Chapter 06 - Changing Education Paradigm

30 CHAPTER 6. MINING ASSOCIATION RULES IN LARGE DATABASES
Constraint-based mining allow users to focus the search for rules by providing metarules, (i.e., pattern templates)
and additional mining constraints. Such mining is facilitated with the use of a declarative data mining
query language and user interface, and poses great challenges for mining query optimization. In particular, the
rule constraint properties of anti-monotonicity and succinctness can be used during mining to guide the
process, leading to more e cient and e ective mining.
Exercises
1. The Apriori algorithm makes use of prior knowledge of subset support properties.
(a) Prove that all non-empty subsets of a frequent itemset must also be frequent.
(b) Prove that the support of any non-empty subset s 0 of itemset s must be as great as the support of s.
(c) Given frequent itemset l and subset s of l, prove that the con dence of the rule \s 0 ) (l , s 0 )" cannot be
more than the con dence of \s ) (l , s)", where s 0 is a subset of s.
2. Section 6.2.2 describes a method for generating association rules from frequent itemsets. Propose a more
e cient method. Explain why it is more e cient than the one proposed in Section 6.2.2. (Hint: Consider
incorporating the properties of Question 1b and 1c into your design).
3. Suppose we have the following transactional data.
(INSERT TRANSACTIONAL DATA HERE).
Assume that the minimum support and minimum con dence thresholds are 3% and 60%, respectively.
(a) Find the set of frequent itemsets using the Apriori algorithm. Show the derivation of Ck and Lk for each
iteration, k.
(b) Generate strong association rules from the frequent itemsets found above.
4. In Section 6.2.3, we studied two methods of scan reduction. Can you think of another approach, which trims
transactions by removing items that do not contribute to frequent itemsets? Show the details of this approach
in pseudo-code and with an example.
5. Suppose that a large store has a transaction database that is distributed among four locations. Transactions in
each component database have the same format, namely Tj : fi1;:::;img, where Tj is a transaction identi er,
and ik (1 k m) is the identi er of an item purchased in the transaction. Propose an e cient algorithm to
mine global association rules (without considering multilevel associations). You may present your algorithm in
the form of an outline. Your algorithm should not require shipping all of the data to one site and should not
cause excessive network communication overhead.
6. Suppose that a data relation describing students at Big-University has been generalized to the following generalized
relation R.