@book{carpineto2004concept, address = {Chichester, England; Hoboken, NJ}, author = {Carpineto, Claudio and Romano, Giovanni}, interhash = {a500f448e7826fe97f0ec54e205c0636}, intrahash = {6adef3d056294240001c83fa88df1eca}, isbn = {0470850558}, publisher = {John Wiley \& Sons}, title = {Concept Data Analysis: Theory and Applications}, year = 2004 } @incollection{springerlink:10.1007/978-3-642-14197-3_15, abstract = {In this paper, we analyze the literature on Formal Concept Analysis (FCA) using FCA. We collected 702 papers published between 2003-2009 mentioning Formal Concept Analysis in the abstract. We developed a knowledge browsing environment to support our literature analysis process. The pdf-files containing the papers were converted to plain text and indexed by Lucene using a thesaurus containing terms related to FCA research. We use the visualization capabilities of FCA to explore the literature, to discover and conceptually represent the main research topics in the FCA community. As a case study, we zoom in on the 140 papers on using FCA in knowledge discovery and data mining and give an extensive overview of the contents of this literature.}, address = {Berlin / Heidelberg}, affiliation = {K.U.Leuven, Faculty of Business and Economics Naamsestraat 69 3000 Leuven Belgium}, author = {Poelmans, Jonas and Elzinga, Paul and Viaene, Stijn and Dedene, Guido}, booktitle = {Conceptual Structures: From Information to Intelligence}, doi = {10.1007/978-3-642-14197-3_15}, editor = {Croitoru, Madalina and Ferré, Sébastien and Lukose, Dickson}, interhash = {713d63f847ff4b2cbf613fc0508eb31b}, intrahash = {9694689a034cc02aae1e27114ca26a94}, isbn = {978-3-642-14196-6}, keyword = {Computer Science}, pages = {139-153}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Formal Concept Analysis in Knowledge Discovery: A Survey}, url = {http://dx.doi.org/10.1007/978-3-642-14197-3_15}, volume = 6208, year = 2010 } @incollection{ganter2010basic, address = {Berlin / Heidelberg}, author = {Ganter, Bernhard}, booktitle = {Formal Concept Analysis}, doi = {10.1007/978-3-642-11928-6_22}, editor = {Kwuida, Léonard and Sertkaya, Baris}, interhash = {f44d214d7176b9183d2bf29b8efbdc00}, intrahash = {1ab6ebc7e975a5b4019814bb7935f9bc}, isbn = {978-3-642-11927-9}, keyword = {Computer Science}, pages = {312-340}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Two Basic Algorithms in Concept Analysis}, url = {http://dx.doi.org/10.1007/978-3-642-11928-6_22}, volume = 5986, year = 2010 } @book{davey1990introduction, address = {Cambridge}, author = {Davey, Brian A. and Priestley, Hilary A.}, interhash = {7255554003c02eb6ddf14a6fcb9b9f72}, intrahash = {df19796e33c1e2c861b613e3c8a86f58}, isbn = {0521365848 9780521365840 0521367662 9780521367660}, publisher = {Cambridge University Press}, refid = {471812885}, title = {Introduction to lattices and order}, url = {http://www.worldcat.org/search?qt=worldcat_org_all&q=0521367662}, year = 1990 } @techreport{rock1997toscanaerkundungssystem, author = {Rock, Tammo and Wille, Rudolf}, institution = {TH Darmstadt}, interhash = {bddc54a042d4340762d3ac150828a9b5}, intrahash = {cf66c378d2516971007ffa26e02d86f8}, publischer = {Amer.~Math.~Soc.}, title = {Ein TOSCANA--Erkundungssystem zur Literatursuche}, type = {FB4--Preprint}, year = 1997 } @article{stumme2002computing, abstract = {We introduce the notion of iceberg concept lattices and show their use in knowledge discovery in databases. Iceberg lattices are a conceptual clustering method, which is well suited for analyzing very large databases. They also serve as a condensed representation of frequent itemsets, as starting point for computing bases of association rules, and as a visualization method for association rules. Iceberg concept lattices are based on the theory of Formal Concept Analysis, a mathematical theory with applications in data analysis, information retrieval, and knowledge discovery. We present a new algorithm called TITANIC for computing (iceberg) concept lattices. It is based on data mining techniques with a level-wise approach. In fact, TITANIC can be used for a more general problem: Computing arbitrary closure systems when the closure operator comes along with a so-called weight function. The use of weight functions for computing closure systems has not been discussed in the literature up to now. Applications providing such a weight function include association rule mining, functional dependencies in databases, conceptual clustering, and ontology engineering. The algorithm is experimentally evaluated and compared with Ganter's Next-Closure algorithm. The evaluation shows an important gain in efficiency, especially for weakly correlated data.