A comprehensive overview on the foundations of formal concept analysis

The immersion of voluminous collection of data is inevitable almost everywhere. The invention of mathematical models to analyse the patterns and trends of the data is an emerging necessity to extract and predict useful information in any Knowledge Discovery from Data (KDD) process. The Formal Concept Analysis (FCA) is an efficient mathematical model used in the process of KDD which is specially designed to portray the structure of the data in a context and depict the underlying patterns and hierarchies in it. Due to the huge increase in the application of FCA in various fields, the number of research and review articles on FCA has raised to a large extent. This review differs from the existing ones in presenting the comprehensive survey on the fundamentals of FCA in a compact and crisp manner to benefit the beginners and its focuses on the scalability issues in FCA. Further, we present the generic anatomy of FCA apart from its origin and growth at a primary level.  https://doi.org/10.34105/j.kmel.2017.09.032

[1]  P. Burmeister Formal concept analysis with ConImp : introduction to the basic features , 2003 .

[2]  Stephen J. H. Yang,et al.  Web content adaptation for mobile device: A fuzzy-based approach , 2012 .

[3]  Isabelle Bloch,et al.  Explanatory Reasoning for Image Understanding Using Formal Concept Analysis and Description Logics , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[4]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[5]  Guoyin Wang,et al.  Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts , 2016, Knowl. Based Syst..

[6]  T. Bosch Using online social networking for teaching and learning: Facebook use at the University of Cape Town , 2009 .

[7]  Vincent Duquenne,et al.  Latticial Structures in Data Analysis , 1999, Theor. Comput. Sci..

[8]  Hernán Astudillo,et al.  Cheating to achieve Formal Concept Analysis over a Large Formal Context , 2011, CLA.

[9]  Douglas R. Vogel,et al.  Complexity Reduction in Lattice-Based Information Retrieval , 2005, Information Retrieval.

[10]  Nathalie Pernelle,et al.  ZooM: a nested Galois lattices-based system for conceptual clustering , 2002, J. Exp. Theor. Artif. Intell..

[11]  G. Grosseck,et al.  Dear teacher, what should I write on my wall? A case study on academic uses of Facebook , 2011 .

[12]  Claudio Carpineto,et al.  Concept data analysis - theory and applications , 2004 .

[13]  Mirko Čubrilo,et al.  Formal concept analysis in F-logic , 2007 .

[14]  R. Wille,et al.  Ein TOSCANA-Erkundungssystem zur Literatursuche , 2000 .

[15]  Rouhollah Khodabandelou,et al.  Perspective of Iranian University Students about Academic Use of Social Networking Sites: A Study of Facebook , 2013 .

[16]  Ramakrishnan Srikant,et al.  Fast algorithms for mining association rules , 1998, VLDB 1998.

[17]  A. Kaplan,et al.  Users of the world, unite! The challenges and opportunities of Social Media , 2010 .

[18]  Radim Belohlávek,et al.  Formal concept analysis over attributes with levels of granularity , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[19]  Yiyu Yao,et al.  Rough-set concept analysis: Interpreting RS-definable concepts based on ideas from formal concept analysis , 2016, Inf. Sci..

[20]  Peter W. Eklund,et al.  Algorithms for Creating Relational Power Context Families from Conceptual Graphs , 1999, ICCS.

[21]  N. Ellison,et al.  Social capital, self-esteem, and use of online social network sites: A longitudinal analysis , 2008 .

[22]  Jesús Medina,et al.  Relating attribute reduction in formal, object-oriented and property-oriented concept lattices , 2012, Comput. Math. Appl..

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

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

[25]  Rudolf Wille,et al.  Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts , 2009, ICFCA.

[26]  Jinhai Li,et al.  Knowledge representation using interval-valued fuzzy formal concept lattice , 2016, Soft Comput..

[27]  Stefan Hrastinski,et al.  Asynchronous and synchronous e-learning : A study of asynchronous and synchronous e-learning methods discovered that each supports different purposes , 2008 .

[28]  Xizhao Wang,et al.  Comparison of reduction in formal decision contexts , 2017, Int. J. Approx. Reason..

[29]  David Forge,et al.  Incremental Construction of Alpha Lattices and Association Rules , 2010, KES.

[30]  G. Grätzer General Lattice Theory , 1978 .

