Takagi-Sugeno-Kang Fuzzy Clustering by Direct Fuzzy Inference on Fuzzy Rules

Takagi-Sugeno-Kang (TSK) fuzzy inference has been widely used in approximating uncertain nonlinear systems because of its high interpretability and precision. However, TSK fuzzy inference models are usually constructed on data in a supervised manner for classification and regression problems. As the first attempt, a novel Takagi-Sugeno-Kang fuzzy clustering (TSK-FC) method from the perspective of unsupervised learning is presented in this paper. The distinctive characteristic of TSK-FC lies in that it groups data points into different clusters directly by fuzzy inference on the TSK fuzzy rules. Therefore, the comprehensibility of the clustering procedure and clustering results of TSK-FC can be obtained. Specifically, all input features in TSK-FC on the IF-parts of all fuzzy rules are randomly assigned with interpretable linguistic terms, which ensures the interpretability of TSK-FC. In addition, TSK-FC explores the potential clusters in data patterns by iteratively updating K consequent parameter vectors of all fuzzy rules in an unsupervised manner, which can represent the K obtained clusters. Particularly, all data points from the same cluster will be as close as possible to the cluster center, and as far as possible from the other cluster centers in the iterative update procedure. Moreover, the optimization problem of TSK-FC can be transformed into a standard difference of convex functions using the concave-convex procedure (CCCP), which can be easily solved by introducing an iterative algorithm. Experimental results on synthetic and benchmark datasets as well as four case studies validate the effectiveness of the proposed fuzzy rule-based TSK-FC. The statistical results on all experiments indicate the feasibility of TSK-FC as a clustering tool.