Suppose we would like to extract positive and negative itemsets from a data set that contains d items.
(a) Consider an approach where we introduce a new variable to represent each negative item. With this approach, the number of items grows from d to 2d. What is the total size of the itemset lattice, assuming that an itemset may contain both positive and negative items of the same variable?
(b) Assume that an itemset must contain positive or negative items of different variables. For example, the itemset {a, a, b, c} is invalid because it contains both positive and negative items for variable a. What is the total size of the itemset lattice?