Geometry-based Adaptive Symbolic Approximation for Fast Sequence Matching on Manifolds: Applications to Activity Analysis

In this paper, we consider the problem of fast and efficient indexing techniques for human activity sequences evolving in Euclidean and non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search and recognition in large databases. The problem is made more challenging when features such as landmarks, contours, and stick-figures etc. are naturally studied in a non-Euclidean setting where even simple operations are much more computationally intensive than their Euclidean counterparts. We propose a geometry and data adaptive symbolic framework that is shown to enable the deployment of fast and accurate algorithms for activity recognition and motif discovery. Toward this end, we present generalizations of key concepts of piece-wise aggregation and symbolic approximation for the case of non-Euclidean manifolds. We show that one can replace expensive geodesic computations with much faster symbolic computations with little loss of accuracy in activity recognition and discovery applications. The framework is general enough to work across both Euclidean and non-Euclidean spaces, depending on appropriate feature representations without compromising on the ultra-low bandwidth, high speed and high accuracy. The proposed methods are ideally suited for real-time systems and low complexity scenarios.