A Search Algorithm for Intertransaction Association Rules

Abstract

The problem analysed in this chapter is the discovery of interesting relations between variables in large databases. The databases are considered to contain transactions that each contain one or more items from a discrete set of items. The relations between the items are expressed in the form of association rules. The problem of searching for association rules has been denoted in the research literature as association rule mining. The initial association rule mining problem ignored any correlation between the transactions and searched for associations only between items inside a transaction (this case is called case intratransaction association rules mining). To search for associations between items across several transactions ordered on a dimension (usually time or space), intertransaction association rule mining has been used. We use the stock market database example to differentiate between intraand intertransaction analysis. If the database contains the price for each stock at the end of the trading day, an intratransaction association rule might be “If stock prices for companies A and B go up for one day, there is a probability of over c% that the price for company C will also go up the same day”. However, analysts might be more interested in rules like “If stock prices for companies A and B go up for one day, there is a probability of over c% that the price for company C will go up two days later.” This rule describes a relationship between items from different transactions, and it can be discovered only by using intertransaction analysis. The main part of association rules mining has been determined to be finding the frequent itemsets. A search algorithm that finds frequent intertransaction itemsets called InterTraSM will be presented, exemplified and analyzed in this chapter. It was first introduced in (Ungureanu & Boicea, 2008). This algorithm is an extension for the intertransactional case of the SmartMiner algorithm presented in (Zou et al., 2002). InterTraSM focuses on mining maximal frequent itemsets (MFI) – itemsets that are not a subset of any other frequent itemset. Once the MFI have obtained all the frequent itemsets can easily be derived, and they can then be counted for support in a single scan of the database. The remainder of this chapter is organized as follows. • Section 2 contains a formal definition for the problem of intertransaction association rules mining.