Learning slow features for behavior analysis

A recently introduced latent feature learning technique for time varying dynamic phenomena analysis is the socalled Slow Feature Analysis (SFA). SFA is a deterministic component analysis technique for multi-dimensional sequences that by minimizing the variance of the first order time derivative approximation of the input signal finds uncorrelated projections that extract slowly-varying features ordered by their temporal consistency and constancy. In this paper, we propose a number of extensions in both the deterministic and the probabilistic SFA optimization frameworks. In articular, we derive a novel deterministic SFA algorithm that is able to identify linear projections that extract the common slowest varying features of two or more sequences. In addition, we propose an Expectation Maximization (EM) algorithm to perform inference in a probabilistic ormulation of SFA and similarly extend it in order to handle two and more time varying data sequences. Moreover, we demonstrate that the probabilistic SFA (EMSFA) algorithm that discovers the common slowest varying latent space of multiple sequences can be combined with dynamic time warping chniques for robust sequence timealignment. The proposed SFA algorithms were applied for facial behavior analysis demonstrating their usefulness and appropriateness for this task.