Learning in the combinatorial neural model

The combinatorial neural model (CNM) is a type of fuzzy neural network for classification problems and, more generally, for the mapping between fuzzy multidimensional spaces. Learning in CNM is a complex task spanning the learning of input-neuron membership functions, of the network topology, and of connection weights. In this paper we are concerned with these various aspects of learning in CNM, most notably with the learning of connection weights, whose complexity comes from the existence of nondifferentiable, nonconvex error functions associated with the learning process. We introduce several algorithms for weight learning, most based on subgradient techniques borrowed from the field of nondifferentiable optimization. All algorithms are based on essentially "local" rules, and are therefore amenable to distributed/parallel implementations. Experimental results are provided on the large-scale problem of monitoring the deforestation of the Amazon region on satellite images. What these results indicate is that a hybrid CNM system outperforms previous results obtained with variations of error backpropagation techniques. In addition, this hybrid system has demonstrated robustness in the context under consideration, therefore constituting an attractive alternative.