document: Support envelopes : a technique for exploring the structure of association patterns This paper introduces support envelopes -- a new tool for analyzing association patterns -- and illustrates some of their properties , applications , and possible extensions . Specifically , the support envelope for a transaction data set and a specified pair of positive integers ( m , n ) consists of the items and transactions that need to be searched to find any association pattern involving m or more transactions and n or more items . For any transaction data set with M transactions and N items , there is a unique lattice of at most M \* N support envelopes that captures the structure of the association patterns in that data set . Because support envelopes are not encumbered by a support threshold , this support lattice provides a complete view of the association structure of the data set , including association patterns that have low support . Furthermore , the boundary of the support lattice -- the support boundary -- has at most min ( M , N ) envelopes and is especially interesting since it bounds the maximum sizes of potential association patterns -- not only for frequent , closed , and maximal itemsets , but also for patterns , such as error-tolerant itemsets , that are more general . The association structure can be represented graphically as a two-dimensional scatter plot of the ( m , n ) values associated with the support envelopes of the data set , a feature that is useful in the exploratory analysis of association patterns . Finally , the algorithm to compute support envelopes is simple and computationally efficient , and it is straightforward to parallelize the process of finding all the support envelopes .
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