Suppose the support threshold is 5. Find the maximal frequent item sets for the data of:

(a) Exercise 6.1.1.

(b) Exercise 6.1.3.

Exercise 6.1.1

Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. Item i is in basket b if and only if i divides b with no remainder. Thus, item 1 is in all the baskets, item 2 is in all fifty of the even-numbered baskets, and so on. Basket 12 consists of items {1, 2, 3, 4, 6, 12}, since these are all the integers that divide 12. Answer the following questions:

(a) If the support threshold is 5, which items are frequent?

(b) If the support threshold is 5, which pairs of items are frequent?

(c) What is the sum of the sizes of all the baskets?

Exercise 6.1.3

Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. Item i is in basket b if and only if b divides i with no remainder. For example, basket 12 consists of items

Repeat Exercise 6.1.1 for this data.