Ganter B. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984, 28 p. Home/Search Document Not in Database Summary Related Articles Check |
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Representing a Concept Lattice By a Graph - Berry, Sigayret (2002) (Correct)
....or properties, saturate it, and extract the sub relation corresponding to the successors of this minimal separator. 6 Generating the closed sets 6. 1 Generating and storing the closed sets Recent work has been done on the e cient generation of the closed sets de ned by a binary relation (see [11], 5] 20] both when one wants to store all the closed sets, and when one simply wants to encounter all of them at least once. 9 In parallel, recent work has been done to generate all the minimal separators or all the minimal xy separators of a graph (see [25] 16] 7] 24] As an ....
....the height of a lattice cannot exceed n. 10 In the worse case, generating an element A B requires O(mjAj) The total time complexity required is in O(nm) per element, which matches the corresponding best time algorithm for generating the elements without storing them, proposed by Ganter (see [11]. 7 Conclusion Though speci c problems such as minimizing the number of times a database is accessed remain to be translated in terms of graph separators, we have presented a new approach to answering queries on the concept lattice of a binary relation, which uses a rapidly growing toolbox: the ....
B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984.
Obtaining and Maintaining Polynomial-Sized Concept Lattices - Berry, Sigayret (2002) (Correct)
....3 2 4 5 6 f e d a b 1 S C 1 C 2 Figure 3. Separator S = fa; d; e; f; 3; 4; 5; 6g of GR . This enables us to use existing algorithms for generating the minimal separators of a graph (see [21] 20] 15] 5] to efficiently generate the concepts, matching the best complexities of [16] and [9]. Moreover, if we add in GR the edges necessary to make S into a clique, defining a new relation R , which is obtained from R by deleting the corresponding crosses, then concept lattice L(R ) is the sub lattice obtained from L(R) by removing all the elements which are not comparable to ....
B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984.
Efficient Concept Generation - Berry, Bordat, Sigayret (Correct)
....sigayret isima.fr LIRMM, 161 Rue Ada, 34392 Montpellier, France. Mail: bordat lirmm.fr. When the concepts do not need to be stored, but only encountered at least once, the space problem becomes easier, though the running time per concept is higher: the best such algorithm, due to Ganter ([9]) runs in O(n ) time per concept, using the interesting notion of lectic order, which avoids scanning all the possible subsets of properties, without, however, avoiding re computing the same concept O(n) times. In this paper, we address the issue of eciently computing all the concepts, ....
B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984.
Representing a Concept Lattice By a Graph - Berry, Sigayret (2002) (Correct)
....as: a 236; b 123; c 125 and d 145. 7 Generating the concepts Recent work has been done on the e cient generation of the concepts de ned by a binary relation. One may want to generate and store all the concepts (see [27] or simply encounter each at least once, without storing them (see [13]) or one may want to compute the concepts along with their structure, i.e. the arcs of the graph representing the relationships between elements of the lattice (see [10] In parallel, recent work has been done to generate all the minimal separators or all the minimal xy separators of a graph ....
....we will never consider a again to generate a successor, unless we want to also generate the structure. In the worse case, generating an element A B requires O(m jAj) which matches the corresponding best time algorithm for generating the elements without storing them, proposed by Ganter (see [13]) as well as for generating the structure, as proposed by Bordat (see [10] It may be that in practise our approach will be reduced to using only linear mean time per element; in our example, no element will be computed several times if we process the vertices in alphabetical order. 8 ....
B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984.
The Management And Visualisation Of Document Collections Using.. - Cole (2000) (1 citation) (Correct)
....spent considerable e#ort trying to ensure that it was possible for the target collection of texts to be able to calculate the concept lattice prior to navigation by the user. This problem can be avoided by calculating sub lattice or sub semilattice on demand rather than a priori. Ganter et al.[36] suggested a modification to his next concept algorithm that would for a given concept calculate the lower cover in linear time and present these additional concepts to the user for selection. The user then selects a more specific concept by a choosing an attribute. More recently, Ferre and Ridoux ....
B. Ganter, "Two basic algorithms in concept analysis," tech. rep., Hochschule Darmstadt, 1984.
A Knowledge Representation For Information Filtering Using.. - Eklund, Cole (Correct)
....conceptual scales augmented with new elements. These new elements are concepts in the concept lattice that correspond to the conjunction of a number of medical concepts in the scale produced by the user. The creation of the lattices for each conceptual scale is performed using Ganter s Algorithm[5]. Figure 4 shows an example of a lattice that results from the conceptual scale in figure 3. This scale has elements labeled MeSH , Disease , Glaucoma , Asthma and Carcinoma . These elements correspond to medical concepts in MeSH, and become the attributes in the concept lattice shown in ....
B Ganter. Two basic algorithms in concept analysis. Technical report, Hochschule Darmstadt, 1984.
Using Conceptual Scaling In Formal Concept Analysis For.. - Cole, Eklund, Walker (1998) (1 citation) (Correct)
....conceptual scales are augmented with new elements. These new elements are concepts in the concept lattice corresponding to the conjunction of a number of medical concepts in the scale produced by the user. The creation of the lattices for each conceptual scale is performed using Ganter s Algorithm[5]. Figure 5 is shows an example of a conceptual scale and a possible lattice that would result from that conceptual scale. The conceptual scale, shown in figure 5(a) has elements labelled MeSH , Disease , Glaucoma , Asthma and Carcinoma . These elements corresponds to medical concepts in ....
