Formal Concept Analysis

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References

2011

2009

  • http://en.wikipedia.org/wiki/Formal_concept_analysis
    • Formal concept analysis is a principled way of automatically deriving an ontology from a collection of objects and their properties. The term was introduced by Rudolf Wille in 1984, and builds on applied lattice and order theory that was developed by Garrett Birkhoff and others in the 1930's.
    • Formal concept analysis refers to both an unsupervised machine learning technique and, more broadly, a method of data analysis. The approach takes as input a matrix specifying a set of objects and the properties thereof, called attributes, and finds both all the "natural" clusters of attributes and all the "natural" clusters of objects in the input data, where
      • a "natural" object cluster is the set of all objects that share a common subset of attributes, and
      • a "natural" property cluster is the set of all attributes shared by one of the natural object clusters.
    • Natural property clusters correspond one-for-one with natural object clusters, and a concept is a pair containing both a natural property cluster and its corresponding natural object cluster. The family of these concepts obeys the mathematical axioms defining a lattice, and is called a concept lattice (in French this is called a Treillis de Galois because the relation between the sets of concepts and attributes is a Galois connection).

2005

  • (Ganter et al., 2005) ⇒ Bernhard Ganter, Gerd Stumme, and Rudolf Wille. (2005). “Formal Concept Analysis: foundations and applications." Springer. ISBN:3540278915
    • Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. It thereby allows us to mathematically represent, analyze, and construct conceptual structures. The formal concept analysis approach has been proven successful in a wide range of application fields. This book constitutes a comprehensive and systematic presentation of the state of the art of formal concept analysis and its applications. The first part of the book is devoted to foundational and methodological topics. The contributions in the second part demonstrate how formal concept analysis is successfully used outside of mathematics, in linguistics, text retrieval, association rule mining, data analysis, and economics. The third part presents applications in software engineering.

2004

  • Uta Pris. (2004). http://www.upriss.org.uk/fca/fca.html
    • Formal Concept Analysis is a theory of data analysis which identifies conceptual structures among data sets. It was introduced by Rudolf Wille in 1982 and has since then grown rapidly. More than 250 papers on the subject have been published, including several textbooks and conference proceedings. Its method of formal data analysis has successfully been applied to many fields, such as medicine and psychology, musicology, linguistic databases, library and information science, software re-engineering, civil engineering, ecology, and others. A strong feature of Formal Concept Analysis is its capability of producing graphical visualizations of the inherent structures among data. Especially for social scientists, who often handle data sets that cannot fully be captured in quantitative analyses, Formal Concept Analysis extends the scientific toolbox of formal analysis methods. Statistics and Concept Analysis complement each other in this sense. In the field of information science there is a further application: the mathematical lattices that are used in Formal Concept Analysis can be interpreted as classification systems. Formalized classification systems can be analysed according to the consistency of their relations. Thesauri can automatically be constructed from classes and their attributes, without having to create a hierarchy of classes by hand. As an example, an on-line library catalog using the Conceptual Diagrams of an automatically constructed class hierarchy has been implemented in the ZIT library in Darmstadt.

1994

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