Order, subset construction and sequential pattern mining

Sequential Pattern Mining (SPM) is a basic task in data mining. It aims to extract the most occurring sequences in a dataset, which turns out to be instrumental in many fields. In [1] we initiated an attempt to formally unify leading pattern mining approaches. This paper builds upon our previous work to first extend the polynomial model to SPM. Next, we devise an efficient implementation termed WASMA that enhances the standard subset construction method. To do so, we first partition the set of states into independent sets based on their labels, and then define three different state ordering. The first is a global id-based order which we use in global exploration. The second is local and used in itemset extension. A geometric ordering is lastly exploited to avoid redundant computations. To handle the memory bottleneck of the determinization, we propose two variants: WASMA-wsc and WASMA-ssc that rely or not on the state existence check clause. Unlike existing approaches that overlook the appearance of repetitive computation paths, the first variant introduces a novel feature, since it avoids recomputing previously explored sub-branches of the problem space. Besides, we refine for the SPM setting the well-known theoretical upper-bound by establishing new complexities in function of the geometric-order topology. Evaluations demonstrate that our solution outperforms existing approaches for SPM instances with very low support thresholds, persisting sole to yield the result while its competitors hit the time limit.