Survey on Social Community Detection <s> Galois lattice <s> Using Galois Lattices to Represent Network Data Author(s): Linton C. Freeman and Douglas R. White Source: Sociological Methodology, Vol. 23 (1993), pp. 127-146 Published by: American Sociological Association Stable URL: http://www.jstor.org/stable/271008 Accessed: 16-03-2017 20:56 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms American Sociological Association is collaborating with JSTOR to digitize, preserve and extend access to Sociological Methodology This content downloaded from 128.200.102.71 on Thu, 16 Mar 2017 20:56:14 UTC All use subject to http://about.jstor.org/terms <s> BIB001 </s> Survey on Social Community Detection <s> Galois lattice <s> Foundations.- Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies.- Semiconcept and Protoconcept Algebras: The Basic Theorems.- Features of Interaction Between Formal Concept Analysis and Algebraic Geometry.- From Formal Concept Analysis to Contextual Logic.- Contextual Attribute Logic of Many-Valued Attributes.- Treating Incomplete Knowledge in Formal Concept Analysis.- States, Transitions, and Life Tracks in Temporal Concept Analysis.- Applications.- Linguistic Applications of Formal Concept Analysis.- Using Concept Lattices for Text Retrieval and Mining.- Efficient Mining of Association Rules Based on Formal Concept Analysis.- Galois Connections in Data Analysis: Contributions from the Soviet Era and Modern Russian Research.- Conceptual Knowledge Processing in the Field of Economics.- Software Engineering.- A Survey of Formal Concept Analysis Support for Software Engineering Activities.- Concept Lattices in Software Analysis.- Formal Concept Analysis Used for Software Analysis and Modelling.- Formal Concept Analysis-Based Class Hierarchy Design in Object-Oriented Software Development.- The ToscanaJ Suite for Implementing Conceptual Information Systems. <s> BIB002
Freeman BIB001 was the first to use Galois lattices in order to represent network data. The underlying assumption is that individuals sharing the same subset of properties define a community. The approach adopted consists of the following: objects, attributes and the set of relations between objects and attributes form a "context", in accordance with Formal Concept Analysis BIB002 . This set of relations can then be represented by a binary bi-adjacency matrix, whereby objects o are the columns, attributes a are the rows and a "1" is placed at the cell corresponding to a pair (o i , a j ) if o i possesses a j . A maximum subset of objects that contain a subset of attributes is defined as a "concept", i.e. a group of objects for which the addition or removal of an attribute changes its constitution. All objects of a concept then form the "extent" and all attributes of a concept give rise to the "intent". A partial order is applied to concepts and serves to establish a hierarchy. According to the definition of Galois hierarchies, an object can appear in all the concepts where it can share the same set of attributes with other objects belonging to other concepts. Figure 3 illustrates a simple example of a Galois lattice in which several individuals are sharing several photos. 