Lattice miner is a formal concept analysis software tool for the construction, visualization and manipulation of concept lattices. Thereby, formal concept analysis has created results that may be of interest even without considering the applications by which they were motivated. Modelling equivalence classes of feature models with concept lattices to assist their extraction from product descriptions. Concept lattices are widely used in machine learning, pattern recognition, expert systems, decision analysis, data mining, information retrieval, computer networks and software engineering, and many other fields 4, 5. Formal concept analysis of twodimensional convex continuum structures. Galois lattices 12 and concept lattices 11 are core structures of a data analysis framework formal concept analysis, or fca for short for extracting an ordered set of concepts from a dataset, called a formal context, composed of objects described by attributes.
Pcompletions of lattices and its applications to formal. Concept analysis concept lattice execution trace class hierarchy software maintenance. Today, a wide range of applications of concept lattices in static and dynamic analysis. Lattices concept lattices and their line diagrams coursera.
Today, a wide range of applications of concept lattices in static and dynamic analysis of software. In this paper, we introduce the notion of an m approximable concept on each context. A selected number of highquality cla 2010 papers will be published as a special issue of fundamenta informaticae 0. Design of class hierarchies based on concept galois lattices. A representation space to structure software variability abstract. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Snelting who used formal concept analysis to analyze legacy. The question if and how iceberg concept lattices can be used in such a supervised learning scenario is an interesting open problem. Analysis of large data sets using formal concept lattices. Objectoriented intervalset concept lattices sciencedirect. Feb 21, 2019 this course is an introduction into formal concept analysis fca, a mathematical theory oriented at applications in knowledge representation, knowledge acquisition, data analysis and visualization. Cla end of june 2020 in tallinn, estonia permanent cla website.
Publications classification analysis using concept lattices. Icfca 2004 included tutorial sessions, demonstrating the practical bene. Software reengineering based on concept lattices gregor snelting universitat passau. Concept lattices stem from the so called formal concept analysis a part of applied mathematics that brings mathematical methods into the field of data anylysis and knowledge processing. In practice often the formal concept lattices are very big and it is difficult to study and say about properties of such lattices. Statistical methods for data mining and knowledge discovery. Introduction formal concept analysis fca was invented in the early 1980s by rudolf wille as a mathematical theory 1. This is the site of my lattice drawing component, a java component for drawing lattices. Introduction to formal concept analysis and its applications in information retrieval and related fields dmitry i. The second is based on artificial intelligence the paradigm is based on lattices, uses logical operations, and is designed for delineating sets of terms or concepts. Using concept lattices to uncover causal dependencies in. The role of concept, context, and component for dependable software development. Second international conference on formal concept analysis, icfca 2004, sydney, australia, february 2326, 2004, proceedings edition 1 available in paperback add to wishlist isbn10. Towards attribute reduction in multiadjoint concept lattices 92103 jesus medina moreno, manuel ojedaaciego.
For example, most data mining tasks can generate a large number of concepts. This overview summarizes important papers from the last ten years, and presents three methods in some detail. Formal concept analysis is a theoretical framework which structures a set of objects described by properties. Cla is an international conference dedicated to formal concept analysis fca and areas closely related to fca such as data mining, information retrieval, knowledge management, data and knowledge engineering, logic, algebra and lattice theory.
A new incremental algorithm for constructing concept lattices. Formal concept analysis is a classification technique that takes data sets of. Concept lattices in software analysis formal concept analysis. By combining these two theories, objectoriented and propertyoriented concept lattices are proposed. Concept lattices in software analysis acm digital library.
Modelling equivalence classes of feature models with. Cla provides a forum for researchers, practitioners, and students. In such a task, the calculation of the whole concept. Computing and visualizing concept lattices tuprints tu darmstadt.
Formal concept analysis and rough set are two kinds of efficient mathematical tools for data analysis and knowledge discovery. After mining concepts that satisfy a minimum support, inclose uses them to output a quiet or clean version of the original cxt le. Each concept in the hierarchy represents the objects sharing some set of properties. The beyond implies that it is of primary importance to. Fca is concerned with the formalization of concepts and conceptual thinking and has been applied in many disciplines such as software. Those subdomains are divided from the target domain. This can then be used to produce a readable concept. Lattices and lattice problems theory and practice lattices, svp and cvp, have been intensively studied for more than 100 years, both as intrinsic mathematical problems and for applications in pure and applied mathematics, physics and cryptography. A parallel algorithm to generate formal concepts for large data. Departmentofcomputerscience,palackyuniversity,tomkova40,77900olomouc, czechrepublic communicated by ph. A unit cell is a volume, when translated through some subset of the vectors of a bravais lattice, can fill up the whole space without voids or.
