### Table 4: Frequent Pseudo-Closed Itemsets and Duquenne-Guigues Basis Extracted from D for minsupp = 2=5.

"... In PAGE 6: ... Example 4 A frequent pseudo-closed itemset I is a frequent non-closed itemset that includes the closures of all frequent pseudo-closed itemsets included in I. The set FP of frequent pseudo- closed itemsets and the Duquenne-Guigues basis for exact association rules extracted from D for minsupp=2=5 and minconf =1=2 are presented in Table4 . The itemset AB is not a frequent pseudo- closed itemset since the closures of A and B (respectively AC and BE) are not included in AB.... ..."

### Table 9: Notations.

"... In PAGE 12: ...1 Generating Duquenne-Guigues Basis for Exact Association Rules The pseudo-code generating the Duquenne-Guigues basis for exact association rules is given in Algorithm 3. Notations are given in Table9 . The algorithm takes as input the sets Li, 1 i k, containing the frequent itemsets and their support, and the sets FCi; 0 i k, containing the frequent closed itemsets and their support.... ..."

### Table 15: Number of Approximate Association Rules Extracted.

"... In PAGE 17: ...2 Number of Rules and Execution Times of the Rule Generation Table 8 shows the total number of exact association rules and their number in the Duquenne- Guigues basis for exact rules. Table15 shows the total number of approximate association rules, their number in the proper basis and in the structural basis for approximate rules, and the number of non-transitive rules in the proper basis for approximate rules (5th column). For example in the context D, rules C ! A and AC ! BE are extracted, as well as the rule C ! ABE which is clearly transitive.... ..."

### Table 1. Rankings generated by the three methods on the basis of their accuracy on all datasets.

2000

"... In PAGE 4: ... This is an estimate of the general advantage/disadvantage of algorithm j over algo- rithm k. Finally, we derive the overall mean success rate ratio for each algo- rithm, SRRj = (Pk SRRj;k) =(m ? 1) where m is the number of algorithms ( Table1 ). The ranking is derived directly from this measure.... In PAGE 4: ... For in- stance, ltree is signi cantly better than c5 on 5 out of the 16 datasets used in this study, thus pwltree,c5 = 5=16 = 0:313. Finally, we calculate the overall esti- mate of the probability of winning for each algorithm, pwj = (Pk pwj;k) =(m?1) where m is the number of algorithms ( Table1 ). The values obtained are used as a basis for constructing the overall ranking.... In PAGE 9: ... 5 Discussion Considering the variance of the obtained C scores, the conclusion that the SRR and AR are both signi cantly better than SW is somewhat surprising. We have observed that the three methods generated quite similar rankings with the performance information on all the datasets used ( Table1 ). However, if we compare the rankings generated using the leave-one-out procedure, we observe that the number of di erently assigned ranks is not negligible.... ..."

Cited by 14

### Table 1: The Example Data Mining Context D.

"... In PAGE 13: ... PB Proper basis for approximate association rules. Table1 0: Notations. The set PB is rst initialized to the empty set (step 1).... In PAGE 14: ... SB Structural basis for approximate association rules. Table1 1: Notations. The set SB is rst initialized to the empty set (step 1).... In PAGE 17: ... In all experiments, we attempted to choose signi cant minimum support and con dence threshold values: we observed threshold values used in other papers for experiments on similar data types and examined rules extracted in the bases. Name Number of objects Average size of objects Number of items T10I4D100K 100,000 10 1,000 Mushrooms 8,416 23 127 C20D10K 10,000 20 386 C73D10K 10,000 73 2,177 Table1 2: Datasets. 6.... In PAGE 17: ...22s 17.93s T10I4D100K Mushrooms Table1 3: Execution Times of Apriori and Apriori-Close. 6.... In PAGE 18: ... Dataset Minsupp Exact rules Duquenne-Guigues basis T10I4D100K 0.5% 0 0 Mushrooms 30% 7,476 69 C20D10K 50% 2,277 11 C73D10K 90% 52,035 15 Table1 4: Number of Exact Association Rules Extracted. References [1] R.... In PAGE 19: ...Minconf Approximate Proper Non-transitive Structural (Minsupp) rules basis basis basis 90% 16,260 16,260 3,511 916 T10I4D100K 70% 20,419 20,419 4,004 1,058 (0.5%) 50% 21,686 21,686 4,191 1,140 30% 22,952 22,952 4,519 1,367 90% 12,911 806 563 313 Mushrooms 70% 37,671 2,454 968 384 (30%) 50% 56,703 3,870 1,169 410 30% 71,412 5,727 1,260 424 90% 36,012 4,008 1,379 443 C20D10K 70% 89,601 10,005 1,948 455 (50%) 50% 116,791 13,179 1,948 455 30% 116,791 13,179 1,948 455 95% 1,606,726 23,084 4,052 939 C73D10K 90% 2,053,896 32,644 4,089 941 (90%) 85% 2,053,936 32,646 4,089 941 80% 2,053,936 32,646 4,089 941 Table1 5: Number of Approximate Association Rules Extracted. Dataset Duquenne-Guigues Proper Non-transitive Structural basis basis basis basis T10I4D100K - 100.... In PAGE 19: ...21% 0.05% Table1 6: Average Relative Size of Bases. [6] G.... ..."

### TABLE 1 Comparing canonical basis multipliers with generating AOPs.

1998

Cited by 23

### Table 2: Time to generate and canonize basis cycles, as well as their number.

2001

"... In PAGE 8: ... Basis. Table2 summarizes the basis generation process. We distinguish the two steps of our algorithm: initial basis generation and canonization.... ..."

Cited by 7

### Table 2: Time to generate and canonize basis cycles, as well as their number.

"... In PAGE 8: ... Basis. Table2 summarizes the basis generation process. We distinguish the two steps of our algorithm: initial basis generation and canonization.... ..."

### Table 2. Algorithm Performance.

"... In PAGE 26: ...atisfied (i.e. the percentage of preference shifts specified in the preference rosters NPi that were satisfied in the final roster NRi). Table2 about here. It is clear from the results in Table 2 that all of the algorithms that employed case-based repair generation were able to find solutions with fewer constraint violations than those that used randomly generated repairs.... In PAGE 26: ... Table 2 about here. It is clear from the results in Table2 that all of the algorithms that employed case-based repair generation were able to find solutions with fewer constraint violations than those that used randomly generated repairs. Figure ?? compares the mean, minimum, and maximum number of constraint violations in the solutions found by each algorithm.... ..."