Consider the transaction data set below (TID is the transaction ID and Items contains a set of items that were bought together):

TID Items

T1 {b, d, e}

T2 {a, b, d, e}

T3 {c, d}

T4 {a, c, d, e}

T5 {b, d}

T6 {a, d, e}

T7 {a, c, d, e}

T8 {b, c, d}

T9 {a, b, d, e}

T10 {a, c, d, e}

Let the minimum support threshold be 25% and the minimum confidence threshold be 40%.

(a) Using the Apriori algorithm, find all frequent itemsets that contain item a. Show all the steps you used in finding the frequent itemsets.

(b) Using the FP-growth algorithm, find all frequent itemsets that contain item a. Show all the steps you used in finding the frequent itemsets.

(c) Find all the strong association rules whose antecedent is a (i.e., a is the left hand side of the rule).

(d) Are there any misleading rules in the rules identified at steps (a) and (b) according the lift measure? If yes, identify them and explain why they are misleading.