Dimensionality Reduction for Long Duration and Complex Spatio-temporal Queries Technical Report 592 Ghazi Al-naymat and Sanjay Chawla University of Sydney

From tracking of moose in Sweden, to movement of traffic in a large metropolis, spatio-temporal data is continuously being collected and made available in the public domain. This provides an opportunity to mine and query spatio-temporal data with the purpose of finding substantial patterns and understand the underlying data generating process. An important class of queries is based on the flock pattern. A flock is a large subset of objects moving along paths close to each other for a certain pre-defined time. The standard approach to process a “flock query” is to map spatio-temporal data into a high dimensional space and reduce the query into a sequence of standard range queries which can be presented using a spatial indexing structure. However, as it is well known, the performance of spatial indexing structures drastically deteriorates in high dimensional space. In this paper we propose a preprocessing strategy which consists of using a random projection to reduce the dimensionality of the transformed space. We prove an ′′2 − δ′′ probabilistic approximation which results from the projection and present experimental results which show, for the first time, the possibility of breaking the curse of dimensionality in a spatio-temporal setting.