Ganter, B., & Wille, R. (1989). Conceptual scaling. In F. Roberts (Ed.), Applications of combinatorics and graph theory to the biological and social sciences. Berlin: Springer, 139-167.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for measuring similarity. Another important question is how the resulting concept lattice shall be presented to the user. We will check which approaches are best fit to this purpose. One way is for instance to use Cernato as we did for this paper. Another way is to de rive conceptual scales [4] by grouping together the most related sets of terms. These conceptual scales can then be visualized using TOSCANA [8, 19, 12] The resulting concept lattice may also be accessed based on iceberg concept lattices [18] or as discussed in [1] or [2] We will test these ap proaches also on ....

B. Ganter and R. Wille. Conceptual scaling. In F.Roberts, editor, Applications of combinatorics and graph theory to the biological and social sciences, pages 139-167, New York, 1989. Springer.

....cosine for measuring similarity. Another important question is how the resulting concept lattice shall be presented to the user. We will check which approaches are best fit to this purpose. One way is for instance to use Cernato as we did for this paper. Another way is to derive conceptual scales [4] by grouping together the most related sets of terms. These conceptual scales can then be visualized using TOSCANA [8, 19, 12] The resulting concept lattice may also be accessed based on iceberg concept lattices [18] or as discussed in [1] or [2] We will test these approaches also on ....

B. Ganter and R. Wille. Conceptual scaling. In F.Roberts, editor, Applications of combinatorics and graph theory to the biological and social sciences, pages 139--167, New York, 1989. Springer.

.... operator is used for both S 1 and S 2 , i.e. # 1 : m 1 (G) and # 2 : m 2 (G) G 2 , a new composition operator acting on the object set of the semi product is given by # 1 # # 2 : m 1 (G) 2 (G) 2 , where: # 1 # # 2 (w 1 , w 2 ) # 1 (w 1 ) # 2 (w 2 ) Wille and Ganter in [24, 15] provide a general framework for understanding conceptual scaling of single valued contexts. A scale for a single valued context K = G, M, I) is introduced as a context S = G S , M S , I S ) The two contexts are connected by a special type of map called an S measure. An S measure from K to S is ....

R. Wille and B. Ganter, "Conceptual scaling," Technical Report of the Fachbereich Mathematik 1174, Technical University of Darmstadt, 1988.

....1. 3 Formal Concept Analysis Formal Concept Analysis (FCA) is a technique of data analysis first introduced by Rudolf Wille as a way to restructure latice theory [15] Since its inception in 1982, FCA has grown into a large field with successful applications in Psychology [16, 17] Social Science [18] Civil Engineering [19] and Software Engineering [20, 21, 22] An exposition of the mathematical foundations of formal concept analysis is beyond the scope of this thesis. For a complete and rigorous presentation of the notation and theorems used in this thesis the reader is directed to Ganter ....

....of extension of a term is trivially converted into a sequence of intervals containing document numbers of documents possessing the term. For example, if the term m is not present in documents 1, 7, 8, 13, 15, 19 then we can generate the sequence of intervals [1 6] 9 12] 14 14] [16 18] . The algorithm split across Figures 2.18 and 2.19 follows the same principle as the algorithm in Figure 2.16 but makes use of intervals. The heap, T , now stores interval attribute pairs. The ordering on the pairs is still generated from the document interval part of the pair with ( a, b] ....

B. Ganter and R. Wille, "Conceptual scaling," in Applications of combinatorics and graph theory to the biological and social sciences (F. Roberts, ed.), pp. 139--167, New York: Springer-Verlag, 1989.

....and comprehensible interpretation of the information seen as a sematic net [25] In our approach the lattice is incrementally changed by adding a new case and refining the existing cases. Conceptual Scaling Conceptual scaling has been introduced in order to deal with many valued attributes [11]. A many valued context is defined as a formal context (K) G, M, W, I) where G is a set of objects, M is a set of attributes, W is a set of attribute values. I is a ternary relation between G, M and W which indicates where an object g has the attributes value w for the attribute m. Then, if ....

Ganter, B. and Wille, R. Conceptual Scaling, In: F. Roberts (ed.): Application of Combinatorics and Graph Theory to the Biological and Social Sciences, Springer, 139-167, 1989.

....lattices, skeletons and specific convex sets to analyse the structure of free bounded distributive lattices generated by finite ordered sets. For the main results of this paper we use the methods of formal concept analysis. This approach was developed by R. Wille and others (see [4] 10] and [3]) In the second section we give the basic definitions and results of formal concept analysis and introduce the skeleton of a finite lattice. The third section contains representations of free bounded distributive lattices generated by an ordered set and their skeletons as concept lattices. The ....

....definition see ( 5, Definition 2, p. 39] The results described in the following sections are based on the theory of formal concept analysis. Therefore we recall some definitions and basic facts of formal concept analysis. Proofs are omitted and interested readers are refered to [4] 10] and [3]. A triple K : G; M; I) is called a context if G and M are sets and I is a binary relation between G and M , i.e. I G Theta M . The elements of G and M are called objects and attributesand I is called the incidence relationbetween G and M . For A G and B M the derivations are defined by ....

