A novel Spatio-Temporal Fuzzy Inference System (SPATFIS) and its stability analysis

Modeling an online time series problem is often a challenging task because of the intrinsic dynamical characteristics of the underlying data distribution and the uncertainty stemming from the data. Hence, we propose a novel Spatio-Temporal Fuzzy Inference System (SPATFIS). One of the prime features of SPATFIS lies in the inclusion of memory type neurons which incorporates both spatial and temporal information of the sequences with a dual recurrent structure in its input and defuzzification layers. SPATFIS also proposes a new self-adaptive learning mechanism to add, eliminate and unify its fuzzy rules. This helps it to attain a parsimonious rule base. Furthermore, stability is rigorously inspected and SPATFIS is proved to be stable using Lyapunov's Input to State Stability theorem. The stability analysis encompasses both the structure and the parameter learning phases. To evaluate the efficacy of SPATFIS numerically, it is compared against state-of-the-art self-adaptive neuro-fuzzy systems with benchmark time series problems from the literature. We also evaluate SPATFS' performance under prequential First-Test-Then-Train protocol to show its suitability in handling data stream. The experimental results distinctly indicate SPATFIS to be significantly faster while retaining competitive accuracy and a compact rule base. A thorough statistical analysis is conducted afterwards to further affirm its advantages