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Multilayer Spline-based Fuzzy Neural Network with Deterministic Initialization

A multilayer spline-based fuzzy neural network (MS-FNN) is proposed. It is based on the concept of multilayer perceptron (MLP) with B-spline receptive field functions (Spline Net). In this paper, B-splines are considered in the framework of fuzzy set theory as membership functions such that the entire network can be represented in form of fuzzy rules. MS-FNN does not rely on tensor-product construction of basis functions. Instead, it is constructed as a multilayered superposition of univariate synaptic functions and thus avoids the curse of dimensionality similarly to MLP, yet with improved local properties. Additionally, a fully deterministic initialization procedure based on principal component analysis is proposed for MS-FNN, in contrast to the usual random initialization of multilayer networks. Excellent performance of MS-FNN with one and two hidden layers, different activation functions, and B-splines of different orders is demonstrated for time series prediction and classification problems.