}, address = {Amsterdam, The Netherlands, The Netherlands}, author = {Stumme, Gerd and Taouil, Rafik and Bastide, Yves and Pasquier, Nicolas and Lakhal, Lotfi}, doi = {10.1016/S0169-023X(02)00057-5}, interhash = {d500ac8a249ca8bf0fb05f382799d48f}, intrahash = {fc31933f0eec502e305b6aecb9ef6e8a}, issn = {0169-023X}, journal = {Data & Knowledge Engineering}, month = aug, number = 2, pages = {189--222}, publisher = {Elsevier Science Publishers B. V.}, title = {Computing iceberg concept lattices with TITANIC}, url = {http://portal.acm.org/citation.cfm?id=606457}, volume = 42, year = 2002 } @article{springerlink:10.1007/s11238-008-9109-z, abstract = {In this paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the Hoede–Bakker index—the notion which computes the overall decisional ‘power’ of a player in a social network. The main drawback of the Hoede–Bakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we separate the influence part from the group decision part, and focus on the description and analysis of the influence part. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations. Finally, we propose a suitable definition of a modified decisional power.}, affiliation = {Université Paris I Panthéon-Sorbonne Centre d’Economie de la Sorbonne 106-112 Bd de l’Hôpital 75013 Paris France}, author = {Grabisch, Michel and Rusinowska, Agnieszka}, doi = {10.1007/s11238-008-9109-z}, interhash = {e905db2be4b4d2e792719e9b8f445951}, intrahash = {37444465dc4376fd111296cc8c9ba1de}, issn = {0040-5833}, issue = {1}, journal = {Theory and Decision}, keyword = {Business and Economics}, pages = {69-96}, publisher = {Springer Netherlands}, title = {A model of influence in a social network}, url = {http://dx.doi.org/10.1007/s11238-008-9109-z}, volume = 69, year = 2010 } @article{octavio1985nonexistence, abstract = {We prove that there is no free object over a countable set in the category of complete distributive lattices with homomorphisms preserving binary meets and arbitrary joins.}, author = {Garcia, Octavio and Nelson, Evelyn}, interhash = {c4a8aeddff294dbdd727c05059ab2050}, intrahash = {d4ce23539ea3bc784068e93dc70387aa}, journal = {Order}, month = {December}, number = 4, pages = {399--403}, title = {On the nonexistence of free complete distributive lattices}, url = {http://dx.doi.org/10.1007/BF00582745}, volume = 1, year = 1985 } @article{faigle1981projective, abstract = {A set of axioms is presented for a projective geometry as an incidence structure on partially ordered sets of "points" and "lines". The axioms reduce to the axioms of classical projective geometry in the case where the points and lines are unordered. It is shown that the lattice of linear subsets of a projective geometry is modular and that every modular lattice of finite length is isomorphic to the lattice of linear subsets of some finite-dimensional projective geometry. Primary geometries are introduced as the incidence-geometric counterpart of primary lattices. Thus the theory of finite-dimensional projective geometries includes the theory of finite- 3-dimensional projective Hjelmslev-spaces of level $n$ as a special case. Finally, projective geometries are characterized by incidence properties of points and hyperplanes.}, author = {Faigle, Ulrich and Herrmann, Christian}, copyright = {Copyright © 1981 American Mathematical Society}, interhash = {c46eccd07dd31a7ca082f971f7dee7cd}, intrahash = {86caaca1e2111b3675308a1a30498c66}, issn = {00029947}, journal = {Transactions of the American Mathematical Society}, jstor_articletype = {research-article}, jstor_formatteddate = {Jul., 1981}, language = {English}, number = 1, pages = {pp. 319-332}, publisher = {American Mathematical Society}, title = {Projective Geometry on Partially Ordered Sets}, url = {http://www.jstor.org/stable/1998401}, volume = 266, year = 1981 } @article{erne1993distributive, abstract = {We study several kinds of distributivity for concept lattices of contexts. In particular, we find necessary and sufficient conditions for a concept lattice to be(1)distributive,(2)a frame (locale, complete Heyting algebra),(3)isomorphic to a topology,(4)completely distributive,(5)superalgebraic (i.e., algebraic and completely distributive).}, affiliation = {Institut für Mathematik Universität Hannover Hannover Germany}, author = {Erné, Marcel}, doi = {10.1007/BF01195382}, interhash = {f30c769c54f5eb98962742b324651451}, intrahash = {dd7f97b10532feab21d486ebb6783939}, issn = {0002-5240}, issue = {4}, journal = {Algebra Universalis}, keyword = {Mathematics and Statistics}, pages = {538-580}, publisher = {Birkhäuser Basel}, title = {Distributive laws for concept lattices}, url = {http://dx.doi.org/10.1007/BF01195382}, volume = 30, year = 1993 } @book{GanterWille, address = {Berlin/Heidelberg}, author = {Ganter, Bernhard and Wille, Rudolf}, interhash = {1b0bf49069eadcdfac42e52addf4eb9d}, intrahash = {ae14b00b5489de8da6e4578ac3062bfc}, publisher = {Springer-Verlag}, title = {Formal Concept Analysis: Mathematical Foundations}, year = 1999 } @article{hales1964nonexistence, author = {Hales, A. W.