## Fast concept analysis (2000)

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Venue: | Working with Conceptual Structures – Contributions to ICCS 2000 |

Citations: | 30 - 1 self |

### BibTeX

@INPROCEEDINGS{Lindig00fastconcept,

author = {Christian Lindig},

title = {Fast concept analysis},

booktitle = {Working with Conceptual Structures – Contributions to ICCS 2000},

year = {2000},

pages = {152--161},

publisher = {Shaker Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Formal concept analysis is increasingly used for large contexts that are built by programs. This paper presents an efficient algorithm for concept analysis that computes concepts together with their explicit lattice structure. An experimental evaluation uses randomly generated contexts to compare the running time of the presented algorithm with two other algorithms. Running time increases quadratically with the number of concepts, but with a small quadratic component. At least contexts with sparsely filled context tables cause concept lattices grow quadratically with respect to the size of their base relation. The growth rate is controlled by the density of context tables. Modest growth combined with efficient algorithms lead to fast concept analysis. 1

### Citations

605 |
The Definition of Standard ML (Revised
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- 1997
(Show Context)
Citation Context ... 0.04699 Lattice 7.76410 -8 0.00116-0.03158 NextConcept 3.25510 -8 0.00026 0.00101 system, a functional programming language and dialect of Standard ML that is known for emitting e#ective native code =-=[5, 9]-=-. All tests were ran on an otherwise idle 200 MHz AMD K6 Linux 2.0 system. The experiment used 1 000 randomly generated contexts (G, M, I). Their corresponding context tables were between 1 2 and 81 8... |

109 |
Introduction to Algorithms. The MIT Electrical Engineering and Computer Science Series
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- 2001
(Show Context)
Citation Context ...o di#erent concepts may share an upper neighbor; it must be identified while processing its lower neighbors as lattice elements are unique. For this purpose all concepts are stored in a search tree L =-=[1]-=-. Each neighbor is first searched (using lookup) in tree L to find previously inserted instances of that concept. In case the concept is found, the existing lists of neighbors are updated; otherwise t... |

108 | Tip: Reengineering Class Hierarchies Using Concept Analysis
- Snelting, F
- 1999
(Show Context)
Citation Context ... concern. But concept analysis is used increasingly for applications like program analysis inside a compiler or is combined with statistical analysis where a large context is constructed by a program =-=[10, 11, 8]-=-. The resulting concept lattice is no longer inspected visually but is considered as a data structure that is part of the program. For these applications the algorithmic complexity of concept analysis... |

105 | Incremental concept formation algorithms based on galois (concept) lattices
- Godin, Missaoui, et al.
- 1995
(Show Context)
Citation Context ...ts detects the lattice structure by post-processing the output of Algorithm NextConcept which takes O(|L| 2 ) time. It basically implements the Algorithm Ganter-Alaoui as described by Godin et al. in =-=[6]-=-. For all algorithms the CPU time spent versus the lattice size is shown in Fig. 4. Although the overall lattice structure has some impact on the running time of all algorithms, running time depends f... |

105 | Identifying Modules Via Concept Analysis
- Siflf, Reps
- 1997
(Show Context)
Citation Context ... concern. But concept analysis is used increasingly for applications like program analysis inside a compiler or is combined with statistical analysis where large contexts are constructed by a program =-=[14, 15, 11]-=-. The resulting concept lattice is no longer inspected visually but is part of an application’s internal data structure. For these 1applications the algorithmic complexity of concept analysis does ma... |

74 | A Lattice Conceptual Clustering System and Its Application to Browsing Retrieval
- Carpineto, Romano
- 1996
(Show Context)
Citation Context ...s that had also a high fill ratio, which means their context table were relatively dense. 5 Comparison Algorithms to compute concept lattices and the size of concept lattices have been studied before =-=[13, 6, 1, 4]-=-. Although the two algorithms presented here do not lead to improved complexity results, they are based on a new theorem that leads to a remarkable simple implementation of concept analysis. Godin et ... |

