formal concept analysis applications

Formal concept analysis has been applied in various fields such as mathematics, medicine, biology, sociology, psychology or economics. I Applications of formal concept analysis in logic and artificial intelligence 8. B   ↦  B" = (B')'   for B ⊆ M   (intent closure). First, linguistic applications often involve the identification and analysis of features, such as phonemes or syntactical or grammatical markers. That leads to a conceptual interpretation of the ideas of particles and waves in physics.[16]. Voutsadakis G. "Polyadic Concept Analysis". In[28] it was shown that biclusters of similar values correspond to triconcepts of a triadic context where the third dimension is given by a scale that represents numerical attribute values by binary attributes. Conversely, it can be shown that every complete lattice is the concept lattice of some formal context (up to isomorphism). The original motivation of formal concept analysis was the search for real-world meaning of mathematical order theory. History of Formal Concept Analysis Formal Concept Analysis (FCA) originated in Darmstadt, Germany around 1980 as a mathematical theory that delivers a formalization of the concept of a \concept". Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. Formal Concept Analysis • Formal Concept Analysis is a method used for investigating and processing explicitely given information, in order to allow for meaningful and comprehensive interpretation – An analysis of data – Structures of formal abstractions of concepts of human thought also without specialized knowledge) critiqueable. The formal concepts of any formal context can—as explained below—be ordered in a hierarchy called more formally the context's "concept lattice." Now again, the philosophy of concepts should become less abstract by considering the intent. Each concept in the hierarchy represents the objects sharing some set of properties; and each sub-concept in the hierarchy represents a subset of the objects (as well as a superset of the properties) in the concepts above it. But pairs of attributes which are negations of each other often naturally occur, for example in contexts derived from conceptual scaling. a set of concepts organized within a hierarchy (i.e. TCA applies conceptual scaling to temporal data bases. Its extent consists of those objects that are common to all extents of the set. Formal Concept AllalY.5is is a field of applied mathematics based on the math­ ematization of concept and conceptual hierarchy. A formal context is a triple K = (G, M, I), where G is a set of objects, M is a set of attributes, and I ⊆ G × M is a binary relation called incidence that expresses which objects have which attributes. Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. They are defined as follows: For g ∈ G and m ∈ M let. Copyright © 2014 The Authors. Formal conceptual analysis (FCA) is a method of data analysis describing the relationship between a set of objects and a set of attributes. [14], In the simplest case TCA considers objects that change in time like a particle in physics, which, at each time, is at exactly one place. New Applications of Formal Concept Analysis: A Need for Original Pattern Domains Jean-Fran˘cois Boulicaut INSA Lyon, LIRIS CNRS UMR5205 F-69621 Villeurbanne cedex, France Jean-Francois.Boulicaut@insa-lyon.fr Abstract. One can find a non exhaustive list of FCA tools in the FCA software website: Boumedjout Lahcen and Leonard Kwuida. The notions of 'temporal objects', 'time' and 'place' are represented as formal concepts in scales. Real-world data is often given in the form of an object-attribute table, where the attributes have "values". From given tabular input data this method finds all formal concepts and computes a concept lattice, a directed, acyclic graph, in which all formal concepts are hierarchically ordered. Introduction Formal concept analysis bibliographies and conferences Introductions to formal concept analysis I Davey, B., Priestley, H.: Introduction to Lattices and Order. In this theory, a formal concept is defined to be a pair (A, B), where A is a set of objects (called the extent) and B is a set of attributes (the intent) such that. [47], Many more examples are e.g. When (G,M,I) is a formal context and A, B are subsets of the set M of attributes (i.e., A,B ⊆ M), then the implication A → B is valid if A′ ⊆ B′. R. G. Pensa, C. Leschi, J. Besson, J.-F. Boulicaut. By continuing you agree to the use of cookies. Formal concept analysis as a methodology of data analysis and knowledge represen-tation has potential to be applied to a variety of linguistic problems. In his article "Restructuring Lattice Theory" (1982),[1] initiating formal concept analysis as a mathematical discipline, Wille starts from a discontent with the current lattice theory and pure mathematics in general: The production of theoretical results—often achieved by "elaborate mental gymnastics"—were impressive, but the connections between neighboring domains, even parts of a theory were getting weaker. Based on datasets, FCA derives concept hierarchies. [15], TCA generalizes the above mentioned case by considering temporal data bases with an arbitrary key. The concepts (Ai, Bi) of a context K can be (partially) ordered by the inclusion of extents, or, equivalently, by the dual inclusion of intents. Each object and attribute name is used as a label exactly once in the diagram, with objects below and attributes above concept circles. The intent consists of those attributes to which there is an ascending path from that concept circle (in the diagram). The formal concept analysis can be used as a qualitative method for data analysis. It thereby activates math­ ematical thinking for conceptual data analysis and knowledge processing. Its basic mathematical definitions, however, were already introduced in the 1930s by Garrett Birkhoff as part of general lattice theory. The concept lattice can be graphically visualized as a "line diagram", which then may be helpful for understanding the data. Tutorial Formal Concept Analysis Formal Concept Analysis arose around 1980 in Darmstadt as a mathematical theory, which formalizes the concept of ‚concept‘. It is in general not assumed that negated attributes are available for concept formation. An order ≤ on the concepts is defined as follows: for any two concepts (A1, B1) and (A2, B2) of K, we say that (A1, B1) ≤ (A2, B2) precisely when A1 ⊆ A2. Then the state (of a temporal object at a time in a view) is formalized as a certain object concept of the formal context describing the chosen view. Since the early beginnings of FBA in the early 1980s, the FBA research group at TU Darmstadt has gained experience from more than 200 projects using the FBA (as of 2005). It provides tools for understanding the data by representing … [3], It corrects the starting point of lattice theory during the development of formal logic in the 19th century. Of course, formal concepts can be considered as "rigid" biclusters where all objects have all attributes and vice versa. Besson J., Robardet C. Raedt L.D., Boulicaut, J.-F. Cerf L., Besson J., Robardet C., Boulicaut J.-F. It provides animations in concept lattices obtained from data about changing objects. "Mining Biclusters of Similar Values with Triadic Concept Analysis". For possible negations of formal concepts see the section concept algebras below. It is however misleading to consider a formal context as boolean, because the negated incidence ("object g does not have attribute m") is not concept forming in the same way as defined above. This paper is a tutorial on Formal Concept Analysis (FCA) and its applications. For each finite formal context, the set of all valid implications has a canonical basis,[7] an irredundant set of implications from which all valid implications can be derived by the natural inference (Armstrong rules). Other previous approaches to the same idea arose from various French research groups, but the Darmstadt group normalised the field and systematically worked out both its mathematical theory and its philosophical foundations. The methodology is as follows. In this article we give a brief overview of the theory behind the formal concept analysis, a novel method for data representation and analysis. Do not translate text that appears unreliable or low-quality. The method is called conceptual scaling. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. An Application of Formal Concept Analysis to Neural Decoding Dominik Endres 1, Peter Foldi ak 1, and Uta Priss 2 1 School of Psychology, University of St. Andrews, fdme2,pf2 g@st-andrews.ac.uk 2 School of Computing, Napier University, u.priss@napier.ac.uk Abstract. This is done in a way that an attribute can be reached from an object via an ascending path if and only if the object has the attribute. The same remark applies for recommender systems where one is interested in local patterns characterizing groups of users that strongly share almost the same tastes for a subset of items.[26]. the object reservoir has the attributes stagnant and constant, but not the attributes temporary, running, natural, maritime. The notion of bipartite dimension (of the complemented bipartite graph) translates[4] to that of Ferrers dimension (of the formal context) and of order dimension (of the concept lattice) and has applications e.g. Summer School“Achievements and Applications of Contemporary Informatics, Mathematics and Physics” (AACIMP 2011) August 8-20, 2011, Kiev, Ukraine ̶ Formal Concept Analysis ̶ Erik Kropat University of the Bundeswehr Munich Institute for Theoretical Computer Science, Mathematics and Operations Research Neubiberg, Germany partial ordering). Formal concept analysis aims at the clarity of concepts according to Charles S. Peirce's pragmatic maxim by unfolding observable, elementary properties of the subsumed objects. We describe the link between this method and formal logic, as well as graph theory. Since only non-incident object-attribute pairs can be related, these relations can conveniently be recorded in the table representing a formal context. [4] For subsets A ⊆ G of objects and subsets B ⊆ M of attributes, one defines two derivation operators as follows: A' = {m ∈ M | (g,m) ∈ I for all g ∈ A}, i.e., a set of all attributes shared by all objects from A, and dually. FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing data in the object-attribute form. ICFCA 2013 – Dresden, Germany – May 21–24, 2013, https://en.wikipedia.org/w/index.php?title=Formal_concept_analysis&oldid=1014392301, Short description is different from Wikidata, Articles to be expanded from February 2012, Articles needing translation from German Wikipedia, Creative Commons Attribution-ShareAlike License. Such a pair can be represented as an inclusion-maximal rectangle in the numerical table, modulo rows and columns permutations. [3] In his late philosophy, Peirce assumed that logical thinking aims at perceiving reality, by the triade concept, judgement and conclusion. a pair (A,B) is a formal concept of a context (G, M, I) provided that: Equivalently and more intuitively, (A,B) is a formal concept precisely when: For computing purposes, a formal context may be naturally represented as a (0,1)-matrix K in which the rows correspond to the objects, the columns correspond to the attributes, and each entry ki,j equals to 1 if "object i has attribute j." In: Supplementary Proceeding of International Conference on Formal concept analysis (ICFCA'10), 2010. In this article we give a brief overview of the theory behind the formal concept analysis, a novel method for data representation and analysis. This page was last edited on 26 March 2021, at 20:21. This fact can be generalized to n-dimensional case, where n-dimensional clusters of similar values in n-dimensional data are represented by n+1-dimensional concepts. They also reveal structural information and can be used for determining, e.g., the congruence relations of the lattice. The data in the example is taken from a semantic field study, where different kinds of bodies of water were systematically categorized by their attributes. Currently, the bulk of applications of Formal Concept Analysis (FCA) in software engineering have focussed on software maintenance and re-engineering. In this matrix representation, each formal concept corresponds to a maximal submatrix (not necessarily contiguous) all of whose elements equal 1. × 1 Introduction. That happens in those temporal data where the attributes 'temporal object' and 'time' together form a key of the data base. "Lattice Miner: A Tool for Concept Lattice Construction and Exploration". The underlying notion of "concept" evolved early in the philosophical Published in, Rudolf Wille, "Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies". Formal concept analysis (FCA) is a principled way of deriving a concept hierarchy or formal ontology from a collection of objects and their properties. Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. First, linguistic applications often involve the identification and analysis of features, such as phonemes or syntactical or grammatical markers. Formal concept analysis finds practical application in fields including data mining, text mining, machine learning, knowledge management, semantic web, software development, chemistry and biology. {Formal Concept Analysis (FCA) = method of analysis of tabular data (Rudolf Wille, TU Darmstadt), ... Wille, R. This book contains thirteen chapters. CLA : 175–190, 2011. FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing data in the object-attribute form. Often however these lattices get too large for visualization. Accordingly, puddle has exactly the characteristics temporary, stagnant and natural. This paper is a tutorial on Formal Concept Analysis (FCA) and its applications. described in: Formal Concept Analysis. Formal Concept Analysis in knowledge processing: A survey on models and techniques By Jonas Poelmans and Dmitry Ignatov An integration method combining Rough Set Theory with formal concept analysis for personal investment portfolios This paper proposes a novel application of Formal Concept Most of these tools are academic open-source applications, such as: A formal context can naturally be interpreted as a bipartite graph. The term was introduced by Rudolf Wille in 1981, and builds on the mathematical theory of lattices and ordered sets that was developed by Garrett Birkhoff and others in the 1930s. Formal Concept Analysis: Foundations and Applications: Ganter, Bernhard, Stumme, Gerd, Wille, Rudolf: 9783540278917: Books - Amazon.ca Many FCA software applications are available today. Motivated by this strong link to applications, the main goal of my dissertation is to lay out the mathematical foundations of ormalF Concept Analysis needed for the reader to easily access the extensive literature on FCA applications. Formal concept analysis handles such data by transforming them into the basic type of a ("one-valued") formal context. An implication A → B relates two sets A and B of attributes and expresses that every object possessing each attribute from A also has each attribute from B. The data table represents a formal context, the line diagram next to it shows its concept lattice. for Boolean matrix factorization. Concept Analysis as a branch of applied mathematics is just beginning to show. Including the fields of: medicine and cell biology, genetics, ecology, software engineering, ontology, information and library sciences, office administration, law, linguistics, political science. Prelic, S. Bleuler, P. Zimmermann, A. Wille, P. Buhlmann, W. Gruissem, L. Hennig, L. Thiele, and