Adaptive FIR Neural Model for Centroid Learning in Self-Organizing Maps

In this paper, a training method for the formation of topology preserving maps is introduced. The proposed approach presents a sequential formulation of the self-organizing map (SOM), which is based on a new model of the neuron, or processing unit. Each neuron acts as a finite impulse response (FIR) system, and the coefficients of the filters are adaptively estimated during the sequential learning process, in order to minimize a distortion measure of the map. The proposed FIR-SOM model deals with static distributions and it computes an ordered set of centroids. Additionally, the FIR-SOM estimates the learning dynamic of each prototype using an adaptive FIR model. A noteworthy result is that the optimized coefficients of the FIR processes tend to represent a moving average filter, regardless of the underlying input distribution. The convergence of the resulting model is analyzed numerically and shows good properties with respect to the classic SOM and other unsupervised neural models. Finally, the optimal FIR coefficients are shown to be useful for visualizing the cluster densities.