Knowledge Representation Using Formal Concept Analysis: A study on Concept Generation

Introduced by Rudolf Wille in the mid-80s, Formal Concept Analysis (FCA) is a mathematical framework that offers conceptual data analysis and knowledge discovery. FCA analyzes the data, which is represented in the form of a formal context, that describe the relationship between a particular set of objects and a particular set of attributes. From the formal context, FCA produces hierarchically ordered clusters called formal concepts and the basis of attribute dependencies, called attribute implications. All the concepts of a formal context form a hierarchical complete lattice structure called concept lattice that reflects the relationship of generalization and specialization among concepts. Several algorithms are proposed in the literature to extract the formal concepts from a given context. The objective of this chapter is to analyze, demonstrate, and compare a few standard algorithms that extract the formal concepts. For each algorithm, the analysis considers the functionality, output, complexity, delay time, exploration type, and data structures involved.

[1]  Claudio Carpineto,et al.  A Lattice Conceptual Clustering System and Its Application to Browsing Retrieval , 1996, Machine Learning.

[2]  Aswani Kumar Ch.  Mining Association Rules Using Non-Negative Matrix Factorization and Formal Concept Analysis , 2011 .

[3]  Partha Ghosh,et al.  Fuzzy graph representation of a fuzzy concept lattice , 2010, Fuzzy Sets Syst..

[4]  Ling Chen,et al.  A fast algorithm for generating concepts , 2008, 2008 International Conference on Information and Automation.

[5]  Derrick G. Kourie,et al.  AddIntent: A New Incremental Algorithm for Constructing Concept Lattices , 2004, ICFCA.

[6]  Uta Priss.  Formal concept analysis in information science , 2006 .

[7]  Robert M. Haralick,et al.  The Diclique Representation and Decomposition of Binary Relations , 1974, JACM.

[8]  Gerd Stumme,et al.  Formal Concept Analysis on Its Way from Mathematics to Computer Science , 2002, ICCS.

[9]  Vilém Vychodil,et al.  Formal Concept Analysis With Background Knowledge: Attribute Priorities , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[10]  Rudolf Wille,et al.  Formal Concept Analysis as Applied Lattice Theory , 2006, CLA.

[11]  G. D. Oosthuizen,et al.  Knowledge discovery in databases using lattices , 1997 .

[12]  K. Sumangali,et al.  Performance evaluation of employees of an organization using formal concept analysis , 2012, International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME-2012).

[13]  Takuo Suganuma,et al.  A Robust P2P Information Sharing System and its Application to Communication Support in Natural Disasters , 2013, Int. J. Softw. Sci. Comput. Intell..

[14]  Jinhai Li,et al.  Knowledge reduction in formal decision contexts based on an order-preserving mapping , 2012, Int. J. Gen. Syst..

[15]  Cherukuri Aswani Kumar,et al.  Designing role-based access control using formal concept analysis , 2013, Secur. Commun. Networks.

[16]  Gerd Stumme,et al.  Efficient Data Mining Based on Formal Concept Analysis , 2002, DEXA.

[17]  Prem Kumar Singh,et al.  A Method for Decomposition of Fuzzy Formal Context , 2012 .

[18]  Amedeo Napoli,et al.  Mining gene expression data with pattern structures in formal concept analysis , 2011, Inf. Sci..

[19]  Yee Leung,et al.  Granular Computing and Knowledge Reduction in Formal Contexts , 2009, IEEE Transactions on Knowledge and Data Engineering.

[20]  Ch. Aswani Kumar,et al.  MINING ASSOCIATIONS IN HEALTH CARE DATA USING FORMAL CONCEPT ANALYSIS AND SINGULAR VALUE DECOMPOSITION , 2010 .

[21]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[22]  Sergei O. Kuznetsov,et al.  Comparing performance of algorithms for generating concept lattices , 2002, J. Exp. Theor. Artif. Intell..

[23]  Rudolf Wille,et al.  The Basic Theorem on Preconcept Lattices , 2006, ICFCA.

[24]  Rokia Missaoui,et al.  A partition-based approach towards constructing Galois (concept) lattices , 2002, Discret. Math..

[25]  Octavian Iordache.  Formal Concept Analysis , 2011 .

[26]  Baris Sertkaya,et al.  On the Complexity of Computing Generators of Closed Sets , 2008, ICFCA.

[27]  Jean-François Boulicaut,et al.  Actionability and Formal Concepts: A Data Mining Perspective , 2008, ICFCA.

[28]  M. H. Margahny,et al.  FAST ALGORITHM FOR MINING ASSOCIATION RULES , 2014 .

[29]  Cherukuri Aswani Kumar,et al.  Knowledge discovery in data using formal concept analysis and random projections , 2011, Int. J. Appl. Math. Comput. Sci..

[30]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[31]  Gerd Stumme,et al.  Formal Concept Analysis , 2009, Handbook on Ontologies.

[32]  Vincenzo Loia,et al.  Hierarchical web resources retrieval by exploiting Fuzzy Formal Concept Analysis , 2012, Inf. Process. Manag..

[33]  Ch. Aswani Kumar,et al.  A Method for Reduction of Fuzzy Relation in Fuzzy Formal Context , 2012 .

[34]  Lhouari Nourine,et al.  A Fast Algorithm for Building Lattices , 1999, Inf. Process. Lett..

[35]  Xiao Zhang,et al.  On rule acquisition in decision formal contexts , 2013, Int. J. Mach. Learn. Cybern..

[36]  Jinhai Li,et al.  A heuristic knowledge-reduction method for decision formal contexts , 2011, Comput. Math. Appl..

