We present a framework for mining frequent trajectories from a database of trajectories and propose various novel optimization techniques for efficiently mining such trajectories. We begin by presenting a methodology for discovering frequent trajectories, frequent trajectories which are translated with respect to each other and frequent trajectories which are both translated and rotated w ith respect to each other. We perform experiments demonstrating the effectiveness and accuracy of our approach. We then proceed to demonstrate a multiresolution methodology base d on the wavelet transformation for speeding up the discovery of frequent trajectories and present some related experiments. We conclude the paper by proposing a met hodology for tackling the so called curse of dimensionality problem of higher dimensional trajectories, by presenting an algor ithm which scales linearly instead of exponentially as we increase the dimension of the trajectories we are interested in mining. Such optimizations are a necessity for mining higher dimensional trajectories. We conclude by pointing out some issues where more work needs to be done and argue that they can provide interest ing topics for future research.

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