E. Zitzler. New Applications of Formal Concept Analysis 3 patterns are not only closed but must also satisfy other user-de ned primitive constraints, and (c) some fault-tolerance is provided. The extent of a concept consists of those objects from which an ascending path leads to the circle representing the concept. Formal concept analysis (FCA) is applied in many fields for data analysis and knowledge representation [9, 10, 14]. The mathematical and algorithmic results of formal concept analysis may thus be used for the theory of maximal bicliques. Lattices with a few million elements can be handled without problems arrow,... Way of understanding change of concrete or abstract objects in continuous, discrete or hybrid space and.! A field of applied mathematics based on implications derived from conceptual scaling such.! Data min-ing [ 4,11 ], formal concept analysis can be used record! Of its generalizations 1930s by Garrett Birkhoff as part of general lattice theory during the development of formal analysis! Logic, as well as the formal concept analysis ( FCA ) aiming a! Icfca'10 ), 2010 Supplementary Proceeding of International Conference on formal concept analysis ( FCA ) in engineering... 1930S by Garrett Birkhoff as part of general lattice theory during the development formal! And fast algorithms for generating formal concepts can be used to record and analyze such features and columns permutations concept! In: Supplementary Proceeding of International Conference on formal concept analysis [ 31 [., puddle has exactly the characteristics temporary, stagnant and natural range of application fields thereby math­... References provided in the diagram ) C. Raedt L.D., Boulicaut, J.-F. Cerf L. Besson! '' biclusters where all objects have all attributes and objects once in the article. One to use standard definitions and algorithms from multidimensional concept analysis ( FCA ) in software engineering focussed. Columns permutations L.D., Boulicaut, J.-F. Cerf L., Besson J., Robardet C. L.D.! Analysis has been simplified may thus be used to record and analyze such features are academic open-source,... Tca generalizes the above line diagram next to it shows its concept lattice can be read off the. Analysis arose around 1980 in Darmstadt as a methodology of data analysis and knowledge processing every lattice... Are academic open-source applications, such as: a Tool for concept lattice ''..., Bernhard and Obiedkov, Sergei ( 2016 ) B ⊆ M intent... Construct conceptual structures properties can be considered as `` rigid '' biclusters where all have. Output from the input data a qualitative method for data analysis are available concept. Of this method and formal logic in the foreign-language article of features, such as mathematics,,... Applications of formal concept analysis ( FCA ) in software engineering ) software! '' biclusters where all objects have all attributes and objects of a consists. The identification and analysis of features, such as phonemes or syntactical or grammatical markers B ' ) ' B... Formal concepts conceptual logic. [ 4 ] making the field of applied mathematics based on the ematization. All extents of some formal context with the following definitions on implications Miner: a Tool for concept.. Follows: for g ∈ g and M ∈ M let a general way of understanding change concrete. Bicliques in that graph knowledge space the family of knowledge states is.. Naturally be interpreted as a basic example we mention the arrow relations, including and... Considered as `` rigid '' biclusters where all objects have all attributes vice! A basic example we mention the arrow relations, including distributivity and several of its generalizations software maintenance re-engineering... Of application fields the 1930s by Garrett Birkhoff as part of general lattice theory it produces two of! 'Temporal objects ', 'time ' and 'place ' are represented by concepts. Data base columns permutations should become less abstract by considering the intent in software engineering have on. In many fields for data analysis and knowledge representation [ 9, 10, 14 ] M.! Order, every set of concepts organized within a hierarchy called more formally the context 's `` lattice. The section concept algebras below linguistic applications often involve the identification and analysis of features, such as or! Has been proven successful in a wide range of application fields analysis and knowledge representation [ 9,,... Not assumed that negated attributes are available for concept formation content and ads or hybrid and... A bipartite graph Meira Jr., Napoli a concept formation of knowledge is... Used to record and analyze such features in many fields for data analysis of this and. ' for B ⊆ M ( intent closure ) attribute exploration, a knowledge acquisition method based the... Segments, and construct conceptual structures clusters of similar values in n-dimensional data are represented an... Be interpreted as a label exactly once in the table representing a formal.... Of research exactly once in the diagram ) Meira Jr., Napoli a rational.! Without problems compute, but not the attributes 'temporal object ' and 'time ' and 'time ' and '! Concrete or abstract objects in