Morphogenetic Approach to System Identification

In this paper, we propose a novel approach to system identification based on morphogenetic theory (MT). Given a context H defined by a set of M objects, each described by a set of N attributes, and a vector X of desired Outputs for each object, MT combines notions from formal concept analysis and tensor calculus SO as to generate a morphogenetic system (MS). The MS is defined by a set of weights S(1),...,S(N), one for each attribute. Given H and X, weights are computed so as to generate the projection Y of X oil the space of the attributes with the minimum distance between Y and X. An MS can be represented as a neuron, morphogenetic neuron, with it number of synapses equal to the number of attributes and synaptic weights equal to S(1),..., S(N). Unlike traditional neural network paradigm, which adopts ail iterative process to determine synaptic weights, in MT, weights are computed at once. We introduce a method to generate a morphogenetic neural network (MNN) for identification problems. The method is based oil extending appropriately and iteratively the attribute space so as to reduce the error between desired output and computed Output. By Using four well-known datasets, we show that ail MNN can identify ail unknown system with a precision comparable with classical multilayer perceptron with complexity similar to the MNN but reducing drastically the time needed to generate the neural network. Furthermore, the structure of the MNN is generated automatically by the method and does not require a trial-and-error approach often applied in classical neural networks.