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## Discovering Frequent Closed Itemsets for Association Rules (1999)

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Citations: | 403 - 13 self |

### Citations

3527 | Fast Algorithms for Mining Association Rules
- Agrawal, Srikant
- 1994
(Show Context)
Citation Context ...y of association rules was first introduced in [1]. This task consists in determining relationships between sets of items in very large databases. Agrawal's statement of this problem is the following =-=[1, 2]-=-. Let I = fi 1 ; i 2 ; : : : ; i m g be a set of m items. Let the database D = ft 1 ; t 2 ; : : : ; t n g be a set of n transactions, each one identified by its unique TID. Each transaction t consists... |

3242 | Mining association rules between sets of items in large databases
- Agrawal, Imielinski, et al.
- 1993
(Show Context)
Citation Context ...d that our approach is very valuable for dense and/or correlated data that represent an important part of existing databases. 1 Introduction The discovery of association rules was first introduced in =-=[1]-=-. This task consists in determining relationships between sets of items in very large databases. Agrawal's statement of this problem is the following [1, 2]. Let I = fi 1 ; i 2 ; : : : ; i m g be a se... |

1413 |
Introduction to Lattices and Order
- Davey, Priestley
- 1990
(Show Context)
Citation Context ...hanism based on the Galois connection, we define the closed itemset lattice which is a sub-order of the itemset lattice, thus often much smaller. This lattice is closely related to the Galois lattice =-=[4, 7]-=- also called concept lattice [19]. The closed itemset lattice can be used as a formal framework for discovering frequent itemsets given the basic properties that the support of an itemset I is equal t... |

800 |
Lattice Theory
- Birkhoff
- 1973
(Show Context)
Citation Context ...hanism based on the Galois connection, we define the closed itemset lattice which is a sub-order of the itemset lattice, thus often much smaller. This lattice is closely related to the Galois lattice =-=[4, 7]-=- also called concept lattice [19]. The closed itemset lattice can be used as a formal framework for discovering frequent itemsets given the basic properties that the support of an itemset I is equal t... |

594 | Dynamic itemset counting and implication rules for market basket data
- Brin, Motwani, et al.
- 1997
(Show Context)
Citation Context ...stical data. The synthetic datasets were generated using the program described in [2]. The census data were extracted from the Kansas 1990 PUMS file (Public Use Microdata Samples), in the same way as =-=[5]-=- for the PUMS file of Washington (unavailable through Internet at the time of the experiments). Unlike in [5] though, we did not put an upper bound on the support, as this distorts each algorithm resu... |

514 | Data Mining : An overview from a database perspective - Chen, Han, et al. - 1996 |

460 | Sampling large databases for association rules
- Toivonen
- 1996
(Show Context)
Citation Context ...om sequences and in finding keys or inclusion as well as functional dependencies from a relation [12]. All existing algorithms use one of the two following approach: a levelwise [12] bottom-up search =-=[2, 5, 13, 16, 17]-=- or a simultaneous bottom-up and top-down search [3, 10, 20]. Although they are dissimilar, all those algorithms explore the subset lattice (itemset lattice) for finding frequent itemsets: they all us... |

452 | Efficiently mining long patterns from databases
- Bayardo
- 1997
(Show Context)
Citation Context ... dependencies from a relation [12]. All existing algorithms use one of the two following approach: a levelwise [12] bottom-up search [2, 5, 13, 16, 17] or a simultaneous bottom-up and top-down search =-=[3, 10, 20]-=-. Although they are dissimilar, all those algorithms explore the subset lattice (itemset lattice) for finding frequent itemsets: they all use the basic properties that all subsets of a frequent itemse... |

426 | An efficient algorithm for mining association rules in large databases
- Savasere, Omiecinski, et al.
- 1995
(Show Context)
Citation Context ...om sequences and in finding keys or inclusion as well as functional dependencies from a relation [12]. All existing algorithms use one of the two following approach: a levelwise [12] bottom-up search =-=[2, 5, 13, 16, 17]-=- or a simultaneous bottom-up and top-down search [3, 10, 20]. Although they are dissimilar, all those algorithms explore the subset lattice (itemset lattice) for finding frequent itemsets: they all us... |

388 | New algorithms for fast discovery of association rules - Zaki, Parthasarathy, et al. - 1997 |

259 | Levelwise search and borders of theories in knowledge discovery
- Mannila, Toivonen
- 1997
(Show Context)
Citation Context ...ks demonstrated that the frequent itemset discovery is also the key stage in the search for episodes from sequences and in finding keys or inclusion as well as functional dependencies from a relation =-=[12]-=-. All existing algorithms use one of the two following approach: a levelwise [12] bottom-up search [2, 5, 13, 16, 17] or a simultaneous bottom-up and top-down search [3, 10, 20]. Although they are dis... |

