The Kohonen self-organizing map method: An assessment

The “self-organizing map” method, due to Kohonen, is a well-known neural network method. It is closely related to cluster analysis (partitioning) and other methods of data analysis. In this article, we explore some of these close relationships. A number of properties of the technique are discussed. Comparisons with various methods of data analysis (principal components analysis, k-means clustering, and others) are presented.

[1]  Manuel Hernández-Pajares,et al.  Astronomical classification of the Hipparcos input catalogue , 1994 .

[2]  Pierre Demartines,et al.  Data Analysis: How to Compare Kohonen Neural Networks to Other Techniques? , 1991, IWANN.

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

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

[5]  Robert J. Schalkoff,et al.  Digital Image Processing and Computer Vision , 1989 .

[6]  M. Hernandez Pajares.  Can a local bulge be differentiated , 1993 .

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

[8]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[9]  Fionn Murtagh,et al.  Multidimensional clustering algorithms , 1985 .

[10]  A. D. Gordon,et al.  Correspondence Analysis Handbook. , 1993 .

[11]  R. Sokal,et al.  Optimisation en Classification Automatique. , 1984 .

[12]  Josef Kittler,et al.  A locally sensitive method for cluster analysis , 1976, Pattern Recognit..

[13]  A. D. Gordon,et al.  Classification : Methods for the Exploratory Analysis of Multivariate Data , 1981 .

[14]  Jorma Laaksonen,et al.  SOM_PAK: The Self-Organizing Map Program Package , 1996 .

[15]  J. Bezdek.  A Physical Interpretation of Fuzzy ISODATA , 1993 .

[16]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[17]  J.-C. Mermilliod,et al.  The Hipparcos input catalogue , 1987 .

[18]  Teuvo Kohonen,et al.  The self-organizing map , 1990 .

[19]  D P Casasent,et al.  Adaptive-clustering optical neural net. , 1990, Applied optics.

[20]  A. Ultsch,et al.  Self-Organizing Neural Networks for Visualisation and Classification , 1993 .

[21]  J. Bezdek.  Cluster Validity with Fuzzy Sets , 1973 .

[22]  Anil K. Jain,et al.  Single-link characteristics of a mode-seeking clustering algorithm , 1979, Pattern Recognit..

[23]  P. M. Narendra,et al.  Image Segmentation with Directed Trees , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  Enric Monte-Moreno,et al.  Application of the LVQ Neural Method to a Stellar Catalogue , 1991, IWANN.

[25]  J. Hartigan.  Direct Clustering of a Data Matrix , 1972 .

[26]  G. W. Milligan,et al.  A study of standardization of variables in cluster analysis , 1988 .

[27]  T. Kohonen.  Self-Organized Formation of Correct Feature Maps , 1982 .

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

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

[30]  Josef Kittler.  Comments on "single-link characteristics of a mode-seeking clustering algorithm" , 1979, Pattern Recognit..

[31]  John E. Moody,et al.  Fast adaptive k-means clustering: some empirical results , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[32]  D. Hand.  Cluster dissection and analysis: Helmuth SPATH Wiley, Chichester, 1985, 226 pages, £25.00 , 1986 .

[33]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[34]  Paul J. Schweitzer,et al.  Problem Decomposition and Data Reorganization by a Clustering Technique , 1972, Oper. Res..

[35]  Alfred Ultsch,et al.  Knowledge Extraction from Self-Organizing Neural Networks , 1993 .

[36]  Emile H. L. Aarts,et al.  Simulated annealing: A pedestrian review of the theory and some applications , 1987 .

[37]  F. James Rohlf,et al.  Function-Point Cluster Analysis , 1973 .

[38]  Phipps Arabie,et al.  The bond energy algorithm revisited , 1990, IEEE Trans. Syst. Man Cybern..

[39]  Bernard Angéniol,et al.  Self-organizing feature maps and the travelling salesman problem , 1988, Neural Networks.