[31]  Cherukuri Aswani Kumar,et al.  Concept lattice reduction using different subset of attributes as information granules , 2017, GRC 2017.

[32]  R. Wille Concept lattices and conceptual knowledge systems , 1992 .

[33]  Sérgio M. Dias,et al.  Knowledge reduction in formal contexts using non-negative matrix factorization , 2015, Math. Comput. Simul..

[34]  Jonas Poelmans,et al.  Formal concept analysis in knowledge processing: A survey on applications , 2013, Expert Syst. Appl..

[35]  Bernardo A. Huberman,et al.  Rhythms of social interaction: messaging within a massive online network , 2006, ArXiv.

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

[37]  K. Sumangali,et al.  Determination of interesting rules in FCA using information gain , 2014, 2014 First International Conference on Networks & Soft Computing (ICNSC2014).

[38]  John V. Winters Why are Smart Cities Growing? Who Moves and Who Stays , 2008, SSRN Electronic Journal.

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

[40]  Richard J. Cole,et al.  The Management And Visualisation Of Document Collections Using Formal Concept Analysis , 2000 .

[41]  Ling Wei,et al.  Relation between concept lattice reduction and rough set reduction , 2010, Knowl. Based Syst..

[42]  Pierre Nicole,et al.  La Logique Ou L'art De Penser,: Contenant Outre Les Regles Communes, Plusieurs Observations Nouvelles, Propres À Former Le Jugement.. , 2010 .

[43]  Maria Eugenia Cornejo,et al.  Attribute and size reduction mechanisms in multi-adjoint concept lattices , 2017, J. Comput. Appl. Math..

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

[45]  Sergei O. Kuznetsov On Computing the Size of a Lattice and Related Decision Problems , 2001, Order.

[46]  Ch. Aswani Kumar,et al.  Knowledge Representation Using Formal Concept Analysis: A study on Concept Generation , 2014 .

[47]  Hüseyin Uzunboylu,et al.  The Use of Social Networking Sites in Education: A Case Study of Facebook , 2013, J. Univers. Comput. Sci..

[48]  Jonas Poelmans,et al.  Fuzzy and rough formal concept analysis: a survey , 2014, Int. J. Gen. Syst..

[49]  Chu Kiong Loo,et al.  Formal concept analysis approach to cognitive functionalities of bidirectional associative memory , 2015, BICA 2015.

[50]  Jiawei Han,et al.  Data Mining: Concepts and Techniques, Second Edition , 2006, The Morgan Kaufmann series in data management systems.

[51]  D. Villiers Academic Use of a Group on Facebook: Initial Findings and Perceptions , 2010 .

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

[53]  Sérgio M. Dias,et al.  Concept lattices reduction: Definition, analysis and classification , 2015, Expert Syst. Appl..

[54]  Mumtaz Ahmad,et al.  ENHANCING QUALITY OF EDUCATION THROUGH E-LEARNING: THE CASE STUDY OF ALLAMA IQBAL OPEN UNIVERSITY , 2010 .

[55]  Jinhai Li,et al.  Concepts reduction in formal concept analysis with fuzzy setting using Shannon entropy , 2017, Int. J. Mach. Learn. Cybern..

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

[57]  H. Ulrich Hoppe,et al.  Semi-automatic creation and exploitation of competence ontologies for trend aware profiling, matching and planning , 2013 .

[58]  Karl Erich Wolff,et al.  A First Course in Formal Concept Analysis How to Understand Line Diagrams , 2003 .

[59]  C. Barczyk,et al.  Facebook in Higher Education Courses: An Analysis of Students' Attitudes, Community of Practice, and Classroom Community , 2013 .

[60]  Pascal Hitzler,et al.  Conceptual Structures in Practice , 2009 .

[61]  Kerk F. Kee,et al.  Is There Social Capital in a Social Network Site?: Facebook Use and College Students’ Life Satisfaction, Trust, and Participation 1 , 2009 .

[62]  Aaron M. Fewkes,et al.  Facebook , 2012 .

[63]  Radim Belohlávek,et al.  Selecting Important Concepts Using Weights , 2011, ICFCA.

[64]  Yoshinori Miyazaki,et al.  Web application for recording learners’ mouse trajectories and retrieving their study logs for data analysis , 2012 .

[65]  Claudio Carpineto,et al.  Order-theoretical ranking , 2000 .

