document: Dense itemsets Frequent itemset mining has been the subject of a lot of work in data mining research ever since association rules were introduced . In this paper we address a problem with frequent itemsets : that they only count rows where all their attributes are present , and do not allow for any noise . We show that generalizing the concept of frequency while preserving the performance of mining algorithms is nontrivial , and introduce a generalization of frequent itemsets , dense itemsets . Dense itemsets do not require all attributes to be present at the same time ; instead , the itemset needs to define a sufficiently large submatrix that exceeds a given density threshold of attributes present . We consider the problem of computing all dense itemsets in a database . We give a levelwise algorithm for this problem , and also study the top - $ k $ variations , i.e. , finding the k densest sets with a given support , or the k best-supported sets with a given density . These algorithms select the other parameter automatically , which simplifies mining dense itemsets in an explorative way . We show that the concept captures natural facets of data sets , and give extensive empirical results on the performance of the algorithms . Combining the concept of dense itemsets with set cover ideas , we also show that dense itemsets can be used to obtain succinct descriptions of large datasets . We also discuss some variations of dense itemsets .
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