A Neighborhood Covering Classifier Based on Optimal Granularity of Fuzzy Quotient Space

Abstract

As one of rapidly developing methodology for dealing with complex problems in line with human cognition, granular computing has made significant achievements in knowledge discovery. Neighborhood classifier, as a typical description of granular computing (GrC), is an effective method for classification of continuous data. However, in the phase of constructing neighborhood rules, the existing neighborhood classifiers are divided into the following two modes and both have defects: (1) The strategy driven by center: There are a lot of overlap and inclusion among neighborhood rules, that is, it need to spend much time to reduce redundancy rules; (2) The strategy driven by rule: There are many rules containing only one object, which cannot form an effective covering, and would affect knowledge acquisition in the incremental environment. Therefore, in this paper, fuzzy quotient space theory is introduced to construct neighborhood rules. Based on optimal granularity of fuzzy quotient space, a neighborhood covering classifier, which has no redundant rules and could form the effective covering, is proposed without any artificial parameter. Second, comprehensively considering the knowledge purity and complexity, the quality measure of granularity is proposed, which guides the optimal granularity selection of HQSS. Third, neighborhood rules are constructed in the optimal granularity. Then, the offset of center is introduced to describe the membership degree of the test object to different neighborhood rules, and the neighborhood allocation strategy is proposed accordingly. Next, an algorithm for the neighborhood covering classifier based on these theories is proposed. Finally, experiments on 13 UCI datasets and 3 real datasets are carried out to verify the performance of the proposed classifier from four common classification indexes.