Learning disjunctive concepts based on fuzzy semantic cell models through principles of justifiable granularity and maximum fuzzy entropy

摘要

Concept modeling and learning is an important topic of machine learning, data mining and knowledge discovery. The main aim of this paper is to explore the learning issue of compound concepts. More precisely, we put forward a novel method for modeling and learning the disjunction of basic concepts based on fuzzy semantic cell models, where each fuzzy semantic cell model is the smallest unit of concepts which is mathematically formalized by a prototype P, a distance function d and a probability density function δ. We introduce two fundamental numeric characteristics, expectation granularity G and fuzzy entropy F, to characterize the abstractness and the vagueness of the underlying disjunctive concept respectively. Then an unsupervised learning strategy for the disjunctive concept is introduced by using the principles of justifiable granularity and maximum fuzzy entropy. The ultimate goal is to derive a disjunctive concept from a given data set which is the most appropriate to describe the data set. Furthermore, we develop an iterative algorithm to solve this learning problem and also provide a detailed convergence analysis for this algorithm. Finally, the proposed method is tested on both synthetic data and publicly available data to demonstrate the performance and some potential applications of this method.