Compact Belief Rule Base Learning for Classification with Evidential Clustering †

The belief rule-based classification system (BRBCS) is a promising technique for addressing different types of uncertainty in complex classification problems, by introducing the belief function theory into the classical fuzzy rule-based classification system. However, in the BRBCS, high numbers of instances and features generally induce a belief rule base (BRB) with large size, which degrades the interpretability of the classification model for big data sets. In this paper, a BRB learning method based on the evidential C-means clustering (ECM) algorithm is proposed to efficiently design a compact belief rule-based classification system (CBRBCS). First, a supervised version of the ECM algorithm is designed by means of weighted product-space clustering to partition the training set with the goals of obtaining both good inter-cluster separability and inner-cluster pureness. Then, a systematic method is developed to construct belief rules based on the obtained credal partitions. Finally, an evidential partition entropy-based optimization procedure is designed to get a compact BRB with a better trade-off between accuracy and interpretability. The key benefit of the proposed CBRBCS is that it can provide a more interpretable classification model on the premise of comparative accuracy. Experiments based on synthetic and real data sets have been conducted to evaluate the classification accuracy and interpretability of the proposal.