Low order dynamics embedding for high dimensional time series

This paper considers the problem of finding low order nonlinear embeddings of dynamic data, that is, data characterized by a temporal ordering. Examples where this problem arises include, among others, appearance-based multi-frame tracking, activity recognition from video and dynamic texture analysis/synthesis. Our main result is a semi-definite programming based manifold embedding algorithm that exploits the dynamical information encapsulated in the temporal ordering of the sequence to obtain embeddings with lower complexity that those produced by existing algorithms, at a comparable computational cost. In addition, the use of spatio-temporal information allows for minimizing the effects of outliers on the manifold structure and for handling fragmented sequences, where some of the data is missing, for instance due to occlusion.