B Ganter. Two basic algorithms in concept analysis. Technical report, Hochschule Darmstadt, 1984.
Incremental concept formation algorithms based on Galois.. - Godin, Missaoui, Alaoui (1995) (38 citations) (Correct)
.... pairs (Godin et al. 1986; Wille, 1992) conceptual graphs and use of feature taxonomies (Godin Mili, 1993; Mineau Godin, 1994) Many algorithms have been proposed for generating the Galois lattice from a binary relation (Bordat, 1986; Carpineto Romano, 1993; Chein, 1969; Fay, 1975; Ganter, 1984; Godin, Missaoui Alaoui, 1991; Malgrange, 1962; Norris, 1978) Only two of these (Carpineto Romano, 1993; Godin et al. 1991) incrementally update the lattice and the corresponding Hasse diagram. This feature is necessary in many applications. As argued in (Frawley, Piatetsky Shapiro ....
Ganter, B. (1984). Two Basic Algorithms in Concept Analysis. Preprint 831, Technische Hochschule Darmstadt.
Comparing Performance of ELL and Ganter Algorithm for.. - LEVY, EMILION, BAKLOUTI (2004) Self-citation (Ganter) (Correct)
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Ganter B. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984, 28 p.
Pseudo-Models and Propositional Horn Inference - Ganter, Krauße (2003) (3 citations) Self-citation (Ganter) (Correct)
....general, an NP complete problem to decide if there is a model at all. When the cumulated clauses are of a special form, things may be easier. Implications, for example, admit a linear time algorithm that nds the smallest model containing a given set. We present an algorithm (similar to that in [2], cf. 4] Section 2.1) that constructs the models of a given set L of cumulated clauses in a certain lexicographical order. To de ne this order, x some linear order of M . In what follows, we shall w.l.o.g. assume that M : f1 2 : ng, but this is only for simplicity (in Section 6 we ....
Bernhard Ganter. Two basic algorithms in concept analysis. FB4{Preprint No 831, TH Darmstadt, 1984.
Pseudo-Models and Propositional Horn Inference - Ganter, Krauße (1999) (3 citations) Self-citation (Ganter) (Correct)
....general, an NP complete problem to decide if there is a model at all. When the cumulated clauses are of a special form, things may be easier. Implications, for example, admit a linear time algorithm that finds the smallest model containing a given set. We present an algorithm (similar to that in [2], cf. 4] Section 2.1) that contructs the models of a given set L of cumulated clauses in a certain lexicographical order. To define this order, fix some linear order of M . In what follows, we shall w.l.o.g. assume that M : f1 2 : ng, but this is only for simplicity (in Section 6 we ....
Bernhard Ganter. Two basic algorithms in concept analysis. FB4--Preprint No 831, TH Darmstadt, 1984.
Building concept (Galois) lattices from parts: Generalizing .. - Valtchev, Missaoui (Correct)
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B. Ganter. Two basic algorithms in concept analysis (preprint). Technical Report 831, Technische Hochschule, Darmstadt, 1984.
Concept Lattices and Undirected Graphs - Berry (2004) (Correct)
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B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt (1984).
A Generic Scheme for the Design of Efficient On-Line.. - Valtchev, Hacene.. (Correct)
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B. Ganter. Two basic algorithms in concept analysis. preprint 831, Technische Hochschule, Darmstadt, 1984.
Towards Scalable Divide-and-Conquer Methods for Computing.. - Valtchev, Duquenne (Correct)
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B. Ganter. Two basic algorithms in concept analysis. preprint 831, Technische Hochschule, Darmstadt, 1984.
Comparing Performance of Algorithms for Generating Concept.. - Kuznetsov, Obedkov (9 citations) (Correct)
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Ganter, B., Two Basic Algorithms in Concept Analysis, FB4-Preprint No. 831, TH Darmstadt, 1984.
A Partition-Based Approach towards Constructing Galois.. - Valtchev, Missaoui.. (2002) (1 citation) (Correct)
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B. Ganter. Two basic algorithms in concept analysis. preprint 831, Technische Hochschule, Darmstadt, 1984.
Characterization of Image Sets: The Galois Lattice Approach - Zenou, Samuelides (2003) (Correct)
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B. Ganter, "Two basics algorithms in concept analysis, " Tech. Rep., Technische Hochschule Darmstadt, 1984.
Representing a Concept Lattice By a Graph - Berry, Sigayret (2004) (Correct)
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B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt (1984).
A Fast Algorithm for Building the Hasse Diagram of a.. - Valtchev, Missaoui.. (Correct)
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B. Ganter. Two basic algorithms in concept analysis (preprint). Technical Report 831, Technische Hochschule, Darmstadt, 1984.
Concepts Can't Afford to Stammer - Berry, Bordat, Sigayret (Correct)
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B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984.
Structuration of Phenotypes / Genotypes through.. - Duquenne.. (2001) (1 citation) (Correct)
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Ganter B.: Two basic algorithms in concept analysis, Preprint THD Darmstadt n 831. German transl. in B. Ganter, R. Wille, K.E. Wolf (eds): Beitrage zur Begriffsanalyse, B. I. Wissenschaftsverlag, Mannheim (1987) 241-254.
Weaving through a Crowd of Minimal Separators - Berry (2003) (Correct)
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B. Ganter. Two basic algorithms in concept analysis. Preprint 831, Technische Hochschule Darmstadt, 1984.
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