## Comparing Performance of Algorithms for Generating Concept Lattices (2002)

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Venue: | JOURNAL OF EXPERIMENTAL AND THEORETICAL ARTIFICIAL INTELLIGENCE |

Citations: | 91 - 8 self |

### BibTeX

@ARTICLE{Kuznetsov02comparingperformance,

author = {Sergei O. Kuznetsov and Sergei Obiedkov},

title = {Comparing Performance of Algorithms for Generating Concept Lattices},

journal = {JOURNAL OF EXPERIMENTAL AND THEORETICAL ARTIFICIAL INTELLIGENCE},

year = {2002},

volume = {14},

pages = {189--216}

}

### Years of Citing Articles

### OpenURL

### Abstract

Several algorithms that generate the set of all formal concepts and diagram graphs of concept lattices are considered. Some modifications of wellknown algorithms are proposed. Algorithmic complexity of the algorithms is studied both theoretically (in the worst case) and experimentally. Conditions of preferable use of some algorithms are given in terms of density/sparseness of underlying formal contexts. Principles of comparing practical performance of algorithms are discussed.

### Citations

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Data structures and algorithms
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(Show Context)
Citation Context ...ial w.r.t. the input. Moreover, some important operations, such as finding a concept, are performed for some representations (spanning trees [2, 10], ordered lists [7], CbO trees [16], 2-3 trees, see =-=[1]-=- for the definition) in polynomial time, but for some other representations (unordered lists) they can be performed only in exponential time. A representation of a concept lattice can be considered re... |

272 |
Formal Concept Analysis
- Ganter, Wille
- 1999
(Show Context)
Citation Context ... with polynomial time delay and space linear in the number of all concepts (modulo some factor polynomial in the input size). First, we give some standard definitions of Formal Concept Analysis (FCA) =-=[8]-=-. A formal context is a triple of sets (G, M, I), where G is called a set of objects, M is called a set of attributes, and I ⊆ G × M. ForA ⊆ G and B ⊆ M: A' ={m ∈ M | ∀g∈A (gIm)}, B' ={g ∈ G | ∀m∈B (g... |

74 | A Lattice Conceptual Clustering System and Its Application to Browsing Retrieval
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(Show Context)
Citation Context ...gorithms are discussed. 1 Introduction Concept (Galois) lattices proved to be a useful tool in many applied domains: machine learning, data mining and knowledge discovery, information retrieval, etc. =-=[3, 6, 9, 22, 23]-=-. The problem of generating the set of all concepts and the concept lattice of a formal context is extensively studied in the literature [2-5, 7, 11, 13, 16, 18–22]. It is known that the number of con... |

53 |
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Citation Context ...ata used for tests. The fact that the choice of the algorithm should be dependent on the input data is not accounted for. Besides, only one of the algorithms considered in [13], namely that of Bordat =-=[2]-=-, constructs the diagram graph; thus, it is hard to compare its time complexity with that of the other algorithms. A later review with more algorithms and more information on experimental data can be ... |

49 |
A Fast Algorithm for Building Lattices
- Nourine, Raynaud
- 1999
(Show Context)
Citation Context ...ests were conducted only for contexts with small number of attributes per object as compared to the number of all attributes. Our experiments (we consider some other algorithms, e.g., that of Nourine =-=[21]-=-) also show that the algorithm proposed in [11] works faster on such contexts than the others do. However, in other situations not covered in [11] this algorithm is far behind some other algorithms. T... |

37 | Conceptual Knowledge Discovery in Databases Using Formal Concept Analysis Methods
- Stumme, Wille, et al.
(Show Context)
Citation Context ...gorithms are discussed. 1 Introduction Concept (Galois) lattices proved to be a useful tool in many applied domains: machine learning, data mining and knowledge discovery, information retrieval, etc. =-=[3, 6, 9, 22, 23]-=-. The problem of generating the set of all concepts and the concept lattice of a formal context is extensively studied in the literature [2-5, 7, 11, 13, 16, 18–22]. It is known that the number of con... |

28 |
Efficient Algorithms for Listing Combinatorial Structures
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Citation Context ...aid to have polynomial delay [14] if it executes at most polynomially many computation steps before either outputting each next structure or halting. An algorithm is said to have a cumulative delay d =-=[12]-=- if it is the case that at any point of time in any execution of the algorithm with any input p the total number of computation steps that have been executed is at most d(p) plus the product of d(p) a... |

25 |
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Citation Context ...ques for building diagram graphs; the attributes of the context in Table 1 describe only construction of the concept set. All the algorithms can be divided into two categories: incremental algorithms =-=[3, 5, 11, 20]-=-, which, at the ith step, produce the concept set or the diagram graph for i first 37S. Kuznetsov & S. Ob’’edkov ICCS’01 Int’l. Workshop on Concept Lattices−based KDD objects of the context, and batc... |

18 |
Construction du treillis de Galois d’une relation binaire
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(Show Context)
Citation Context ...ting concept lattices and their diagram graphs is a challenging and multifaceted one. The first comparative study of several algorithms constructing the concept set and diagram graphs can be found in =-=[13]-=-. However, the formulation of the algorithms is not always correct, and the description of the results of the experimental tests lacks any information about data used for tests. The fact that the choi... |

