Fuzzy Ordered $c$-Means Clustering and Least Angle Regression for Fuzzy Rule-Based Classifier: Study for Imbalanced Data

This article introduces a new classifier design method that is based on a modification of the traditional fuzzy clustering. First, a new fuzzy ordered c-means clustering is proposed. This method can be considered as a generalization of the concept of the conditional fuzzy clustering by introducing ordering and weighting distances from data to cluster prototypes. As a result, a more local impact of data on created groups and increased repulsive force between group prototypes are obtained. The proposed method provides a better representation of the data classes, in particular for classes with small cardinality in the training set (imbalanced data). A special initialization of the prototypes is also introduced. Next, the proposed clustering method is used to construct the premises of if-then rules of a fuzzy classifier. The conclusions of the rules are obtained by the least angle regression algorithm, which selects only those rules, that maximize the generalization ability of a classifier. Each if-then rule is represented in easily interpretable Mamdani-Assilian form. Finally, an extensive experimental analysis on 89 benchmark balanced and imbalanced datasets is performed to demonstrate the validity of the introduced classifier. Its competitiveness to state-of-the-art classifiers, with respect to both performance and interpretability, is shown as well.