Indexing Spatio-Temporal Trajectories with Orthogonal Polynomials

—In this paper we consider d-dimensional spatiotemporal data (d 1) and ways to approximate and index it. We focus on indexing such data for similarity matching using orthogonal polynomial approximations. There are many ways to choose an approximation scheme for d-dimensional spatiotemporal trajectories. Some of them have been studied before. In this paper we extend the approach proposed in [6] and show that not only Chebychev orthogonal polynomials but any orthogonal polynomial scheme satis es Lower Bounding Lemma and, therefore, can be successfully used for approximating and indexing d-dimensional spatio-temporal trajectories. The basic result of the paper is Lower Bounding Lemma (a generalization of [6] result). That is, we prove that the Euclidean distance between two d-dimensional trajectories is lower bounded by Euclidean distance between the two vectors of orthogonal polynomial coef cients.