Multidimensional Scaling and Kohonen's Self-organizing Maps

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 di erent 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 nd a lower dimensional representation that preserves exactly the topography of high dimensional data An error function is de ned 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