Highly interpretable hierarchical deep rule-based classifier

Pioneering the traditional fuzzy rule-based (FRB) systems, deep rule-based (DRB) classifiers are able to offer both human-level performance and transparent system structure on image classification problems by integrating zero-order fuzzy rule base with a multi-layer image-processing architecture that is typical for deep learning. Nonetheless, it is frequently observed that the inner structure of DRB can become over sophisticated and not interpretable for humans when applied to large-scale, complex problems. To tackle the issue, one feasible solution is to construct a tree structural classification model by aggregating the possibly huge number of prototypes identified from data into a much smaller number of more descriptive and highly abstract ones. Therefore, in this paper, we present a novel hierarchical deep rule-based (H-DRB) approach that is capable of summarizing the less descriptive raw prototypes into highly generalized ones and self-arranging them into a hierarchical prototype-based structure according to their descriptive abilities. By doing so, H-DRB can offer high-level performance and, most importantly, full transparency and human-interpretability on various problems including large-scale ones. The proposed concept and generical principles are verified through numerical experiments based on a wide variety of popular benchmark image sets. Numerical results demonstrate that the promise of H-DRB

A multi-granularity locally optimal prototype-based approach for classification

Prototype-based approaches generally provide better explainability and are widely used for classification. However, the majority of them suffer from system obesity and lack transparency on complex problems. In this paper, a novel classification approach with a multi-layered system structure self-organized from data is proposed. This approach is able to identify local peaks of multi-modal density derived from static data and filter out more representative ones at multiple levels of granularity acting as prototypes. These prototypes are then optimized to their locally optimal positions in the data space and arranged in layers with meaningful dense links in-between to form pyramidal hierarchies based on the respective levels of granularity accordingly. After being primed offline, the constructed classification model is capable of self-developing continuously from streaming data to self-expend its knowledge base. The proposed approach offers higher transparency and is convenient for visualization thanks to the hierarchical nested architecture. Its system identification process is objective, data-driven and free from prior assumptions on data generation model with user- and problem- specific parameters. Its decision-making process follows the “nearest prototype” principle, and is highly explainable and traceable. Numerical examples on a wide range of benchmark problems demonstrate its high performance

Local optimality of self-organising neuro-fuzzy inference systems

Optimality of the premise, IF part is critical to a zero-order evolving intelligent system (EIS) because this part determines the validity of the learning results and overall system performance. Nonetheless, a systematic analysis of optimality has not been done yet in the state-of-the-art works. In this paper, we use the recently introduced self-organising neuro-fuzzy inference system (SONFIS) as an example of typical zero-order EISs and analyse the local optimality of its solutions. The optimality problem is firstly formulated in a mathematical form, and detailed optimality analysis is conducted. The conclusion is that SONFIS does not generate a locally optimal solution in its original form. Then, an optimisation method is proposed for SONFIS, which helps the system to attain local optimality in a few iterations using historical data. Numerical examples presented in this paper demonstrate the validity of the optimality analysis and the effectiveness of the proposed optimisation method. In addition, it is further verified numerically that the proposed concept and general principles can be applied to other types of zero-order EISs with similar operating mechanisms