Ex. 11 (pp.409) Given the lattice structure shown in Figure 6.33 and the transactions given in Table 6.24, label each node with the following letter(s):

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Ex. 11 (pp.409) Given the lattice structure shown in Figure 6.33 and the transactions given in Table 6.24, label each node with the following letter(s): M if the node is a maximal frequent itemset, C if it is a closed frequent itemset, N if it is frequent but neither maximal nor closed, and I if it is infrequent. Assume that the support threshold is equal to 30%.

Ex. 11 (pp.409)

Ex. 11 (pp.409)

Exercise 17 (pp. 413) Suppose we have market basket data consisting of 100 transactions and 20 items. The support for item a is 25%, the support for item b is 90% and the support for itemset {a, b} is 20%. Let the support and confidence thresholds be 10% and 60%, respectively. (a) Compute the confidence of the association rule {a} → {b}. Is the rule interesting according to the confidence measure? Answer: Confidence is 0.2/0.25 = 80%. The rule is interesting because it exceeds the confidence threshold. (b) Compute the interest measure for the association pattern {a, b}. Describe the nature of the relationship between item a and item b in terms of the interest measure. The interest measure is 0.2/(0.25 × 0.9) = 0.889. The items are negatively correlated according to interest measure. (c) What conclusions can you draw from the results of parts (a) and (b)? High confidence rules may not be interesting.

Ex. 11 (pp. 480) maxgap = 3 maxspan = 5 (a) For each of the sequences w =< e1e2 . . . ei . . . ei+1 . . . elast > given below, determine whether they are subsequences of the sequence < {1, 2, 3}{2, 4}{2, 4, 5}{3, 5}{6} > subjected to the following timing constraints: maxgap = 3 maxspan = 5 w =< {1}{2}{3} > Answer: Yes. w =< {1, 2, 3, 4}{5, 6} > Answer: No. w =< {2, 4}{2, 4}{6} > w =< {1}{2, 4}{6} > w =< {1, 2}{3, 4}{5, 6} >

Ex. 11 (pp. 480) (b) Determine whether each of the subsequences w given in the previous question are contiguous subsequences of the following sequences s. s =< {1, 2, 3, 4, 5, 6}{1, 2, 3, 4, 5, 6}{1, 2, 3, 4, 5, 6} > w =< {1}{2}{3} > Answer: Yes. w =< {1, 2, 3, 4}{5, 6} > w =< {2, 4}{2, 4}{6} > w =< {1}{2, 4}{6} > w =< {1, 2}{3, 4}{5, 6} >

Ex. 11 (pp. 480) s =< {1, 2, 3, 4}{1, 2, 3, 4, 5, 6}{3, 4, 5, 6} > w =< {1}{2}{3} > Answer: Yes. w =< {1, 2, 3, 4}{5, 6} > w =< {2, 4}{2, 4}{6} > w =< {1}{2, 4}{6} > w =< {1, 2}{3, 4}{5, 6} >

Ex. 11 (pp. 480) s =< {1, 2}{1, 2, 3, 4}{3, 4, 5, 6}{5, 6} > w =< {1}{2}{3} > Answer: Yes. w =< {1, 2, 3, 4}{5, 6} > w =< {2, 4}{2, 4}{6} > Answer: No. w =< {1}{2, 4}{6} > w =< {1, 2}{3, 4}{5, 6} >

Ex. 11 (pp. 480) s =< {1, 2, 3}{2, 3, 4, 5}{4, 5, 6} > w =< {1}{2}{3} > Answer: No. w =< {1, 2, 3, 4}{5, 6} > w =< {2, 4}{2, 4}{6} > w =< {1}{2, 4}{6} > Answer: Yes. w =< {1, 2}{3, 4}{5, 6} >