The Pattern Ordering Problem

Many pattern discovery methods provide fast tools for finding the frequently occurring patterns in large data sets. Such pattern collections can also be used to approximate the underlying joint distribution, and they summarize the data set well. However, a large set of patterns is unintuitive and not necessarily easy to use. In this paper we consider the problem of ordering a collection of patterns so that each prefix of the ordering gives as good a summary of the data as possible. We formulate this problem for general loss functions, show that the problem has an efficient solution, and prove that its natural variant is NP-complete but the greedy approximation algorithm gives an e/(e-1) ≈ 1.58 approximation quality. We apply the general technique to approximation of frequencies of frequent sets, and show that the method gives good empirical results.