}, interhash = {2e2b85532b56b6caaac29b23e33f972f}, intrahash = {4d17473cee1aa8c33d821aacf2fbb95c}, journal = {Fundamentae Mathematica}, pages = {45-66}, title = {On the non-existence of free complete Boolean algebras}, url = {http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=54}, volume = 54, year = 1964 } @article{Duquenne1991133, abstract = {The meet-core of a finite lattice L is its minimal -- in fact minimum -- partial meet- subsemilattice of which the filter lattice is isomorphic to L. This gives a representation theory for finite lattices, in particular which extends Birkhoff's correspondence between ordered sets and distributive lattices, and is linked with Wille's notion of scaffolding. The meet-cores (and dually the join-cores) of modular, geometric and join-meet-distributive lattices are characterized locally by some obligatory sublattices or by some construction procedures otherwise.}, author = {Duquenne, Vincent}, doi = {10.1016/0012-365X(91)90005-M}, interhash = {3fcc87180a838828f74fd82d7b6ac209}, intrahash = {3754f36ef7da2a619c34a7c863ba3427}, issn = {0012-365X}, journal = {Discrete Mathematics}, number = {2-3}, pages = {133 - 147}, title = {The core of finite lattices}, url = {http://www.sciencedirect.com/science/article/B6V00-45GMF6D-5/2/1120caa94c245d57b16992536b46325d}, volume = 88, year = 1991 } @inproceedings{doerfel2010scaffolding, abstract = {The scaffolding of a complete lattice L of finite length was introduced by Rudolf Wille in 1976 as a relative subsemilattice of L that can be constructed using subdirect decomposition. The lattice is uniquely defined by its scaffolding and can be reconstructed from it. Using bonds, we demonstrate how the scaffolding can be constructed from a given formal context and thereby extend the notion of the scaffolding to doubly founded lattices. Further, we explain the creation of a suitable graphical representation of the scaffolding from the context.}, author = {Doerfel, Stephan}, booktitle = {Concept Lattices and Their Applications 2010}, editor = {Kryszkiewicz, Marzena and Obiedkov, Sergei}, interhash = {b654c8f4b9c1604e0ec842a7db47a08b}, intrahash = {2584354f8e496d5747eb1025478c31ec}, month = {November}, pages = {283-293}, publisher = {CEUR-WS}, title = {The Scaffolding of a Formal Context}, url = {http://ceur-ws.org/Vol-672/paper25.pdf}, vgwort = {18}, volume = 672, year = 2010 } @inproceedings{kdml26, abstract = {We study the problem of listing all closed sets of a closure operator $\sigma$ that is a partial function on the power set of some finite ground set $E$, i.e., $\sigma : {\cal F} \to {\cal F}$ with ${\cal F} \subseteq {\cal P}(E)$. A very simple divide-and-conquer algorithm is analyzed that correctly solves this problem if and only if the domain of the closure operator is a strongly accessible set system. Strong accessibility is a strict relaxation of greedoids as well as of independence systems. This algorithm turns out to have delay $O (|E| (T_{\cal F} +T_\sigma + |E|))$ and space $O(|E| + S_{\cal F} S_\sigma)$, where $T_{\cal F}$, $S_{\cal F}$, $T_\sigma$, and $S_\sigma$ are the time and space complexities of checking membership in $\cal F$ and computing $\sigma$, respectively. In contrast, we show that the problem becomes intractable for accessible set systems. We relate our results to the data mining problem of listing all support-closed patterns of a dataset and show that there is a corresponding closure operator for all datasets if and only if the set system satisfies a certain confluence property.}, address = {Kassel, Germany}, author = {Boley, Mario and Horvath, Tamas and Poigne, Axel and Wrobel., Stefan}, booktitle = {Proceedings of LWA2010 - Workshop-Woche: Lernen, Wissen {\&} Adaptivitaet}, crossref = {lwa2010}, editor = {Atzmüller, Martin and Benz, Dominik and Hotho, Andreas and Stumme, Gerd}, interhash = {49ca7e8ee8dcb2236232e9653cb576d1}, intrahash = {75f0dabe405564eb640a8261edfce283}, presentation_end = {2010-10-06 10:45:00}, presentation_start = {2010-10-06 10:22:30}, room = {0446}, session = {kdml4}, title = {Listing closed sets of strongly accessible set systems with applications to data}, track = {kdml}, url = {http://www.kde.cs.uni-kassel.de/conf/lwa10/papers/kdml26.pdf}, year = 2010 }