A Novel Measure for Quantifying the Topology Preservation of Self-Organizing Feature Maps MU-CHUN SU, HSIAO-TE CHANG* and CHIEN-HSING CHOU* Department of Computer Science and Information Engineering, National Central University, Taiwan, R.O.C. (*Corresponding author, Department of Electrical Engineering, Tamkang University, Taiwan, R.O.C.; tel: 8862-3-4227151-4500, fax: 886-3-4226681) Abstract. Recently, feature maps have been applied to various problem domains. The success of some of these applications critically depends on whether feature maps are topologically ordered. In this paper, we propose a novel measure for quantifying the neighborhood preserving property of feature maps. Two data sets were tested to illustrate the performance of the proposed method. Key words: neural networks, feature maps, SOM algorithm, topological property 1. Introduction The self-organizing feature map (SOM) algorithm developed by Kohonen [1] has been successfully applied to various problem domains ö cluster analysis, motor control, speech recognition, vector quantization, etc. Kohonen et al. [2] and Ritter and Schulten [3] provide partial reviews. It should be emphasized the success of some of these applications critically depends on the correctness of feature maps (i.e. whether feature maps are topologically ordered). An immediate question is how to quantitatively characterize how ‘good’ this pres- ervation actually is. If category information is available a priori, neighborhood violations in maps can be detected by visually inspecting the maps calibrated by the labeled data. That is, if a labeled map is too fragmented then the map is not topologically ordered. What if no category information is available? Can we measure the preservation of neighborhood relations? Various qualitative and quantitative methods for measuring the preservation or violation of neighborhood relations in feature maps have been proposed [4^10]. A number of different measures of neighborhood preservation in topographic mappings were overviewed in [11]. Each approach has its own considerations, merits, and limitations. In this paper we propose a novel measure to check whether a feature map is topologically ordered. An appealing property of this measure is that it is very straightforward and simple. The remaining of the paper is organized as follows. The next section presents the proposed measure for quantifying the neighborhood preservation of feature maps. Simulation results of two data sets are provided in the third section. The conclusions are given in the last section. Neural Processing Letters 15: 137^145, 2002. 137 # 2002 Kluwer Academic Publishers. Printed in the Netherlands.