Discovering Frequent Closed Itemsets for Association Rules

Abstract

In this paper, we address the problem of nding frequent itemsets in a database. Using the closed itemset lattice framework, we show that this problem can be reduced to the problem of nding frequent closed itemsets. Based on this statement, we can construct e cient data mining algorithms by limiting the search space to the closed itemset lattice rather than the subset lattice. Moreover, we show that the set of all frequent closed itemsets su ces to determine a reduced set of association rules, thus addressing another important data mining problem: limiting the number of rules produced without information loss. We propose a new algorithm, called A-Close, using a closure mechanism to nd frequent closed itemsets. We realized experiments to compare our approach to the commonly used frequent itemset search approach. Those experiments showed that our approach is very valuable for dense and/or correlated data that represent an important part of existing databases.

Efficient Mining of Association Rules Based on Formal Concept Analysis

“…The first set of algorithms that were explicitly designed to compute frequent closed itemsets were Close [39], Apriori-Close [37] and A-Close [38]. Inspired by Apriori [2], all these algorithms traverse the database in a level-wise approach.…”

“…For several years, a wide range of applications in various domains have benefited from KDD techniques and many work has been conducted on this topic. The problem of mining frequent itemsets arose first as a sub-problem of mining association rules [1], but it then turned out to be present in a variety of problems [24]: mining sequential patterns [3], episodes [32], association rules [2], correlations [12,43], multi-dimensional patterns [26,28], maximal itemsets [7,54,29], closed itemsets [47,37,38,41]. Since the complexity of this problem is exponential in the size of the binary database input relation and since this relation has to be scanned several times during the process, efficient algorithms for mining frequent itemsets are required.…”

Mining All Non-derivable Frequent Itemsets

“…However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be prohibitively large. To overcome this problem, recently several proposals have been made to construct a concise representation of the frequent itemsets, instead of mining all frequent itemsets [13,3,6,5,14,15,7,11].…”

Hash-Close: A Hash-Based Algorithm for Mining Frequent Closed Itemsets

“…In addition, it decreases redundant rules and increases mining efficiency. Many algorithms have been presented for mining frequent closed item sets [2], and A-close proved to be a fundamental one [3].…”