time items A,B 10 A,B AC A,C A,B,C B 50 10 A 50C 30 A,B SA 50 60 C Consider the database table above. Each sequence is comprised of itemset-events that happen at the same time. For example, sequence si can be considered to be a sequence of itemsets (AB)10(B)20(AB)30(AC)40, where symbols within brackets are considered to co-occur at the same time, which is given in the subscripts. The itemsets-sequences can be of any length as long as they are frequent. The minsup is set to 3. X is a frequent maximal pattern in a data set S if there exists no frequent proper super-pattern Y and X satisfies minimum support. X is a closed pattern in a data set S if there exists no proper super-pattern Y such that Y has the same support count as X in S, and X satisfies minimum support. 1. Given minsup = 3, are the following sequences frequent ? (2 pts) a. without time constraints i- (AB)B ii- (AC)A iii- AC iv- ABC b. with time-constraints Max-Gap = 10 2. Find all frequent itemset-sequences without time constraints. Provide details. (5 pts) 3. Give two frequent maximal itemset-sequences. Explain. (1 pt) 4. Give two frequent closed itemset-sequences that are not maximal. (1 pt) 5. ITEMSET mining : a. Explain the similarity and difference between positive and negative borders of frequent itemsets. (1 pt) b. Given a negative border of frequent itemsets, describe an algorithm that can generate the positive border of these frequent itemsets. (3 pts) time items A,B 10 A,B AC A,C A,B,C B 50 10 A 50C 30 A,B SA 50 60 C Consider the database table above. Each sequence is comprised of itemset-events that happen at the same time. For example, sequence si can be considered to be a sequence of itemsets (AB)10(B)20(AB)30(AC)40, where symbols within brackets are considered to co-occur at the same time, which is given in the subscripts. The itemsets-sequences can be of any length as long as they are frequent. The minsup is set to 3. X is a frequent maximal pattern in a data set S if there exists no frequent proper super-pattern Y and X satisfies minimum support. X is a closed pattern in a data set S if there exists no proper super-pattern Y such that Y has the same support count as X in S, and X satisfies minimum support. 1. Given minsup = 3, are the following sequences frequent ? (2 pts) a. without time constraints i- (AB)B ii- (AC)A iii- AC iv- ABC b. with time-constraints Max-Gap = 10 2. Find all frequent itemset-sequences without time constraints. Provide details. (5 pts) 3. Give two frequent maximal itemset-sequences. Explain. (1 pt) 4. Give two frequent closed itemset-sequences that are not maximal. (1 pt) 5. ITEMSET mining : a. Explain the similarity and difference between positive and negative borders of frequent itemsets. (1 pt) b. Given a negative border of frequent itemsets, describe an algorithm that can generate the positive border of these frequent itemsets. (3 pts)
