Abstract representations and generalized frequent pattern discovery

Abstract

We discuss the frequent pattern mining problem in a general setting. From an analysis of abstract representations, summarization and frequent pattern mining, we arrive at a generalization of the problem. Then, we show how the problem can be cast into the powerful language of algorithmic information theory. We formulate and prove a universal pruning theorem analogous to the well-known Downward Closure Lemma in data mining. This result allows us to formulate a simple algorithm to mine all frequent patterns given an appropriate compressor to recognize patterns.