: Data mining, exploratory data analysis, multivariate analysis, neural networks, self-organizing map, SOM

Thesis for the degree of Doctor of Technology to be presented with due permission for public examination and criticism in Auditorium F1 of the Helsinki University of Technology on the 21st of March, at 12 o'clock noon.

ABSTRACT

Finding structures in vast multidimensional data sets, be they measurement data, statistics, or textual documents, is difficult and time-consuming. Interesting, novel relations between the data items may be hidden in the data. The self-organizing map (SOM) algorithm of Kohonen can be used to aid the exploration: the structures in the data sets can be illustrated on special map displays.

In this work, the methodology of using SOMs for exploratory data analysis or data mining is reviewed and developed further. The properties of the maps are compared with the properties of related methods intended for visualizing high-dimensional multivariate data sets. In a set of case studies the SOM algorithm is applied to analyzing electroencephalograms, to illustrating structures of the standard of living in the world, and to organizing full-text document collections.

Measures are proposed for evaluating the quality of different types of maps in representing a given data set, and for measuring the robustness of the illustrations the maps produce. The same measures may also be used for comparing the knowledge that different maps represent.

Feature extraction must in general be tailored to the application, as is done in the case studies. There exists, however, an algorithm called the adaptive-subspace self-organizing map, recently developed by Kohonen, which may be of help. It extracts invariant features automatically from a data set. The algorithm is here characterized in terms of an objective function, and demonstrated to be able to identify input patterns subject to different transformations. Moreover, it could also aid in feature exploration: the kernels that the algorithm creates to achieve invariance can be illustrated on map displays similar to those that are used for illustrating the data sets.

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• PREFACE
• Contents
• LIST OF PUBLICATIONS
• THE AUTHOR'S CONTRIBUTION
• LIST OF SYMBOLS AND ABBREVIATIONS
• INTRODUCTION
• METHODS FOR EXPLORATORY DATA ANALYSIS
  • Visualization of high-dimensional data items
  • Clustering methods
  • Projection methods
    • Linear projection methods
      • Principal component analysis
      • Projection pursuit.
    • Nonlinear projection methods
      • Multidimensional scaling
      • Principal curves.
      • Other methods.
  • Self-organizing maps
    • The self-organizing map algorithm
    • Properties useful in exploring data
      • Ordered display.
      • Visualization of clusters.
      • Missing data.
      • Outliers.
    • Mathematical characterizations
      • Relation to K-means clustering.
      • Relation to principal curves.
      • A decomposition of the cost function.
    • Some variants
    • Notes on statistical accuracy
  • Relations and differences between SOM and MDS
    • Relations of the mappings in the ideal case.
    • Computational properties.
    • Combinations of the methods.
• STAGES OF SOM-BASED EXPLORATORY DATA
  ANALYSIS
  • Preprocessing
  • Computation of the maps
  • Choosing good maps
    • Note 1: Sparse data.
    • Note 2: High dimensionality.
    • Note 3: Computational complexity.
  • Interpretation, evaluation, and use of the maps
    • Interpretation.
    • Evaluation.
    • Use of the organized maps for exploratory data analysis.
• CASE STUDIES
  • Multichannel EEG signal
  • Statistical tables
  • Full-text document collections
    • Recent developments
• FURTHER DEVELOPMENTS
  • Feature exploration with the adaptive-subspace SOM
  • Comparison of knowledge areas
• CONCLUSION
• References
• APPENDIX: KEY TO THE COUNTRY NAMES
• About this document ...