234 | Efficient algorithms for discovering association rules
- Mannila, Toivonen, et al.
- 1994
(Show Context)
Citation Context ...om sequences and in finding keys or inclusion as well as functional dependencies from a relation [12]. All existing algorithms use one of the two following approach: a levelwise [12] bottom-up search =-=[2, 5, 13, 16, 17]-=- or a simultaneous bottom-up and top-down search [3, 10, 20]. Although they are dissimilar, all those algorithms explore the subset lattice (itemset lattice) for finding frequent itemsets: they all us... |

169 |
Concept Lattices and Conceptual Knowledge Systems, in
- Wille
- 1992
(Show Context)
Citation Context ...on, we define the closed itemset lattice which is a sub-order of the itemset lattice, thus often much smaller. This lattice is closely related to the Galois lattice [4, 7] also called concept lattice =-=[19]-=-. The closed itemset lattice can be used as a formal framework for discovering frequent itemsets given the basic properties that the support of an itemset I is equal to the support of its closure and ... |

136 | Familles minimales d’implications informatives resultant d’un tableau de données binaries - Guigues, Duquenne - 1986 |

124 | Pincer search: A new algorithm for discovering the maximum frequent set
- Lin, Kedem
- 1998
(Show Context)
Citation Context ... dependencies from a relation [12]. All existing algorithms use one of the two following approach: a levelwise [12] bottom-up search [2, 5, 13, 16, 17] or a simultaneous bottom-up and top-down search =-=[3, 10, 20]-=-. Although they are dissimilar, all those algorithms explore the subset lattice (itemset lattice) for finding frequent itemsets: they all use the basic properties that all subsets of a frequent itemse... |

105 |
Lattice Theory
- Birkho
- 1967
(Show Context)
Citation Context ...chanism based on the Galois connection, we dene the closed itemset lattice which is a sub-order of the itemset lattice, thus often much smaller. This lattice is closely related to the Galois lattice =-=[4, 7]-=- also called concept lattice [19]. The closed itemset lattice can be used as a formal framework for discovering frequent itemsets given the basic properties that the support of an itemset I is equal t... |

102 | Pruning and Grouping Discovered Association Rules
- Toivonen, Klemettinen, et al.
- 1995
(Show Context)
Citation Context ...since there can be thousands of association rules holding in a database, reducing the number of rules produced without information loss is an important problem for the understandability of the result =-=[18]-=-. Empirical evaluations comparing A-Close to an optimized version of Apriori showed that they give nearly always equivalent results for weakly correlated data (such as synthetic data) and that A-Close... |

74 | Fast sequential and parallel algorithms for association rule mining: A comparison
- Mueller
- 1995
(Show Context)
Citation Context ...ermines which generators are contained in an object 7 , i.e. generators that are subsets of f(fog). For this purpose, generators are stored in a prefix-tree structure derived from the one proposed in =-=[14]-=-. 4.4 AC-Generator Function The function takes the set G i of frequent i-generators as argument. Based on Lemma 1 and 2, it returns the set G i+1 of frequent (i+1)-generators. The pseudocode of the fu... |

40 |
Implications partielles dans un contexte
- Luxenburger
- 1991
(Show Context)
Citation Context ... I 1 )h(I 1 ) \Gamma I 1 j I 1 2 FPg is a basis for all exact valid association rules. 8r 0 2 AR where confidence(r 0 ) = 1 we have BE j= r 0 . Theorem 2 (Reduced set of approximate association rules =-=[11]-=-). Let C be the set of closed itemsets and R the set of approximate association rules in D. The set A = fr : I 1 c \Gamma! I 2 \Gamma I 1 j I 2 ae I 1sI 1 ; I 2 2 Cg is a correct reduced set for all a... |

38 |
An ecient algorithm for mining association rules in large databases
- Savasere, Omiecinski, et al.
(Show Context)
Citation Context ...from sequences and insnding keys or inclusion as well as functional dependencies from a relation [12]. All existing algorithms use one of the two following approach: a levelwise [12] bottom-up search =-=[2, 5, 13, 16, 17]-=- or a simultaneous bottom-up and top-down search [3, 10, 20]. Although they are dissimilar, all those algorithms explore the subset lattice (itemset lattice) forsnding frequent itemsets: they all use ... |

27 | Finding all closed sets: a general approach - Ganter, Reuter - 1991 |

23 | L.: Pruning closed itemset lattices for association rules
- Pasquier, Taouil, et al.
(Show Context)
Citation Context ... the frequent closed itemset supports. A different algorithm for finding frequent closed itemsets and algorithms for deriving frequent itemsets and generating valid association rules are presented in =-=[15]-=-. Using the result of A-Close, we can directly generate the reduced set of valid association rules defined in Section 3.4 instead of determining all frequent itemsets. The procedure is the following: ... |