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We discuss topological preservation under feature extraction transformations. Transformations that preserve the order of all distances in any neighborhood of vectors in p-space are defined as metric topology preserving (MTP) transformations. We give a necessary and sufficient condition for this property in terms of Spearman's rank correlation coefficient. A modification of Kohonen's self-organizing feature map algorithm that extracts vectors in q-space from data in p-space is given. Three methods are empirically compared: principal components analysis; Sammon's algorithm; and our extension of the self-organizing feature map algorithm. Our MTP index shows that the first two methods preserve distance ranks on six data sets much more effectively than extended SOFM.
Neural Networks, 1993. IJCNN '93-Nagoya. Proceedings of 1993 International Joint Conference on (Volume:3 )
Date of Conference: 25-29 Oct. 1993