On the Use of Modular Indistinguishability Operators in RBFNN-Like Models

Radial Basis Function Neural Networks (RBFNN) have become popular machine learning models with a simple structure but at the same time strong non-linear function approximation and effective modeling capabilities. In this work, we explore the use of Modular Indistinguishability Operators (MIO) in RBFNN-like structures to replace the RBFs that populate the hidden layer, to give rise to MIO-based Neural Networks (MIO-NN). In this respect, we introduce a new distance function and prove that it is a modular metric, to next use it to derive two MIOs to be evaluated as the key component of MIO-NNs. As an additional contribution, we describe Self-Defining MIO-NN (SD-MIO-NN) as an approach capable of configuring MIO-NNs in a parameterless way. SD-MIO-NN comprises a first step that defines the size of the hidden layer, a second step that determines the parameters of the hidden neurons and a last step that calculates the weights of the hidden-to-output layer connections. The experimental results show the effectiveness of the proposed MIOs for multi-class classification, and by extension of SD-MIO-NN, which in turn compares well with other similar solutions.