Exploring Different Paradigms to Extract Proper Implications From High Dimensional Formal Contexts

Abstract

Formal Concept Analysis (FCA) is an applied mathematical technique for data analysis, in which the relations between objects and attributes are identified. It introduces the notion of concepts and their hierarchical structure, from which we can obtain a set of implications between attributes that characterize a knowledge domain. The volume of information to be processed makes the use of FCA difficult in domains with a high number of dimensions, creating a demand for new solutions and algorithms for FCA applications. This article explores different approaches to extract proper implications from high dimensional contexts based on constraints to obtain the set of implications rules. We propose algorithms that use a data structure called Binary Decision Diagram (BDD) to represent the formal context, which reduces its size and, due to this, operates more efficiently. We also propose a heuristic to obtain proper implications by reducing the unnecessary generation of premises. In addition, we implemented a parallel computing model for generating and obtaining different implications. To analyze the proposed algorithms, we used different synthetic contexts with a varying number of objects, attributes, and density. The results obtained presented speed gains of up to 22 times when compared to the solutions proposed in the literature such as Impec and PropIm.

Keywords

• Formal concept analysis
• proper implications
• binary decision diagram