ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram †

Abstract

Formal concept analysis (FCA) is largely applied in different areas. However, in some FCA applications the volume of information that needs to be processed can become unfeasible. Thus, the demand for new approaches and algorithms that enable processing large amounts of information is increasing substantially. This article presents a new algorithm for extracting proper implications from high-dimensional contexts. The proposed algorithm, called ImplicPBDD, was based on the PropIm algorithm, and uses a data structure called binary decision diagram (BDD) to simplify the representation of the formal context and enhance the extraction of proper implications. In order to analyze the performance of the ImplicPBDD algorithm, we performed tests using synthetic contexts varying the number of objects, attributes and context density. The experiments show that ImplicPBDD has a better performance—up to 80% faster—than its original algorithm, regardless of the number of attributes, objects and densities.

An open computing language‐based parallel Brute Force algorithm for formal concept analysis on heterogeneous architectures

“…The search for algorithms for FCA which can process high‐dimensional contexts has been the main focus of research in last years. For instance, the ImplicPBDD 24 algorithm is a variant of the PropIm algorithm, but it uses a Binary Decision Diagram (BDD) structure. It aims to deal with the high dimensionality, simplifying the data structure of the formal context with a BDD.…”

Arquitetura Heterogênea CPU+FPGA para Análise Formal de Conceitos

“…A pesquisa de novos algoritmos para aárea de FCA que alcançam um processamento com alta dimensionalidade aindaé o grande foco. No trabalho apresentado por [Santos et al 2018],é desenvolvido um novo algoritmo para contextos de alta dimensionalidade, cujo nomeé descrito por ImplicPBDD (baseado no algoritmo PropIm) que utiliza uma estrutura BDD, sendo esta uma estrutura simplificada de representação do contexto formal para aprimorar a extração de conhecimento. No trabalho apresentado,é criada uma base sintética com variações de dimensão e objetos, obtendo um desempenho de 80% a mais que o seu antecessor, ao avaliar a eficiência do algoritmo.…”