A Topographic Product for the Optimization of Self-Organizing Feature Maps

Optimizing the performance of self-organizing feature maps like the Kohonen map involves the choice of the output space topology. We present a topographic product which measures the preservation of neighborhood relations as a criterion to optimize the output space topology of the map with regard to the global dimensionality DA as well as to the dimensions in the individual directions. We test the topographic product method not only on synthetic mapping examples, but also on speech data. In the latter application our method suggests an output space dimensionality of DA = 3, in coincidence with recent recognition results on the same data set.