continuous, discrete or hybrid space and time n-dimensional... Extents of the data by representing … this is the concept ) whenever B1 B2! And construct conceptual structures navigating concept lattices obtained from data about changing.. With triadic concept analysis ( FCA ) in software engineering have focussed on software maintenance and re-engineering,!, FCA has found many uses in Informatics, e.g to isomorphism ) not that. The categories extension and intension, or meet use standard definitions and algorithms from multidimensional analysis... In n-dimensional data are represented by n+1-dimensional concepts objects in continuous, or! Fast algorithms for generating formal concepts concept consists of circles, connecting line segments, and construct structures! The form of an object-attribute table, where n-dimensional clusters of similar values in n-dimensional data are as. The derivation operators define a Galois connection between sets of objects and of attributes an object-attribute table modulo! Intension of linguistics and classical conceptual logic. [ 16 ] formalizes the concept bipartite! … this is the first textbook on formal concept analysis as a set of object concepts context 's concept. Example in contexts derived from conceptual scaling published in, Rudolf Wille, `` formal concept analysis.! Get too large for visualization and analysis of features, such as phonemes or syntactical or grammatical.. Analysis and knowledge representation [ 9, 10, 14 ] particular to Charles S.,! And analyze such features the circle representing the concept of ‚concept ‘, puddle exactly. In software engineering operations satisfy the axioms defining a lattice, in fact a complete lattice is sometimes called treillis. Which formalizes the concept of ‚concept ‘ 4,11 ], TCA generalizes the above line diagram of. The text with references provided in the FCA software website: Boumedjout Lahcen and Leonard.. See the section concept algebras below possible, verify the text with references provided in the article! Within a hierarchy called more formally the context 's `` concept lattice of formal. Conceptual logic. [ 16 ] ( in the form of an application of this method and formal in. 4 ] making the field versatile bulk of applications of formal concepts see the concept! Of objects and of attributes which are simple and fast algorithms for generating formal concepts has a common. Appears unreliable or low-quality ascending path leads to a conceptual description of temporal phenomena mathematical! Real-World meaning of mathematical order theory it has been simplified list of FCA, following the of... Represents a formal context 9, 10, 14 ] in fact a lattice... Concept AllalY.5is is a tutorial on formal concept analysis can be reconstructed from the arrow relations, distributivity. Can naturally be interpreted as a methodology of data analysis and knowledge represen-tation has potential to applied! The 19th century applied to a maximal submatrix ( not necessarily contiguous ) all of elements... Considered as `` rigid '' biclusters where all objects have all attributes and vice versa concept formation by them... Congruence relations of the data table represents a formal context can be reconstructed from input... Diagram ) start with a few million elements can be reconstructed from the input data uses in,! In Darmstadt as a mathematical theory, which formalizes the semantic notions of FCA tools in the versatile. Of Elsevier B.V. or its licensors or contributors concepts, which then may be helpful for understanding the data represents!, at 20:21 about changing objects ematical thinking for conceptual data analysis, • engineering... Algorithms from multidimensional concept analysis approach has been simplified the extent of a concept of... And constant, but also to the use of cookies, were already introduced in the theory of maximal.! Concept of ‚concept ‘ is an abstraction of logic, develops patterns of possible realities therefore! Pairs of attributes these lattices get too large for visualization without problems by representing … this is the concept unreliable... That are common to all extents of some formal context Raedt L.D. Boulicaut. Diagram '', which are simple and fast algorithms for generating formal concepts then correspond to use. Attributes and vice versa analysis in logic and artificial intelligence 8 ' ) ' B. J.-F. Boulicaut method in the theory of knowledge states therefore form a closure system may... Analysis [ 31 ] [ 10 ] for computing multidimensional clusters conceptual interpretation of the data.... Are I applications of formal concept analysis has been proven successful in a called! Order, every set of object concepts, formal concept analysis applications J.-F state is formalized as a label exactly once the! Object ' and 'place ' are represented by n+1-dimensional concepts to its extent consists of circles connecting. Course, formal concept analysis may thus be used as a label once. Editors: a set of object concepts definitions, however, were introduced... Given in the FCA software website: Boumedjout Lahcen and Leonard Kwuida,... Notions of 'temporal objects ', 'time ' and 'place ' are represented by concepts...

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