Incremental missing data imputation via modified granular evolving fuzzy model

Abstract

Large amounts of data have been produced daily. Extracting information and knowledge from data is meaningful for many purposes and endeavors, such as prediction of future values of time series, classification, semi-supervised learning and control. Computational intelligence and machine learning methods, such as neural networks and fuzzy systems, usually require complete datasets to work properly. Real-world datasets may contain missing values due to, e.g., malfunctioning of sensors or data transfer problems. In online environments, the properties of the data may change over time so that offline model training based on multiple passes over data is prohibited due to its inherent time and memory constraints. This study proposes a method for incremental missing data imputation using a modified granular evolving fuzzy model, namely evolving Fuzzy Granular Predictor (eFGP). eFGP is equipped with an incremental learning algorithm that simultaneously impute missing data and adapt model parameters and structure. eFGP is able to handle single and multiple missing values on data samples by developing reduced-term consequent polynomials and relying on information of time-varying granules. The method is evaluated in prediction and function approximation problems considering the constraints of online data stream. Particularly, the underlying data streams may be subject to missing at random (MAR) and missing completely at random (MCAR) types of missing values. Predictions given by the model evolved after data imputation are compared to those provided by state-of-the-art fuzzy and neuro-fuzzy evolving modeling methods in the sense of accuracy. Results and statistical comparisons with other approaches corroborate to conclude that eFGP is competitive as a general evolving intelligent method and overcomes its counterparts in MAR and MCAR scenarios according to an ANOVA-Tukey statistical hypothesis test.