Problem 4. Pattern Mining Concepts \& Algorithms (20 points) Given you have transaction database from a grocery store shown in Table 2 and the corresponding product table in Table 3, please answer the following questions. Table 2: Transaction Database Table 3: Product Table (1) (4 points) Given an association rule BC(s,c), what are its relative support s and confidence c ? (2) Given a collection of constraints as follows, identify their types (monotone, anti-monotone, data anti-monotone, succinct, convertible). If multiple types coexist in the following constraints, please list them all. (i) (2 points) Total price of all purchased items is less than $250. (ii) (2 points) Total price of all purchased items is at least $200. (iii) (2 points) The minimal price of the purchased item is less than $50. (3) (8 points) Construct the FP-tree from the transaction database above, when the minimum relative support is 0.5 . Please show intermediate steps to get all credits. Note that you can use any software (hand drawing is also allowed) to draw the FP-tree and insert a screenshot of this FP-tree into the submitted file. (4) (6 points) Why is FP-growth more efficient than Apriori algorithm? Is FP-growth always faster than Apriori? Why