An improved algorithm for frequent patterns mining problem

Frequent pattern mining is a basic problem in data mining and knowledge discovery. The discovered patterns can be used as the input for analyzing association rules, mining sequential patterns, recognizing clusters, and so on. However, discovering frequent patterns in large scale datasets is an extremely time consuming task. Most research in the area of association rule discovery has focused on the method of efficient frequent pattern discovery, e.g. Park, Chen & Yu (1995); Savasere, Omiecinski & Navathe (1995); Han, Pei & Yin (2000); Pei, Han, Lu, Nishio, Tang & Yang (2001). When seeking all associations that satisfy constraints on support and confidence, once frequent patterns have been identified, generating the association rules is trivial. In the last decade, various algorithms have been proposed on this problem, e.g. maximal pattern mining - Grahne & Zhu (2003); closed pattern mining - Pei, Han & Mao (2000); Grahne & Zhu (2003); mining the most interesting frequent patterns - Fu, Kwong & Tang (2000); Han, Wang, Lu & Tzvetkov (2002, 2005); Hirate, Iwahashi & Yamana (2004). However, some challenges are still existed and need to be overcome. In this paper, a mathematical space will be introduced with some new related concepts and propositions to design a new algorithm for solving frequent patterns mining problem. It is hoped that such an improved algorithm will be simple to implement and more efficient.