Optimal Operator Space Pursuit: A Framework for Video Sequence Data Analysis

High dimensional data sequences, such as video clips, can be modeled as trajectories in a high dimensional space and, and usually exhibit a low dimensional structure intrinsic to each distinct class of data sequence [1]. In this paper, we exploit a fibre bundle formalism to model various realizations of each trajectory, and characterize these high dimensional data sequences by an optimal operator subspace. Each operator is calculated as a matched filter corresponding to a standard Gaussian output with the data as input. The low dimensional structure intrinsic to the data is further explored, by minimizing the dimension of the operator space under data driven constraints. The dimension minimization problem is reformulated as a convex nuclear norm minimization problem, and an associated algorithm is proposed. Moreover, a fast method with superior performance for video based human activity classification is implemented by searching for an optimal operator space and adapted to the data. Illustrating examples demonstrating the performance of this approach are presented.