73 |
R.: TOSCANA - a graphical tool for analyzing and exploring data
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- 1994
(Show Context)
Citation Context ...uted concept lattices. Contexts in these applications tend to have a modest size because otherwise the resulting concept lattices are hard to analyze visually, even with support of tools like Toscana =-=[13]-=-. The algorithmic complexity of concept analysis for these applications is consequently a minor concern. But concept analysis is used increasingly for applications like program analysis inside a compi... |

73 |
Formale Begriffsanalyse. Mathematische Grundlagen
- Ganter, Wille
- 1996
(Show Context)
Citation Context ... context tables. Modest growth combined with efficient algorithms lead to fast concept analysis. 1 Introduction Concept analysis has proven to be a valuable tool for gaining insight into complex data =-=[5, 16]-=-. In many applications of concept analysis experts learn from formal contexts by inspecting their carefully layed out concept lattices. Contexts in these applications tend to have a modest size. Other... |

50 | A.: Experimental comparison of navigation in a Galois lattice with conventional information retrieval method
- Godin, Missaoui, et al.
- 1993
(Show Context)
Citation Context ...ry variable relates to the notion of attributes per object used earlier. Their experiments, as well as ours, show a quadratic growth of the number of concepts with increasing context size. In [6] and =-=[7]-=- Godin et al. suspected the lattice size to increase linearly with the number of attributes per object. Our experiments suggest that this may be only the case when this number is small: looking at a f... |

28 | Concept-based component retrieval
- Lindig
- 1995
(Show Context)
Citation Context ...4. . . 0.06 0.00032621 0.26237 52.876 685 51 2286 0.08. . . 0.08 0.00048146 0.29659 36.275 697 74 2856 0.08. . . 0.10 0.00067034 0.29714 40.730 849 105 3792 libraries where sparse contexts are common =-=[6, 8]-=-. While looking for functional relations between a context and its number of concepts, di#erent context parameter were considered. The context parameter found to predict the size of a lattice best was... |

7 | Stepwise construction of the Dedekind-MacNeille completion
- Ganter, Kuznetsov
- 1998
(Show Context)
Citation Context ... results. 1 Figure 1: Scetch for Theorem 1; shown are the extents of concepts. 2 Computing the Concept Lattice Ganter's algorithm NextConcept is probably the best known algorithm for concept analysis =-=[2, 3]-=-. It computes all concepts L(G, M, I) from a context (G, M, I) in a total lectical order. The algorithm's asymptotic running time O(|G| 2s|M|s|L(G, M,I)|) depends only linearly on the size of the conc... |

5 |
Formale Begri sanalyse: Mathematische Grundlagen
- Ganter, Wille
- 1996
(Show Context)
Citation Context ...f context tables. Modest growth combined with e#cient algorithms leads to fast concept analysis. 1 Introduction Concept analysis has proven to be a valuable tool for gaining insight into complex data =-=[4, 12]-=-. In many applications of concept analysis experts learn from formal contexts by inspecting their carefully layouted concept lattices. Contexts in these applications tend to have a modest size because... |

5 |
Algorithmen zur Begriffsanalyse und ihre Anwendung bei
- Lindig
- 1999
(Show Context)
Citation Context ... concern. But concept analysis is used increasingly for applications like program analysis inside a compiler or is combined with statistical analysis where large contexts are constructed by a program =-=[14, 15, 11]-=-. The resulting concept lattice is no longer inspected visually but is part of an application’s internal data structure. For these 1applications the algorithmic complexity of concept analysis does ma... |

4 | Identifying modules via concept analysis
- Si, Reps
- 1997
(Show Context)
Citation Context ... concern. But concept analysis is used increasingly for applications like program analysis inside a compiler or is combined with statistical analysis where a large context is constructed by a program =-=[10, 11, 8]-=-. The resulting concept lattice is no longer inspected visually but is considered as a data structure that is part of the program. For these applications the algorithmic complexity of concept analysis... |

