  In this paper, we consider the problem of fast and efficient indexing
techniques for sequences evolving in 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 very high dimensional spaces.
The problem is made more challenging when representations such as landmarks,
contours, and human skeletons 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, dynamic texture recognition, 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.
