Skip to main content
Top

2018 | OriginalPaper | Chapter

Bounding Stability in Formal Concept Analysis

Authors : Bikram P. Bhuyan, Arindam Karmakar, Shyamanta M. Hazarika

Published in: Advanced Computational and Communication Paradigms

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In Formal Concept Analysis, stability is an important utility measure to rank concepts. However, computation of stability is considered to be a hard problem. Efficient algorithms having good bounds to estimate stability holds promise. In this paper, an effective graph-based technique is proposed to estimate stability. Our estimation algorithm has a polynomial time complexity of \(O({|A|^2})\) where |A| is the number of vertices.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Belohlavek, R., Trnecka, M.: Basic Level in Formal Concept Analysis: Interesting Concepts and Psychological Ramifications. In IJCAI, pp. 1233–1239, June, 2013 Belohlavek, R., Trnecka, M.: Basic Level in Formal Concept Analysis: Interesting Concepts and Psychological Ramifications. In IJCAI, pp. 1233–1239, June, 2013
2.
go back to reference Wille, R.: Formal concept analysis as mathematical theory of concepts and concept hierarchies. Formal Concept Anal. 3626, 1–33 (2005)MATH Wille, R.: Formal concept analysis as mathematical theory of concepts and concept hierarchies. Formal Concept Anal. 3626, 1–33 (2005)MATH
3.
go back to reference Carpineto, C., Romano, G.: Concept Data Analysis: Theory and Applications. Wiley (2004)CrossRef Carpineto, C., Romano, G.: Concept Data Analysis: Theory and Applications. Wiley (2004)CrossRef
4.
5.
go back to reference Kuzuetsov, S.O.: Stability as an Estimate of thie Degree of Substantiation of Hypotheses Derived on the Basis of Operational, Similarity (1990) Kuzuetsov, S.O.: Stability as an Estimate of thie Degree of Substantiation of Hypotheses Derived on the Basis of Operational, Similarity (1990)
7.
go back to reference Roth, C., Obiedkov, S., Kourie, D.G.: On succinct representation of knowledge community taxonomies with formal concept analysis. Int. J. Found. Comput. Sci. 19(02), 383–404 (2008)MathSciNetCrossRef Roth, C., Obiedkov, S., Kourie, D.G.: On succinct representation of knowledge community taxonomies with formal concept analysis. Int. J. Found. Comput. Sci. 19(02), 383–404 (2008)MathSciNetCrossRef
8.
go back to reference Buzmakov, A., Kuznetsov, S.O., Napoli, A.: Is concept stability a measure for pattern selection? Procedia Comput. Sci. 31, 918–927 (2014)CrossRef Buzmakov, A., Kuznetsov, S.O., Napoli, A.: Is concept stability a measure for pattern selection? Procedia Comput. Sci. 31, 918–927 (2014)CrossRef
9.
go back to reference Babin, M., Kuznetsov, S.: Approximating concept stability. Form. Concept Anal. 7–15 (2012) Babin, M., Kuznetsov, S.: Approximating concept stability. Form. Concept Anal. 7–15 (2012)
10.
go back to reference Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets, pp. 445–470. Springer, Netherlands (1982)CrossRef Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets, pp. 445–470. Springer, Netherlands (1982)CrossRef
11.
go back to reference Wolff, K.E.: A first course in formal concept analysis. StatSoft 93, 429–438 (1993) Wolff, K.E.: A first course in formal concept analysis. StatSoft 93, 429–438 (1993)
12.
go back to reference Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer Science & Business Media (2012) Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer Science & Business Media (2012)
13.
go back to reference Roth, C., Obiedkov, S., Kourie, D.: Towards concise representation for taxonomies of epistemic communities. Lect. Notes Comput. Sci. 4923, 240–255 (2008)CrossRef Roth, C., Obiedkov, S., Kourie, D.: Towards concise representation for taxonomies of epistemic communities. Lect. Notes Comput. Sci. 4923, 240–255 (2008)CrossRef
14.
go back to reference Zhi, H.L.: On the calculation of formal concept stability. J. Appl. Math. (2014) Zhi, H.L.: On the calculation of formal concept stability. J. Appl. Math. (2014)
16.
go back to reference Hopcroft, J., Tarjan, R.: Efficient algorithms for graph manipulation (No. STAN-CS-71-207). Department of Computer Science, Stanford University, California (1971) Hopcroft, J., Tarjan, R.: Efficient algorithms for graph manipulation (No. STAN-CS-71-207). Department of Computer Science, Stanford University, California (1971)
17.
18.
go back to reference Nikiforov, V.: Some inequalities for the largest eigenvalue of a graph. Comb. Probab. Comput. 11(2), 179–189 (2002)MathSciNetCrossRef Nikiforov, V.: Some inequalities for the largest eigenvalue of a graph. Comb. Probab. Comput. 11(2), 179–189 (2002)MathSciNetCrossRef
19.
go back to reference Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14(2–3), 189–216 (2002)CrossRef Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14(2–3), 189–216 (2002)CrossRef
20.
go back to reference Wille, R.: Concept lattices and conceptual knowledge systems. Comput. Math. Appl. 23(6–9), 493–515 (1992)CrossRef Wille, R.: Concept lattices and conceptual knowledge systems. Comput. Math. Appl. 23(6–9), 493–515 (1992)CrossRef
Metadata
Title
Bounding Stability in Formal Concept Analysis
Authors
Bikram P. Bhuyan
Arindam Karmakar
Shyamanta M. Hazarika
Copyright Year
2018
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-8237-5_53