Computational Complexity of Finding Highly Co-occurrent Itemsets in Market Basket Databases

Yeon-Dae KWON  Yasunori ISHIHARA  Shougo SHIMIZU  Minoru ITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.12   pp.2723-2735
Publication Date: 2000/12/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: General Fundamentals and Boundaries
data mining,  large itemset,  highly co-occurrent itemset,  computational complexity,  

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Data mining is to analyze all the data in a huge database and to obtain useful information for database users. One of the well-studied problems in data mining is the search for meaningful association rules in a market basket database which contains massive amounts of sales transactions. The problem of mining meaningful association rules is to find all the large itemsets first, and then to construct meaningful association rules from the large itemsets. In our previous work, we have shown that it is NP-complete to decide whether there exists a large itemset with a given size. Also, we have proposed a subclass of databases, called k-sparse databases, for which we can efficiently find all the large itemsets. Intuitively, k-sparsity of a database means that the supports of itemsets of size k or more are sufficiently low in the database. In this paper, we introduce the notion of (k,c)-sparsity, which is strictly weaker than the k-sparsity in our previous work. The value of c represents a degree of sparsity. Using (k,c)-sparsity, we propose a larger subclass of databases for which we can still efficiently find all the large itemsets. Next, we propose alternative measures to the support. For each measure, an itemset is called highly co-occurrent if the value indicating the correlation among the items exceeds a given threshold. In this paper, we define the highly co-occurrent itemset problem formally as deciding whether there exists a highly co-occurrent itemset with a given size, and show that the problem is NP-complete under whichever measure. Furthermore, based on the notion of (k,c)-sparsity, we propose subclasses of databases for which we can efficiently find all the highly co-occurrent itemsets.