Regression problem; Representer theorem Fuzzy partition; p-d kernel; Machine learning

We contribute to the general theory of supervised machine learning by describing a feature extraction methodology using fuzzy partitions and their generative kernels. We explain how the Representer theorem applies to RKHS, whose kernel is related to a uniform fuzzy partition. We show that the connection with fuzzy modeling helps impart semantic meaning to the parameters defining a kernel-based regression model. We developed a neural network architecture that validates our theoretical results and solves the regression problem, including prediction. We describe all the steps of our method and demonstrate how to initialize the parameters of the corresponding neural network. This contributes to the explainability of the neural network design and execution.

We contribute to the general theory of supervised machine learning by describing a feature extraction methodology using fuzzy partitions and their generative kernels. We explain how the Representer theorem applies to RKHS, whose kernel is related to a uniform fuzzy partition. We show that the connection with fuzzy modeling helps impart semantic meaning to the parameters defining a kernel-based regression model. We developed a neural network architecture that validates our theoretical results and solves the regression problem, including prediction. We describe all the steps of our method and demonstrate how to initialize the parameters of the corresponding neural network. This contributes to the explainability of the neural network design and execution.