3 |
Beitraäge zur Begriffsanalyse. Chapter Algorithmen zur Formalen Begriffsanalyse, BI-Wissenschaftsverlag
- Ganter
- 1987
(Show Context)
Citation Context ...rithm for computing the concept lattice and some empirical complexity results. 2 Computing the Concept Lattice Ganter’s algorithm NextConcept is probably the best known algorithm for concept analysis =-=[3, 4]-=-. It computes all concepts L(G, M, I) from a context (G, M, I) in a total lectical order. The algorithm’s asymptotic running time O(|G| 2 × |M| × |L(G, M, I)|) depends only linearly on the size of the... |

2 |
Concepts. ftp://ftp.ips.cs.tu-bs.de/pub/local/softech/misc/ concepts-0.3d.tar.gz
- Lindig
- 1997
(Show Context)
Citation Context ... NextConcept and Lattice. Additionally, a third Algorithm Concepts was applied; it is used in the author's program concepts which has gained some popularity for computing concept lattices in the past =-=[7]-=-. It was re-implemented in Objective Caml and utilizes Algorithm NextConcept internally. Algorithm Concepts detects the lattice structure by post-processing the output of Algorithm NextConcept which t... |

1 |
Beitrage zur Begri#sanalyse, Kapitel Algorithmen zur Formalen Begri#sanalyse. BI-Wissenschaftsverlag
- Ganter
- 1987
(Show Context)
Citation Context ... results. 1 Figure 1: Scetch for Theorem 1; shown are the extents of concepts. 2 Computing the Concept Lattice Ganter's algorithm NextConcept is probably the best known algorithm for concept analysis =-=[2, 3]-=-. It computes all concepts L(G, M, I) from a context (G, M, I) in a total lectical order. The algorithm's asymptotic running time O(|G| 2s|M|s|L(G, M,I)|) depends only linearly on the size of the conc... |

1 |
Objective Caml. Open-Source licensed functional programming language. http://caml.inria.fr
- Leroy
(Show Context)
Citation Context ... 0.04699 Lattice 7.76410 -8 0.00116-0.03158 NextConcept 3.25510 -8 0.00026 0.00101 system, a functional programming language and dialect of Standard ML that is known for emitting e#ective native code =-=[5, 9]-=-. All tests were ran on an otherwise idle 200 MHz AMD K6 Linux 2.0 system. The experiment used 1 000 randomly generated contexts (G, M, I). Their corresponding context tables were between 1 2 and 81 8... |

1 |
Algorithmen zur Begri#sanalyse und ihre Anwendung bei Softwarebibliotheken
- Lindig
- 1999
(Show Context)
Citation Context ... concern. But concept analysis is used increasingly for applications like program analysis inside a compiler or is combined with statistical analysis where a large context is constructed by a program =-=[10, 11, 8]-=-. The resulting concept lattice is no longer inspected visually but is considered as a data structure that is part of the program. For these applications the algorithmic complexity of concept analysis... |

1 |
Open Source implementation of concept analysis
- 3d
- 1997
(Show Context)
Citation Context ... NextConcept and Lattice. Additionally, a third Algorithm Concepts was applied; it is used in the author’s program concepts which has gained some popularity for computing concept lattices in the past =-=[10]-=-. It was re-implemented in Objective Caml and utilizes Algorithm NextConcept internally. Algorithm Concepts detects the lattice structure by post-processing the output of Algorithm NextConcept which t... |

1 |
Abschätzung f”ur die Anzahl der Begriffe von Kontexten
- Schütt
- 1987
(Show Context)
Citation Context ...s that had also a high fill ratio, which means their context table were relatively dense. 5 Comparison Algorithms to compute concept lattices and the size of concept lattices have been studied before =-=[13, 6, 1, 4]-=-. Although the two algorithms presented here do not lead to improved complexity results, they are based on a new theorem that leads to a remarkable simple implementation of concept analysis. Godin et ... |