An efficient algorithm for increasing the granularity levels of attributes in formal concept analysis

In the basic setting of formal concept analysis, a many-valued attribute needs to be replaced with several one-valued attributes. These one-valued attributes can be interpreted as a certain level of granularity of the corresponding many-valued attribute. In this paper, we explore theoretical relationships between concepts before and after increasing the granularity level of one attribute, based on which we introduce an efficient method of concept classification. Moreover, a new preprocessing routine is proposed to help generate new concepts and restore lattice order relation. These two procedures can considerably reduce the comparisons between sets, compared to the original Zoom-In algorithm. By employing these two procedures, we introduce an efficient algorithm, referred to as Unfold, to increase the granularity levels of attributes. The algorithm can perform a Zoom-In operation on a concept lattice associated with a coarser data granularity to obtain a new one that consists of finer formal concepts without building the new lattice from scratch. We describe the algorithm and present an experimental evaluation of its performance and comparison with another Zoom-In algorithm. Empirical analyses demonstrate that our algorithm is superior when applied to various types of datasets. (C) 2015 Elsevier Ltd. All rights reserved.