Kalman Filter Implementation of Self-Organizing Feature Maps

Abstract

The self-organizing learning algorithm of Kohonen and most of its extensions are controlled by two learning parameters, the learning coefficient and the width of the neighborhood function, which have to be chosen empirically because neither rules nor methods for their calculation exist. Consequently, often time-consuming parameter studies precede neighborhood-preserving feature maps of the learning data. To circumvent those lengthy numerical studies, this article describes the learning process by a state-space model in order to use the linear Kalman filter algorithm training the feature maps. Then the Kalman filter equations calculate the learning coefficient online during the training, while the width of the neighborhood function needs to be estimated by a second extended Kalman filter for the process of neighborhood preservation. The performance of the Kalman filter implementation is demonstrated on toy problems as well as on a crab classification problem. The results of crab classification are compared to those of generative topographic mapping, an alternative method to the self-organizing feature map.