Nonnegative Decompositions for Dynamic Visual Data Analysis.

The analysis of high-dimensional, possibly temporally misaligned, and time-varying visual data is a fundamental task in disciplines, such as image, vision, and behavior computing. In this paper, we focus on dynamic facial behavior analysis and in particular on the analysis of facial expressions. Distinct from the previous approaches, where sets of facial landmarks are used for face representation, raw pixel intensities are exploited for: 1) unsupervised analysis of the temporal phases of facial expressions and facial action units (AUs) and 2) temporal alignment of a certain facial behavior displayed by two different persons. To this end, the slow features nonnegative matrix factorization (SFNMF) is proposed in order to learn slow varying parts-based representations of time varying sequences capturing the underlying dynamics of temporal phenomena, such as facial expressions. Moreover, the SFNMF is extended in order to handle two temporally misaligned data sequences depicting the same visual phenomena. To do so, the dynamic time warping is incorporated into the SFNMF, allowing the temporal alignment of the data sets onto the subspace spanned by the estimated nonnegative shared latent features amongst the two visual sequences. Extensive experimental results in two video databases demonstrate the effectiveness of the proposed methods in: 1) unsupervised detection of the temporal phases of posed and spontaneous facial events and 2) temporal alignment of facial expressions, outperforming by a large margin the state-of-the-art methods that they are compared to.

Probabilistic Slow Features for Behavior Analysis.

A recently introduced latent feature learning technique for time-varying dynamic phenomena analysis is the so-called slow feature analysis (SFA). SFA is a deterministic component analysis technique for multidimensional sequences that, by minimizing the variance of the first-order time derivative approximation of the latent variables, 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 particular, 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 formulation of SFA and similarly extend it in order to handle two and more time-varying data sequences. Moreover, we demonstrate that the probabilistic SFA (EM-SFA) algorithm that discovers the common slowest varying latent space of multiple sequences can be combined with dynamic time warping techniques for robust sequence time-alignment. The proposed SFA algorithms were applied for facial behavior analysis, demonstrating their usefulness and appropriateness for this task.