Suppose we have market basket data consisting of 100 transactions and 20 items. If 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?
(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.
(c) What conclusions can you draw from the results of parts (a) and (b)?
(d) Prove that if the confidence of the rule {a} → {b} is less than the support of {b}, then:
i. c({} → {b}) > c({a} → {b}),
ii. c({} → {b}) > s({b}),
where c(∙) denote the rule confidence and s(∙) denote the support of an itemset.