Smoothing.

Smoothing by SOMs has been commonly used for treating the unit weights of discrete observation density HMMs [Monte, 1992,Zhao and Rowden, 1991,Kim et al., 1994]. Classical algorithms for the smoothing are the floor smoothing and the deleted interpolation [Rabiner, 1989,Rabiner et al., 1983,Jelinek and Mercer, 1980].

The adaptation of the neighborhood of the BMU in the self-organizing process offers a very natural way of smoothing the parameters by using additional samples falling nearby. So the group of units where a certain input will be mapped, if it is subject to some slight variation, are estimated by partly the same set of training samples ensuring the continuity of the PDF. The size of the neighborhood controls the amount of smoothing by affecting the extent of the overlap between the training samples falling for nearby units. The normal training concept of SOMs uses a large neighborhood in the beginning and gradually shrinks it as the training proceeds. This is well motivated by the smoothing point of view as well. Large neighborhood provides a high level of smoothing for every unit and then closer adaptation to the training data occurs in the areas well represented by the training data.