Similarity search over incomplete symbolic sequences

Reliable measure of similarity between symbolic sequences is an important problem in the fields of database and data mining. A lot of distance functions have been developed for symbolic sequence data in the past years. However, most of them are focused on the distance between complete symbolic sequences while the distance measurement for incomplete symbolic sequences remains unexplored. In this paper, we propose a method to process similarity search over incomplete symbolic sequences. Without any knowledge about the positions and values of the missing elements, it is impossible to get the exact distance between a query sequence and an incomplete sequence. Instead of calculating this exact distance, we map a pair of symbolic sequences to a real-valued interval, i.e, we propose a lower bound and an upper bound of the underlying exact distance between a query sequence and an incomplete sequence. In this case, similarity search can be conducted with guaranteed performance in terms of either recall or precision. The proposed method is also extended to handle with real-valued sequence data. The experimental results on both synthetic and real-world data show that our method is both efficient and effective.