Fuzzy system approaches for data streams and functional data regression

With the arrival of the data explosion era, data modelling/prediction has become one of the most important research areas. Many datasets in our real-life are essentially data streams and functional data. This thesis investigates fuzzy system-based regression approaches for these two representative datasets. In line with the data types, this thesis is divided into two scenarios. The first part focuses on the data stream regression problem with input/output being real vectors. It is widely known that evolving fuzzy systems (EFSs) are effective approaches for solving data stream regression problems, in that EFSs are structurally self-organized, capable of updating structure/parameters in an online manner, and acting as the one-pass approaches without the requirement of storing historical data. However, current state-of-the-art studies indicate that the existing evolving structure/parameters approaches would impose a negative impact on the optimality of EFSs. To our best knowledge, research on proposing optimal EFSs was still rare. Furthermore, selecting predefined thresholds to control the structure/parameters evolution of EFSs is of importance, which has not been systematically investigated thus far. In this part, this thesis focuses on addressing the aforementioned two EFSs-related problems, which might provide implications for the research on the data stream. From an optimality viewpoint, EFS learning approaches for both Takagi-Sugeno and Mamdani fuzzy systems, that is, local error optimization approach (LEOA) and identifying evolving Mamdani fuzzy systems from the parameter optimization aspect (EMFSPO), are proposed. To automatically tuning the thresholds, two approaches, i.e. the self-evolving fuzzy system (SEFS), and an extended work based on SEFS, that is, EFS with self-learning/adaptive thresholds (EFS-SLAT), are proposed. Finally, through a wide range of benchmark examples, LEOA, EMFSPO, SEFS, and EFS-SLAT are shown to be capable of improving the accuracy compared with many state-of-the-art approaches. The second part of this thesis focuses on the functional data regression problem, where inputs/outputs are functions. Current techniques for functional data regression are mainly statistical models with certain assumptions and restrictions for a specific model. Since the kernel functions should be used in integral in these approaches, the resulting models were lack of interpretability and difficult to understand especially for the nonlinear case. More importantly, they were mainly offline models, which were not suitable to handle big functional data/functional streaming data considering the computational cost for storing a vast of historical information during model analysis. To improve these weaknesses, a pioneering functional regression approach, i.e. the functional fuzzy system (FFS), is developed. It acts as an operator between two functional spaces. FFS is an offline nonlinear regression model enabling its inputs/outputs to be functions. It has a flexible structure that can explain any nonlinear relationship between functions using an interpretable ``If-Then" fuzzy inference. In order to make the model applicable, the corresponding learning approach is proposed for identifying FFS. Since FFS is an offline model, it is not suitable for big functional datasets and functional streaming data. To overcome such bottlenecks, the first functional real-time regression model known as evolving functional fuzzy system (EFFS) is developed. EFFS is endowed with an exceptional advantage of learning from data online in addition to inheriting all the superior characteristics of FFS. EFFS provides a potential approach for handling big functional data by processing functional streaming data with each data point being a function. Finally, it demonstrates that FFS and EFFS outperform many of the state-of-the-art approaches through comparison experiments on various benchmark examples. These numerical results verify the effectiveness of FFS and EFFS.