Design of class hierarchies based on concept galois lattices 5 helped identify nontrivial generalizations, but at the same time, suffered from the lack of aggregation as a concept. About ten years ago, the first serious applications of concept lattices in software analysis were published. In formal concept analysis, one fundamental result states that every concept lattice is complete, and conversely, each complete lattice is isomorphic to a concept lattice. The theme of the 2004 conference was concept lattices to acknowledge the colloquial term used for the line diagrams that appear in almost every paper in this volume. Formal concept analysis fca is a principled way of deriving a concept hierarchy or formal ontology from a collection of objects and their properties. Fca is concerned with the formalization of concepts and conceptual thinking and has been applied in many disciplines such as software engineering, knowledge discovery and information retrieved during the last two decades. Revealing java class structure with concept lattices. Formal concept analysis is a method of conceptual knowledge. Concept analysis a new framework for program understanding. Fca software formal concept analysis applications and demos. Analysis of large data sets using formal concept lattices 104115 simon andrews, constantinos orphanides. Galicia fcastone format conversion software and commandline lattice generation. Concept neighbourhoods in rogets thesaurus and wordnet. It provides tools for understanding the data by representing it as a hierarchy of concepts or, more exactly, a concept.
An entropybased weighted concept lattice for merging. Concept lattices in software analysis gregor snelting universitat passau abstract about ten years ago, the rst serious applications of concept lattices in software analysis were published. Analysis of large data sets using formal concept lattices ceur. Concept lattices second international conference on formal. Ontology construction using multiple concept lattices. Formal concept analysis for knowledge discovery and data mining. Concept lattices in software analysis springerlink. Discovery of such causal dependencies can be an important step to understanding the structure of undocumented, legacy code. A lattice is a partially ordered set lsuch that for any two elements x,y. There is also an issue in computing large numbers of formal concepts. Concept lattices defined from implication operators. Exploring structural characteristics of lattices in real world. This overview summarizes important papers from the last ten years, and presents three.
But was disappointed because even small, well known lattices. This paper is a tutorial on formal concept analysis. Formal concept analysis fca is a mathematical theory of data analysis using formal contexts and concept lattices. In this paper we describe a methodology based on formal concept analysis that uncovers possible causal dependencies in execution trace streams. The concept lattices are created using formal concept analysis which hierarchically organizes the results in the form of clusters of particular objects composed of the documents with the. Revealing java class structure with concept lattices research thesis submitted in partial fulfillment of the requirements for the degree of master of science in. This theory is, in fact, a theory of sharp bivalent concepts. From its beginnings 20 years ago this theory has evolved into a commercially applicable toolfor dataanalysisthroughthe toscana software. Program analysis component inside a compiler or software engineering system see, for example 67, 69, 49. Concept lattices in software analysis semantic scholar. In this paper we will push this kind of analysis a bit further. Applying formal concept analysis in a data mining environment.
Adult degreesexpay lattice in conexp inclose does this automatically. To our knowledge the first effort to apply closure concepts to software engineering was by gregor. Many fca software applications are available today. A representation space to structure software variability. Concept lattices with a few million elements can be handled without problems. An introduction to the theory of lattices and applications. Concepts is a simple python implementation of formal concept analysis fca provides a mathematical model for describing a set of objects e. For proofs, citations, and further details we refer to 2. To reduce or correct the big formal concept lattices to lattices with well studied properties is usual problem of the theory of formal concept analysis. This course is an introduction into formal concept analysis fca, a mathematical theory oriented at applications in knowledge representation, knowledge acquisition, data analysis and visualization. Willeknowledge acquisition by methods of formal concept analysis e. Concept lattices in software analysis researchgate.
Analysis of large data sets using formal concept lattices 109 fig. Concept lattices in software analysis formal concept. Today, a wide range of applications of concept lattices in static and dynamic analysis of software artefacts is known. It allows the generation of formal concepts and association rules as well as the transformation of formal contexts via apposition, subposition, reduction and objectattribute generalization, and the manipulation of concept lattices via approximation, projection and.
Second international conference on formal concept analysis, icfca 2004, sydney, australia, february 2326, 2004, proceedings lecture notes in computer science 2961 on free shipping on qualified orders. Concept lattices and order in fuzzy logic radim belohlavek. Formal concept analysis is a theoretical framework which structures a set of. One such possibility of very general nature is that data tables can be transformed into algebraic structures called complete lattices. This section gives only a brief overview of the basic notations of the theory for formal concept analysis. Concept lattices second international conference on formal concept analysis, icfca 2004, sydney, australia, february 2326, 2004, proceedings. There are instructions at the end of this page for getting the source code. Formal concept analysis is a classification technique that takes data sets of objects and their attributes, and extracts relations between these. Keywords formal concept analysisrelational datarelational concept analysis concept latticesknowledge representationdescription logics mathematics subject classifications 2010 06a9906b9968r99 1 introduction knowledge discovery from data kdd is the process of distilling useful facts from a dataset.
Overview concept analysis provides a way to identify groupings of objects that have common attributes. Cla is an international conference dedicated to formal concept analysis fca, homepage and closely related areas. These keywords were added by machine and not by the authors. Crystal structure 3 unit cell and lattice constants. Drawing a concept lattice diagram constructing concept. Kolaitis abstract the theory of concept lattices i. Using concept lattices to uncover causal dependencies in software. About ten years ago, the first serious applications of concept lattices in.
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