Discovering Similar Multidimensional Trajectories

We investigate techniques for analysis and retrieval of object trajectories in a two or three dimensional space. Examples include features extracted from video clips, animal mobility experiments, sign language recognition, mobile phone usage and so on. Such data usually contain a great amount of noise, that degrades the performance of previously used metrics. Therefore, here we formalize non-metric similarity functions based on the Longest Common Subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to the similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translating of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and Time Warping distance functions (for real and synthetic data) and show the superiority of our approach, especially under the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach.