Indexing Spatio-Temporal Trajectories with Chebyshev Polynomials

In this paper, we attempt to approximate and index a ddimensional (d 1) spatio-temporal trajectory with a low order continuous polynomial. There are many possible ways to choose the polynomial, including (continuous) Fourier transforms, splines, non-linear regression, etc. Some of these possibilities have indeed been studied before. We hypothesize that one of the best possibilities is the polynomial that minimizes the maximum deviation from the true value, which is called the minimax polynomial. Minimax approximation is particularly meaningful for indexing because in a branch-and-bound search (i.e., for finding nearest neighbours), the smaller the maximum deviation, the more pruning opportunities there exist. However, in general, among all the polynomials of the same degree, the optimal minimax polynomial is very hard to compute. However, it has been shown that the Chebyshev approximation is almost identical to the optimal minimax polynomial, and is easy to compute [16]. Thus, in thi...

• Type: Conference
• Year: 2004
• Where: SIGMOD
• Authors: Yuhan Cai, Raymond T. Ng
• Keywords: Chebyshev Coefficients, Chebyshev Indexing, Database, Optimal Minimax Polynomial, SIGMOD 2004