Multiobjective Evolutionary Optimisation for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification, while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimise the training error of the models on historical training data or alternatively, to iteratively minimise the intra-cluster variance of the clusters obtained via online data partitioning. This recognises the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimising the training error may potentially lead to overfitting, whilst minimising the intra-cluster variance does not necessarily ensure the optimised prototype-based models to attain improved classification outcomes. To achieve better classification performance whilst avoiding overfitting for zero-order EISs, this paper presents a novel multi-objective optimisation approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final non-dominated set of the resulting optimised models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimisation approach in improving the classification performance of zero-order EISs.