The Apriori property of sequence pattern mining with wildcard gaps

In biological sequence analysis, long and frequently occurring patterns tend to be interesting. Data miners designed pattern growth algorithms to obtain frequent patterns with periodical wildcard gaps, where the pattern frequency is defined as the number of pattern occurrences divided by the number of offset sequences. However, the existing definition set does not facilitate further research works. First, some extremely frequent patterns are obviously uninteresting. Second, the Apriori property does not hold; consequently, state-of-the art algorithms are all Apriori-like and rather complex. In this paper, we propose an alternative definition of the number of offset sequences by adding a number of dummy characters at the tail of sequence. With the new definition, these uninteresting patterns are no longer frequent, and the Apriori property holds, hence our Apriori algorithm can mine all frequent patterns with minimal endeavor. Moreover, the computation of the number of offset sequences becomes straightforward. Experiments with a DNA sequence indicate 1) the pattern frequencies under two definition sets have little difference, therefore it is reasonable to replace the existing one with the new one in practice, and 2) our algorithm runs less rounds than the best case of MMP which is based on the existing definition set.