[66]  Abdullah Gani,et al.  A comprehensive survey on formal concept analysis, its research trends and applications , 2016, Int. J. Appl. Math. Comput. Sci..

[67]  Sérgio M. Dias,et al.  Reducing the Size of Concept Lattices: The JBOS Approach , 2010, CLA.

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

[69]  Bernhard Ganter,et al.  Attribute Exploration with Background Knowledge , 1999, Theor. Comput. Sci..

[70]  Shyamanta M. Hazarika,et al.  Formal concept analysis: current trends and directions , 2013, Artificial Intelligence Review.

[71]  Vincent Duquenne,et al.  Structuration of phenotypes and genotypes through galois lattices and implications , 2003, Appl. Artif. Intell..

[72]  Douglas R. Vogel,et al.  Can learning be virtually boosted? An investigation of online social networking impacts , 2010, Comput. Educ..

[73]  Duo Pei,et al.  Attribute reduction in decision formal context based on homomorphism , 2011, Int. J. Mach. Learn. Cybern..

[74]  Karl Erich Wolff,et al.  Comparison of Biplot Analysis and Formal Concept Analysis in the case of a Repertory Grid , 1991 .

[75]  Václav Snásel,et al.  On Concept Lattices and Implication Bases from Reduced Contexts , 2008, ICCS Supplement.

[76]  Fred S. Roberts,et al.  Applications of combinatorics and graph theory to the biological and social sciences , 1989 .

[77]  Yuhua Qian,et al.  Three-way cognitive concept learning via multi-granularity , 2017, Inf. Sci..

[78]  Rokia Missaoui,et al.  Experimental Comparison of Navigation in a Galois Lattice with Conventional Information Retrieval Methods , 1993, Int. J. Man Mach. Stud..

[79]  Falahah,et al.  Study of Social Networking usage in Higher Education Environment , 2012 .

[80]  Gerald C. Kane,et al.  Community relations 2.0. , 2009, Harvard business review.

[81]  Miao He,et al.  Concept lattice compression in incomplete contexts based on K-medoids clustering , 2016, Int. J. Mach. Learn. Cybern..

[82]  Concept Lattices , 2004, Lecture Notes in Computer Science.

[83]  Zane L. Berge,et al.  Learning analytics as a tool for closing the assessment loop in higher education , 2012 .

[84]  Das Amrita,et al.  Mining Association Rules between Sets of Items in Large Databases , 2013 .

[85]  Ming-Wen Shao,et al.  A data reduction method in formal fuzzy contexts , 2017, Int. J. Mach. Learn. Cybern..

[86]  Nedim Karakayali,et al.  More Network Conscious Than Ever? Challenges, Strategies, and Analytic Labor of Users in the Facebook Environment , 2013, J. Comput. Mediat. Commun..

[87]  James Minogue,et al.  Investigating the impact of video games on high school students' engagement and learning about genetics , 2009, Comput. Educ..

[88]  Cherukuri Aswani Kumar,et al.  Bipolar fuzzy graph representation of concept lattice , 2014, Inf. Sci..

[89]  Weihua Xu,et al.  Granular Computing Approach to Two-Way Learning Based on Formal Concept Analysis in Fuzzy Datasets , 2016, IEEE Transactions on Cybernetics.

[90]  Michal Krupka,et al.  Removing an Incidence from a Formal Context , 2014, CLA.

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

[92]  Cherukuri Aswani Kumar,et al.  Critical Analysis on Open Source LMSs using FCA , 2013, Int. J. Distance Educ. Technol..

[93]  Jinhai Li,et al.  Concept Compression in Formal Concept Analysis Using Entropy-Based Attribute Priority , 2017, Appl. Artif. Intell..

[94]  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).

[95]  Amedeo Napoli,et al.  Many-Valued Concept Lattices for Conceptual Clustering and Information Retrieval , 2008, ECAI.

[96]  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).

[97]  Sergei O. Kuznetsov,et al.  On the Intractability of Computing the Duquenne?Guigues Bas , 2004, J. Univers. Comput. Sci..

[98]  Ling Wei,et al.  Constructing three-way concept lattices based on apposition and subposition of formal contexts , 2017, Knowl. Based Syst..

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

[100]  P. Nijkamp,et al.  Smart Cities in Europe , 2011 .