New Cluster Validation with Input-Output Causality for Context-Based Gk Fuzzy Clustering

In this paper, a cluster validity concept from an unsupervised to a supervised manner is presented. Most cluster validity criterions were established in an unsupervised manner, although many clustering methods performed in supervised and semi-supervised environments that used context information and performance results of the model. Context-based clustering methods can divide the input spaces using context-clustering information that generates an output space through an inputoutput causality. Furthermore, these methods generate and use the context membership function and partition matrix information. Additionally, supervised clustering learning can obtain superior performance results for clustering, such as in classification accuracy, and prediction error. A cluster validity concept that deals with the characteristics of cluster validities and performance results in a supervised manner is considered. To show the extended possibilities of the proposed concept, it demonstrates three simulations and results in a supervised manner and analyzes the characteristics. Keywords—Cluster Validation; Fuzzy clustering; GustafsonKessel clustering; Fuzzy covariance; Context based clustering; Input-output causality