Mining Approximate Frequent Itemsets In the Presence of Noise: Algorithm and Analysis

Frequent itemset mining is a popular and important first step in the analysis of data arising in a broad range of applications. The traditional “exact” model for frequent itemsets requires that every item occurs in each supporting transaction. Real data is typically subject to noise and measurement error. To date, the effects of noise on exact frequent pattern mining algorithms have been addressed primarily through simulation studies, and there has been limited attention to the development of noise tolerant algorithms. In this paper we propose a noise tolerant itemset model, which we call approximate frequent itemsets (AFI). Like frequent itemsets, the AFI model requires that an itemset has a minimum number of supporting transactions. However, the AFI model places constraints on the fraction of errors permitted in each item and the fraction of errors permitted in each supporting transaction. Motivating this model are theoretical results (and a supporting simulation study presented here) which state that, in the presence of even low levels of noise, large frequent itemsets are broken into fragments of logarithmic size; thus the itemsets cannot be recovered by a routine application of frequent itemset mining. By contrast, we provide theoretical results showing that the AFI criterion is well suited to recovery of block structures in noise. We developed and implemented an algorithm to mine AFIs that generalizes the level-wise enumeration of frequent itemsets by allowing noise. We propose the noise-tolerant support threshold, a relaxed version of support, which varies by the length of the itemset and noise threshold. We exhibit an Apriori property that permits the pruning of an itemset if any of its sub-itemset is not sufficiently supported. Several experiments presented demonstrate that the AFI algorithm enables better recoverability of frequent patterns under noisy conditions. Noise-tolerant support pruning also renders an order of magnitude performance gain over existing methods.