Activity Video Analysis via Operator-Based Local Embedding

High dimensional data sequences, such as video clips, can be modeled as trajectories in a high dimensional space, and usually exhibit a low dimensional structure intrinsic to each distinct class of data sequence [1]. In this paper, we proposed a novel geometric framework to investigate the temporal relations as well as spatial features in a video sequence. Important visual features are preserved by mapping a high dimensional video sequence to operators in a circulant operator space (image operator space). The corresponding operator sequence is subsequently embedded into a low dimensional space, in which the temporal dynamics of each sequence is well preserved. In addition, an algorithm for human activity video classification is implemented by employing Markov models in the low dimensional embedding space, and illustrating examples and classification performance are presented.