Incremental Missing-Data Imputation for Evolving Fuzzy Granular Prediction

Missing values are common in real-world data stream applications. This article proposes a modified evolving granular fuzzy-rule-based model for function approximation and time-series prediction in an online context, where values may be missing. The fuzzy model is equipped with an incremental learning algorithm that simultaneously imputes missing data and adapts model parameters and structure over time. The evolving fuzzy granular predictor (eFGP) handles single and multiple missing values on data samples by developing reduced-term consequent polynomials and utilizing time-varying granules. Missing at random (MAR) and missing completely at random (MCAR) values in nonstationary data streams are approached. Experiments to predict monthly weather conditions, the number of bikes hired on a daily basis, and the sound pressure on an airfoil from incomplete data streams show the usefulness of eFGP models. Results were compared with those of state-of-the-art fuzzy and neuro-fuzzy evolving modeling methods. A statistical hypothesis test shows that eFGP outperforms other evolving intelligent methods in online MAR and MCAR settings, regardless of the application.