A two-layer neural network is developed in which the neuron model computes a user-defined similarity function between inputs and weights. The neuron model is formed by the composition of an adapted logistic function with the mean of the partial input-weight similarities. The model is capable of dealing directly with variables of potentially different nature (continuous, ordinal, categorical); there is also provision for missing values. The network is trained using a fast two-stage procedure and involves the setting of only one parameter. In our experiments, the network achieves slightly superior performance on a set of challenging problems with respect to both RBF nets and RBF-kernel SVMs.