Unification of Complementary Feature Map Models

Selforganizing feature maps serve as models for the organization of primary sensory areas and have many applications in technical pattern recognition. In most models the evolution of receptive field centers w : X → Ω is driven by the excitation ew(υ) in the neuronal tissue: ẇ =< (υ - w)ew(υ) >, where < … >, denotes the average over the stimulus distribution P(υ). The models differ, however, in the way ew(υ) is determined. In the Kohonen model [1] a hard competition for the stimulus takes place and the excitation then spreads into the neighborhood of the winning neuron. This very effcient algorithm, however, generates only simple network excitations, which is biologically unrealistic. Complementary to that, the elastic net algorithm [2] uses a neighborhood in input space. Here, however, the”elastic” neuronal interaction has no obvious biological interpretation. In this contribution we present a model unifying both approaches. The elastic net and the Kohonen model turn out to be asymptotic cases of this convolution model. For the elastic net we obtain the elasticity parameter β directly from a small, but finite neighborhood range in the neuronal layer.