### Multidimensional scaling and Kohonen's self-organizing maps.

Wlodzislaw Duch and Antoine Naud.

Department of Informatics,
Nicolaus Copernicus University,

Grudziadzka 5, 87-100 Torun, Poland.

Proceedings of the Second Conference on Neural Networks and their applications, Orle Gniazdo, 30.IV-4.V.1996, pp. 138-143

Two methods providing representation of high-dimensional (input) data in a lower-dimensional (target) space are compared. Although multidimensional scaling (MDS) and Kohonen's self-organizing maps (SOM) are dedicated to very different applications both methods are based on an iterative process that tends to approximate the topography of high-dimensional data and both can be used to model self-organization and unsupervised learning. In general it is impossible to find a lower-dimensional representation that preserves exactly the topography of high-dimensional data. An error function is defined to measure the quality of representations and is minimized in an iterative process. The minimal error measures the unavoidable distortion of the original topography represented in the target space.

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