Lattice algebra approach to single-neuron computation

Recent advances in the biophysics of computation and neurocomputing models have brought to the foreground the importance of dendritic structures in a single neuron cell. Dendritic structures are now viewed as the primary autonomous computational units capable of realizing logical operations. By changing the classic simplified model of a single neuron with a more realistic one that incorporates the dendritic processes, a novel paradigm in artificial neural networks is being established. In this work, we introduce and develop a mathematical model of dendrite computation in a morphological neuron based on lattice algebra. The computational capabilities of this enriched neuron model are demonstrated by means of several illustrative examples and by proving that any single layer morphological perceptron endowed with dendrites and their corresponding input and output synaptic processes is able to approximate any compact region in higher dimensional Euclidean space to within any desired degree of accuracy. Based on this result, we describe a training algorithm for single layer morphological perceptrons and apply it to some well-known nonlinear problems in order to exhibit its performance.