Ganter B. and Wille R., Conceptual scaling, In F. Roberts: Applications of combinatorics and graph theory in the biological and social sciences, Springer-Verlag, New York, 1989, pp. 139--167.

..... The triple (G; M;R) is called a context. The lattice arises from that context by applying a Galois connection between the power sets of G and M . This Galois connection is a particular one, called the polar ( 8] Various applications of concept lattices have been reported in the literature ([9, 5, 6, 10]) Typically, such an application assumes a subset of G (resp. M) to be given as input for which a corresponding subset of M (resp. G) is computed (if such exists) by searching the concept lattice (knowledge base) for a concept having the smallest extent containing the given subset of G. So, for ....

Ganter, B. and Wille, R. (1989) Conceptual scaling. In F. Roberts (editor), Applications of combinatorics and graph theory to the biological and social sciences, 139-167, SpringerVerlag.

.... is found in (Fisher et al. 1991; Gennari et al. 1990) The practical application of using Galois lattices has resulted in many developments concerning the visualization of the lattice using computer generated diagrams (Wille, 1984) its simplification through decompositions or pruning heuristics (Ganter Wille, 1989; Godin Mili, 1993; Mephu Nguifo, 1993) its use in an interactive knowledge acquisition process and the generation of rules from the lattice (Guigues Duquenne, 1986; Wille, 1992) which can be used for knowledge discovery in databases (Godin Missaoui, 1994) In (Missaoui Godin, 1994) we ....

Ganter, B. & Wille, R. (1989). Conceptual Scaling. In F. Roberts (Eds.), Applications of Combinatorics and Graph Theory to the Biological and Social Sciences, (pp. 139-167). New York: Springer-Verlag.

....inherently different properties. CHAPTER 11. CONCLUSION 123 We propose an alternate approach for reducing the set of potential indices through the use of formal concept analysis [153] Formal concept analysis is based on a mathematical, set theoretic model of concepts and conceptual hierarchies [62, 155]. It was developed as a new approach to data analysis that permits structural analysis of data without reducing the data. Concept analysis provides a formal, objective, data driven technique for automatically constructing a hierarchy of relationships from a set of objects (e.g. landscape models) ....

B. Ganter and R. Wille. Conceptual scaling. In F. Roberts, editor, Applications of Combinatorics and Graph Theory to the Biological Sciences, volume 17, pages 139--167. Springer-Verlag, New York, 1989.

....to transform a many valued context ( Omega ; Y; O; I) into a formal context ( Omega ; P; E) whose extents can be thought of as the meaningful subsets of Omega . From this formal context, conceptual hierachies can be explored and represented by line diagrams based on concept lattices (cf. [5]) It must be emphasized that the transformation itself can never be conducted automatically because it depends on the research questions. Hence, scaling is a first, purpose oriented interpretation of the data. The approach of logical scaling itself was developed when we tried to integrate the ....

Ganter, B. / Wille, R. (1989): Conceptual scaling, in: F. Roberts (ed.): Applications of combinatorics and graph theory to the biological and social sciences, Springer--Verlag, New York, 139 -- 167

....area information systems such as Nebula. It is a new approach to the analysis of information, which provides the mathematical foundation for faceted, synthetic classification. This is the appropriate model for the organization of knowledge in dynamic view oriented NIDR systems. Conceptual scaling [4] provides the mathematical foundation for faceted analysis via the user s view and interpretation of information. A flexible dynamic organizing browsing mechanism, based on ideas from conceptual scaling, is important as publishing moves from a push model, where an editor determines what readers ....

....of documents (see Figure 2 in [1] Nebula contexts are instances of the Concept Analysis notion of a many valued context. The unanalyzed and uninterpreted data of many application domains can often be conceptualized as a constrained collection of many valued contexts. A many valued context [4] is a quadruple hG; N;D; OEi, where: G is a set of objects, which models the set of file objects and views in Nebula; N is a set of sorts, which model attribute tags in Nebula (and database or entity relationship attributes) D = fD a j a 2Ng is an N indexed collection of domains of values, ....

Bernhard Ganter and Rudolf Wille. Conceptual scaling. In F. Roberts, editor, Applications of Combinatorics and Graph Theory in the Biological and Social Sciences, pages 139--167. Springer, New York, 1989.

No context found.

Ganter, B., & Wille, R. (1989). Conceptual scaling. In F. Roberts (Ed.), Applications of combinatorics and graph theory to the biological and social sciences. Berlin: Springer, 139-167.

No context found.

B. Ganter and R. Wille. Conceptual scaling. In F. Roberts, editor, Applications of combinatorics and graph theory to the biological and social sciences, pages 139--167, New York, 1989. Springer-Verlag.

No context found.

Ganter, B. and Wille, R. (1989). Conceptual Scaling, In: F. Roberts (ed.): Application of Combinatorics and Graph Theory to the Biological and Social Sciences, Springer, 139167.

No context found.

Ganter, B., R. Wille; Conceptual Scaling. In: F.Roberts (ed.) Applications of combinatorics and graph theory to the biological and social sciences,139-167. Springer Verlag, New York, 1989. 213

No context found.

Bernhard Ganter, Rudolf Wille (1989): Conceptual Scaling. In: F.Roberts (ed.): Applications of combinatorics and graph theory to the biological and social sciences. Springer Verlag, New York, 139-167.

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