Leveraging Homomorphisms and Bitmaps to Enable the Mining of Embedded Patterns from Large Data Trees

Abstract

Finding interesting tree patterns hidden in large datasets is an important research area that has many practical applications. Along the years, research has evolved from mining induced patterns to mining embedded patterns. Embedded patterns allow for discovering useful relationships which cannot be captured by induced patterns. Unfortunately, previous contributions have focused almost exclusively on mining patterns from a set of small trees. The problem of mining embedded patterns from large data trees has been neglected. This is mainly due to the complexity of this task related to the problem of unordered tree embedding test being NP-Complete. However, mining embedded patterns from large trees is important for many modern applications that arise naturally and in particular with the explosion of big data.

In this paper, we address the problem of mining unordered frequent embedded tree patterns from large trees. We propose a novel approach that exploits efficient homomorphic pattern matching algorithms to compute pattern support incrementally and avoids the costly enumeration of all pattern matchings required by previous approaches. A further originality of our approach is that matching information of already computed patterns is materialized as bitmaps. This technique not only minimizes the memory consumption but also reduces CPU costs by translating pattern evaluation to bitwise operations. An extensive experimental evaluation shows that our approach not only mines embedded patterns from real datasets up to several orders of magnitude faster than state-of-the-art tree mining algorithms applied to large data trees but also scales well empowering the extraction of patterns from large datasets where previous approaches fail.

The research of this author was supported by the National Natural Science Foundation of China under Grant No. 61202035 and 61272110.