Safe MBR-transformation in similar sequence matching

When a multidimensional index is used for similar sequence matching, the traditional approach is to transform high-dimensional window sequences to low-dimensional sequences and bounding them into a low-dimensional minimum bounding rectangle (MBR). In this paper, we propose a new approach which constructs a low-dimensional MBR by directly transforming a high-dimensional MBR (called MBR-transformation) bounding the high-dimensional sequences. This approach significantly reduces the number of lower-dimensional transformations needed in similar sequence matching. However, it poses a risk that some transformed sequences may fall outside the transformed low-dimensional MBR. We thus propose safe MBR-transformation which has the property that every possible transformed sequence is inside a safe MBR-transformed MBR. Then, considering the discrete Fourier transform (DFT) and the discrete Cosine transform (DCT), we prove that they are not safe as MBR-transformations, and modify them to become safe MBR-transformations (called mbrDFT if DFT-based and mbrDCT if DCT-based). Then, we prove the safeness and optimality of mbrDFT and mbrDCT. Analyses and experiments show that the mbrDFT and mbrDCT reduce the execution time by several orders of magnitude due to the reduction in the number of lower-dimensional transformations. The proposed safe MBR-transformation provides a useful framework for a variety of applications that require a direct transformation of a high-dimensional MBR to a low-dimensional MBR.