Topology Preservation in SOFM: An Euclidean versus Manhattan Distance Comparison

The Self-Organising Feature Map (SOFM) is one of the unsupervised neural models of most widespread use. Several studies have been carried out in order to determine the degree of topology-preservation for this data projection method, and the influence of the distance measure used, usually Euclidean or Manhattan distance. In this paper, by using a new topology-preserving representation of the SOFM and the well-known Sammon’s stress, graphical and numerical comparisons are shown between both possibilities for the distance measure. Our projection method, based on the relative distances between neighbouring neurons, gives similar information to those of the Sammon projection, but in a graphical way.

[1]  Martín del Brío Bonifacio.  Procesamiento neuronal con mapas autoorganizados: arquitecturas digitales , 1995 .

[2]  B. Martin-del-Brio,et al.  A low-cost neuroprocessor board for emulating the SOFM neural model , 1998, 1998 IEEE International Conference on Electronics, Circuits and Systems. Surfing the Waves of Science and Technology (Cat. No.98EX196).

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

[4]  Pierre Demartines.  Analyse de donnees par reseaux de neurones auto-organises , 1994 .

[5]  Thomas Villmann,et al.  Topology preservation in self-organizing feature maps: exact definition and measurement , 1997, IEEE Trans. Neural Networks.

[6]  Anil K. Jain,et al.  A nonlinear projection method based on Kohonen's topology preserving maps , 1992, IEEE Trans. Neural Networks.

[7]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

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

[9]  Bonifacio Martín del Brío,et al.  Redes neuronales y sistemas borrosos: introducción teórica y práctica , 1997 .

[10]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

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

[12]  Christopher J. Merz,et al.  UCI Repository of Machine Learning Databases , 1996 .

[13]  Bonifacio Martín del Brío,et al.  Predicción de la quiebra bancaria mediante el empleo de redes neuronales artificiales , 1993 .