Approximating a collection of frequent sets

...The problem of summarizing frequent graph patterns is related to that of summarizing frequent item sets, which has been extensively investigated in [15], [12], [16], and [17]...
...Afrati et al. [15] uses K frequent item sets at border to approximate the collection of frequent item sets...
...When the method in [15] is applied to graph databases, support information in a large number of frequent graph patterns will be lost because it is aimed at obtaining a subset of maximal frequent patterns...

...To achieve a concise summary or representatives of frequent itemsets, recent works such as the closed pattern (Pasquier et al. 1999), the spanning set approach (Afrati et al. 2004), the clusteringbased approach (Xin et al. 2005), the profile-based approach (Yan et al. 2005), the Markov random field approach (Wang and Parthasarathy 2006) and the regression-based approach (Jin et al. 2008) are developed...

...The concept of summarization is also common in frequent itemset analysis, where various techniques have been developed to generate a compact approximation to a collection of frequent itemsets [5][6], or other multidimensional summaries [7]...

...Summarization is a common method for representing huge amounts of patterns [5,6,7,8,9,10]...
...Note that most of the existing methods use the same language for P and S [5,6,7,8]...
...Table 2 highlights some characteristics of the approaches closest to ours [10,6,5,8,7,9] . We comment the table below...
...each pattern is covered by at least a pattern of the summary, contrary to other methods which provide summaries that approximately cover the set of association rules [5,8]...
...Reference [9] [6] [5] [10] [7] [8] Our method...
...Regeneration: The main objective of some approaches is to build summaries so that they can be used to regenerate the original itemsets [5] or their frequency [8,7,10] whereas the others are interested in the representation of the patterns for future exploration [6,9]...
...The measure used in [5] calculates the size of the subset of patterns which are really covered by at least one pattern of the summary...

...Frequent Itemsets are huge when the given threshold is low; consequently, the condensed representations of frequent itemsets including closed itemsets[19], maximal itemsets[6][7][8][9][18][22], free itemsets[12], approximate k-sets[10], weighted itemsets[21], and non-derivable itemsets[14] were proposed; in addition, [20] focused on discovering a minimal set of unexpected itemsets...

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