ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup>
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 subs...
Main Authors: | , , , , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2018-10-01
|
Series: | Information |
Subjects: | |
Online Access: | https://www.mdpi.com/2078-2489/9/11/266 |
id |
doaj-b103b775e4b14c75b41e815eb546ac0d |
---|---|
record_format |
Article |
spelling |
doaj-b103b775e4b14c75b41e815eb546ac0d2020-11-24T21:45:45ZengMDPI AGInformation2078-24892018-10-0191126610.3390/info9110266info9110266ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup>Phillip G. Santos0Pedro Henrique B. Ruas1Julio C. V. Neves2Paula R. Silva3Sérgio M. Dias4Luis E. Zárate5Mark A. J. Song6Department of Computer Science, Pontifical Catholic University of Minas Gerais (PUC Minas), Belo Horizonte 31980-110, BrazilDepartment of Computer Science, Pontifical Catholic University of Minas Gerais (PUC Minas), Belo Horizonte 31980-110, BrazilDepartment of Computer Science, Pontifical Catholic University of Minas Gerais (PUC Minas), Belo Horizonte 31980-110, BrazilLaboratory of Artificial Intelligence and Decision Support (LIAAD), INESC TEC, Porto 4200-465, PortugalDepartment of Computer Science, Pontifical Catholic University of Minas Gerais (PUC Minas), Belo Horizonte 31980-110, BrazilDepartment of Computer Science, Pontifical Catholic University of Minas Gerais (PUC Minas), Belo Horizonte 31980-110, BrazilDepartment of Computer Science, Pontifical Catholic University of Minas Gerais (PUC Minas), Belo Horizonte 31980-110, BrazilFormal 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.https://www.mdpi.com/2078-2489/9/11/266formal concept analysisproper implicationbinary decision diagram |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Phillip G. Santos Pedro Henrique B. Ruas Julio C. V. Neves Paula R. Silva Sérgio M. Dias Luis E. Zárate Mark A. J. Song |
spellingShingle |
Phillip G. Santos Pedro Henrique B. Ruas Julio C. V. Neves Paula R. Silva Sérgio M. Dias Luis E. Zárate Mark A. J. Song ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup> Information formal concept analysis proper implication binary decision diagram |
author_facet |
Phillip G. Santos Pedro Henrique B. Ruas Julio C. V. Neves Paula R. Silva Sérgio M. Dias Luis E. Zárate Mark A. J. Song |
author_sort |
Phillip G. Santos |
title |
ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup> |
title_short |
ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup> |
title_full |
ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup> |
title_fullStr |
ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup> |
title_full_unstemmed |
ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram <sup>†</sup> |
title_sort |
implicpbdd: a new approach to extract proper implications set from high-dimension formal contexts using a binary decision diagram <sup>†</sup> |
publisher |
MDPI AG |
series |
Information |
issn |
2078-2489 |
publishDate |
2018-10-01 |
description |
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. |
topic |
formal concept analysis proper implication binary decision diagram |
url |
https://www.mdpi.com/2078-2489/9/11/266 |
work_keys_str_mv |
AT phillipgsantos implicpbddanewapproachtoextractproperimplicationssetfromhighdimensionformalcontextsusingabinarydecisiondiagramsupsup AT pedrohenriquebruas implicpbddanewapproachtoextractproperimplicationssetfromhighdimensionformalcontextsusingabinarydecisiondiagramsupsup AT juliocvneves implicpbddanewapproachtoextractproperimplicationssetfromhighdimensionformalcontextsusingabinarydecisiondiagramsupsup AT paularsilva implicpbddanewapproachtoextractproperimplicationssetfromhighdimensionformalcontextsusingabinarydecisiondiagramsupsup AT sergiomdias implicpbddanewapproachtoextractproperimplicationssetfromhighdimensionformalcontextsusingabinarydecisiondiagramsupsup AT luisezarate implicpbddanewapproachtoextractproperimplicationssetfromhighdimensionformalcontextsusingabinarydecisiondiagramsupsup AT markajsong implicpbddanewapproachtoextractproperimplicationssetfromhighdimensionformalcontextsusingabinarydecisiondiagramsupsup |
_version_ |
1725904405898723328 |