[37]  L. John Old,et al.  Modelling Lexical Databases with Formal Concept Analysis , 2004, J. Univers. Comput. Sci..

[38]  Xindong Wu,et al.  Fundamentals of association rules in data mining and knowledge discovery , 2011, Wiley Interdiscip. Rev. Data Min. Knowl. Discov..

[39]  Ch. Aswanikumar,et al.  Concept lattice reduction using fuzzy K-Means clustering , 2010, Expert Syst. Appl..

[40]  武星.  Image File Storage System Resembling Human Memory , 2015 .

[41]  Gerd Stumme,et al.  Conceptual Knowledge Discovery in Databases Using Formal Concept Analysis Methods , 1998, PKDD.

[42]  Radim Belohlávek,et al.  Formal concept analysis with hierarchically ordered attributes , 2004, Int. J. Gen. Syst..

[43]  Rokia Missaoui,et al.  An Incremental Concept Formation Approach for Learning from Databases , 1994, Theor. Comput. Sci..

[44]  Qiang Hua,et al.  The Formal Concept Analysis of the Documents Clusters , 2007, 2007 International Conference on Machine Learning and Cybernetics.

[45]  Chengming Qi,et al.  Incremental Formation Algorithm Based on Concept Semilattice , 2008, 2008 International Symposium on Computational Intelligence and Design.

[46]  Alexey Neznanov,et al.  Comparing and analyzing the computational complexity of FCA algorithms , 2010, SAICSIT '10.

[47]  N. J. Davies,et al.  Concept Lattices for Knowledge Management , 1999 .

[48]  Yves Bastide,et al.  Intelligent Structuring and Reducing of Association Rules with Formal Concept Analysis , 2001, KI/ÖGAI.

[49]  Anne Berry,et al.  A local approach to concept generation , 2007, Annals of Mathematics and Artificial Intelligence.

[50]  Gerd Stumme,et al.  Computing iceberg concept lattices with T , 2002, Data Knowl. Eng..

[51]  Sérgio M. Dias,et al.  Applying the JBOS reduction method for relevant knowledge extraction , 2013, Expert Syst. Appl..

[52]  Jinhai Li,et al.  Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction , 2013, Int. J. Approx. Reason..

[53]  Xiao Zhang,et al.  Multi-confidence rule acquisition oriented attribute reduction of covering decision systems via combinatorial optimization , 2013, Knowl. Based Syst..

[54]  Jonas Poelmans,et al.  Formal Concept Analysis in Knowledge Discovery: A Survey , 2010, ICCS.

[55]  Cherukuri Aswani Kumar,et al.  Interval-valued fuzzy graph representation of concept lattice , 2012, 2012 12th International Conference on Intelligent Systems Design and Applications (ISDA).

[56]  Vilém Vychodil,et al.  Replacing full rectangles by dense rectangles: concept lattices and attribute implications , 2006, 2006 IEEE International Conference on Information Reuse & Integration.

[57]  Amedeo Napoli,et al.  Using Formal Concept Analysis for Discovering Knowledge Patterns , 2010, CLA.

[58]  Vilém Vychodil,et al.  Advances in Algorithms Based on CbO , 2010, CLA.

[59]  Ch. Aswani Kumar,et al.  Analysis of a Vector Space Model, Latent Semantic Indexing and Formal Concept Analysis for Information Retrieval , 2012 .

[60]  Gerd Stumme,et al.  Formal Concept Analysis: foundations and applications , 2005 .

[61]  Rudolf Wille,et al.  Why can concept lattices support knowledge discovery in databases? , 2002, J. Exp. Theor. Artif. Intell..

[62]  Jinhai Li,et al.  Knowledge reduction in decision formal contexts , 2011, Knowl. Based Syst..

[63]  Simon Polovina,et al.  Conceptual Structures: Knowledge Architectures for Smart Applications, 15th International Conference on Conceptual Structures, ICCS 2007, Sheffield, UK, July 22-27, 2007, Proceedings , 2007, ICCS.

[64]  Dipak Laha,et al.  Handbook of Computational Intelligence in Manufacturing and Production Management , 2007 .

[65]  Cherukuri Aswani Kumar,et al.  FUZZY CLUSTERING-BASED FORMAL CONCEPT ANALYSIS FOR ASSOCIATION RULES MINING , 2012, Appl. Artif. Intell..

[66]  Jitender S. Deogun,et al.  Monotone concepts for formal concept analysis , 2004, Discret. Appl. Math..

[67]  Eric Bouillet,et al.  Semantic Matching, Propagation and Transformation for Composition in Component-Based Systems , 2009, Int. J. Softw. Sci. Comput. Intell..

[68]  Anne Berry,et al.  Generating All the Minimal Separators of a Graph , 2000, Int. J. Found. Comput. Sci..

[69]  Rokia Missaoui,et al.  Generating frequent itemsets incrementally: two novel approaches based on Galois lattice theory , 2002, J. Exp. Theor. Artif. Intell..

[70]  Olegas Vasilecas,et al.  Formal Concept Analysis for Concept Collecting and Their Analysis , 2009 .

[71]  Supriyo Roy,et al.  Computational Intelligence Approach on a Deterministic Production-Inventory Control Model with Shortages , 2008 .

[72]  Sergei O. Kuznetsov,et al.  Machine Learning and Formal Concept Analysis , 2004, ICFCA.

[73]  Rokia Missaoui,et al.  Formal Concept Analysis for Knowledge Discovery and Data Mining: The New Challenges , 2004, ICFCA.