An MBR-Safe Transform for High-Dimensional MBRs in Similar Sequence Matching

Abstract

In this paper we propose a formal approach that transforms a high-dimensional MBR itself to a low-dimensional MBR directly, and show that the approach significantly reduces the number of lower-dimensional transformations in similar sequence matching. To achieve this goal, we first formally define a new notion of MBR-safe. We say that a transform is MBR-safe if it constructs a low-dimensional MBR by containing all the low-dimensional sequences to which an infinite number of high-dimensional sequences in an MBR are transformed. We then propose an MBR-safe transform based on DFT. For this, we prove the original DFT-based lower-dimensional transformation is not MBR-safe and define a new transform, called mbrDFT, by extending definition of DFT. We also formally prove this mbrDFT is MBR-safe. Analytical and experimental results show that our mbrDFT reduces the number of lower-dimensional transformations drastically and improves performance significantly compared with the traditional method.