NeuDen: A Framework for the Integration of Neuromorphic Evolving Spiking Neural Networks with Dynamic Evolving Neuro-Fuzzy Systems for Predictive and Explainable Modelling of Streaming Data

This paper introduces a novel framework, called here 'NeuDen' for the integration of neuromorphic evolving spiking neural networks (eSNN), that learn efficiently multiple time series in their temporal association and interaction, with dynamic evolving neuro-fuzzy systems (deNFS), that learn incrementally extracted from the eSNN feature vectors, to predict future time-series values and to produce interpretable fuzzy rules. The new framework aims to make the best out of the dominant features of the two types of models. First, spike-time-dependent plasticity (STDP) learning is used in SNN to learn temporal interaction between multiple time series, connected to a dynamic eSNN (deSNN) as a regressor/classifier. Then, feature-vectors are extracted from the trained deSNN for further learning, fuzzy inference and rule extraction in a deNFS, here exemplified by DENFIS, resulting in an accurate prediction results and explainable dynamic fuzzy rules. The NeuDen, framework and model, overcomes both the explainability problems of eSNN and the limitations of deNFS to model multiple streaming time series in their temporal interaction. NeuDen surpasses both deSNN and DENFIS by providing multiple regression models and achieving higher accuracy. NeuDen is demonstrated on bench mark data and on financial and economic time series, achieving from 3 to 100 times smaller RMSE when compared with other evolving systems. The proposed framework opens a new direction for the development of more efficient evolving systems by integrating eSNN with other methods, such as other neuro-fuzzy systems, deep neural networks and quantum classifiers for specific applications.