12 |
Algorithme de recherche des sous-matrices premières d’une matrice
- Chein
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(Show Context)
Citation Context ...etsov & S. Ob’’edkov ICCS’01 Int’l. Workshop on Concept Lattices−based KDD objects of the context, and batch ones, which build the concept set and its diagram graph for the whole context from scratch =-=[2, 4, 7, 16, 18, 24]-=-. Besides, any batch algorithm typically adheres to one of the two strategies: top–down (from the maximal extent to the minimal one) or bottom–up (from the minimal extent to the maximal one). However,... |

12 |
Formalizing Hypotheses with Concepts
- Ganter, Kuznetsov
(Show Context)
Citation Context ...gorithms are discussed. 1 Introduction Concept (Galois) lattices proved to be a useful tool in many applied domains: machine learning, data mining and knowledge discovery, information retrieval, etc. =-=[3, 6, 9, 22, 23]-=-. The problem of generating the set of all concepts and the concept lattice of a formal context is extensively studied in the literature [2-5, 7, 11, 13, 16, 18–22]. It is known that the number of con... |

12 |
Interpretation on Graphs and Complexity Characteristics of a Search for Specific Patterns, Automatic Documentation and
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- 1989
(Show Context)
Citation Context ...18–22]. It is known that the number of concepts can be exponential in the size of the input context (e.g., when the lattice is a Boolean one) and the problem of determining this number is #P-complete =-=[15]-=-. Therefore, from the standpoint of the worst-case complexity, an algorithm generating all concepts and/or a concept lattice can be considered optimal if it generates the lattice with polynomial time ... |

9 |
A Fast Algorithm for Computing All Intersections of Objects in a Finite Semi-lattice
- Kuznetsov
- 1993
(Show Context)
Citation Context ...atter in time polynomial w.r.t. the input. Moreover, some important operations, such as finding a concept, are performed for some representations (spanning trees [2, 10], ordered lists [7], CbO trees =-=[16]-=-, 2-3 trees, see [1] for the definition) in polynomial time, but for some other representations (unordered lists) they can be performed only in exponential time. A representation of a concept lattice ... |

8 |
Algorithm for the Construction of the Set of All Concepts and Their Line Diagram
- Kuznetsov, Ob’’edkov
- 2000
(Show Context)
Citation Context ... the concept set construct also the diagram graph, we attempted to modify some algorithms making them able to construct diagram graphs. The versions of algorithms used for comparison are presented in =-=[17]-=-. As mentioned above, data structures that realize concept sets and diagram graphs of concept lattices are of great importance. Since their sizes can be exponential w.r.t. the input size, some their n... |

8 |
Using Lattice-Based Framework As a Tool for Feature Extraction, in Feature Extraction, Construction and Selection: A Data Mining
- Nguifo, E, et al.
- 1998
(Show Context)
Citation Context ...rmance of this algorithm with those considered above and testing the algorithms on large databases, including “classical” ones, will be the subject of the further work. We can also mention works [3], =-=[19]-=- where similar algorithms were applied for machine learning and data analysis, e.g., in [19] a Bordat-type algorithm was used. The choice of an algorithm for construction of the concept lattice should... |

6 | Lakhal L., Fast Computation of Concept Lattices Using Data Mining Techniques
- Stumme, Taouil, et al.
(Show Context)
Citation Context |

5 | Algorithmen zur Begriffsanalyse und ihre Anwendung bei - Lindig - 1999 |

3 |
On the Irredundant Generation of Knowledge Spaces
- Dowling
- 1993
(Show Context)
Citation Context ...ques for building diagram graphs; the attributes of the context in Table 1 describe only construction of the concept set. All the algorithms can be divided into two categories: incremental algorithms =-=[3, 5, 11, 20]-=-, which, at the ith step, produce the concept set or the diagram graph for i first 37S. Kuznetsov & S. Ob’’edkov ICCS’01 Int’l. Workshop on Concept Lattices−based KDD objects of the context, and batc... |

3 |
Two Basic Algorithms
- Ganter
(Show Context)
Citation Context ...educed to the latter in time polynomial w.r.t. the input. Moreover, some important operations, such as finding a concept, are performed for some representations (spanning trees [2, 10], ordered lists =-=[7]-=-, CbO trees [16], 2-3 trees, see [1] for the definition) in polynomial time, but for some other representations (unordered lists) they can be performed only in exponential time. A representation of a ... |

2 |
Plausible Reasoning in Systems of JSM Type, Itogi Nauki i Tekhniki
- Finn
- 1991
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Citation Context |

1 |
Finding All Closed Sets: A
- Ganter, Reuter
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Citation Context ...ph and thus cannot be reduced to the latter in time polynomial w.r.t. the input. Moreover, some important operations, such as finding a concept, are performed for some representations (spanning trees =-=[2, 10]-=-, ordered lists [7], CbO trees [16], 2-3 trees, see [1] for the definition) in polynomial time, but for some other representations (unordered lists) they can be performed only in exponential time. A r... |

1 |
On Generating all
- Johnson, Yannakakis, et al.
- 1988
(Show Context)
Citation Context ...rithms not only in terms of input and output sizes, but also in terms of (cumulative) delay. Recall that an algorithm for listing a family of combinatorial structures is said to have polynomial delay =-=[14]-=- if it executes at most polynomially many computation steps before either outputting each next structure or halting. An algorithm is said to have a cumulative delay d [12] if it is the case that at an... |