Supervised and Unsupervised Information Granulation

In this study, we are concerned with information granulation realized both in supervised and unsupervised mode. Our focus is on the exploitation of the technology of hyperboxes and fuzzy sets as a fundamental conceptual vehicle of information granulation. In case of supervised learning (classification), each class is described by one or more fuzzy hyperboxes defined by their corresponding minimumand maximum vertices and the corresponding hyperbox membership function. Two types of hyperboxes are formed, namely inclusion hyperboxes that contain input patterns belonging to the same class, and exclusion hyperboxes that contain patterns belonging to two or more classes, thus representing contentious areas of the pattern space. With these two types of hyperboxes each class fuzzy set is represented as a union of inclusion hyperboxes of the same class minus a union of exclusion hyperboxes. The subtraction of sets provides for efficient representation of complex topologies of pattern classes without resorting to a large number of small hyperboxes to describe each class. The proposed fuzzy hyperbox classification is compared to the original Min-Max Neural Network and the General Fuzzy Min-Max Neural Network and the origins of the improved performance of the proposed classification are identified. When it comes to the unsupervised mode of learning, we revisit a well-known method of Fuzzy C-Means (FCM) by incorporating Tchebyschev distance using which we naturally form hyperbox-like prototypes. The design of hyperbox information granules is presented and the constructs formed in this manner are evaluated with respect to their abilities to capture the structure of data.