Several neural networks have been proposed in the general literature for pattern recognition and clustering, but little empirical comparison with traditional methods has been done. The results reported here compare neural networks using Kohonen learning with a traditional clustering method (K-means) in an experimental design using simulated data with known cluster solutions. Two types of neural networks were examined, both of which used unsupervised learning to perform the clustering. One used Kohonen learning with a conscience and the other used Kohonen learning without a conscience mechanism. The performance of these nets was examined with respect to changes in the number of attributes, the number of clusters, and the amount of error in the data. Generally, the K-means procedure had fewer points misclassified while the classification accuracy of neural networks worsened as the number of clusters in the data increased from two to five.

Kohonen self-organizing interval maps are considered. In this model a linear graph is embedded randomly into the unit interval. At each time a point is chosen randomly according to a fixed distribution. The nearest vertex and some of its nearby neighbors are moved closer to the point. These models have been proposed as models of learning in the audio-cortex. The models possess not only the structure of a Markov chain, but also the added structure of a random dynamical system. This structure is used to show that for a large class of these models, in a strong way, the initial conditions are unimportant and only the dynamics govern the future. A contractive condition is proven in spite of the fact that the maps are not continuous. This, in turn, shows that the Markov chain is uniformly ergodic.