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 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 timealignment. The proposed SFA algorithms were applied for facial behavior analysis demonstrating their usefulness and appropriateness for this task.
Abstract-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. IndexTerms-Behavior analysis, linear dynamical system (LDS), slow feature analysis (SFA), temporal alignment.
Abstract. The predominant strategy for facial expressions analysis and temporal analysis of facial events is the following: a generic facial landmarks tracker, usually trained on thousands of carefully annotated examples, is applied to track the landmark points, and then analysis is performed using mostly the shape and more rarely the facial texture. This paper challenges the above framework by showing that it is feasible to perform joint landmarks localization (i.e. spatial alignment) and temporal analysis of behavioural sequence with the use of a simple face detector and a simple shape model. To do so, we propose a new component analysis technique, which we call Autoregressive Component Analysis (ARCA), and we show how the parameters of a motion model can be jointly retrieved. The method does not require the use of any sophisticated landmark tracking methodology and simply employs pixel intensities for the texture representation.
In this paper, we combine the principles of temporal slowness and nonnegative parts-based learning into a single framework that aims to learn slow varying parts-based representations of time varying sequences. We demonstrate that the proposed algorithm arises naturally by embedding the Slow Features Analysis trace optimization problem in the nonnegative subspace learning framework and derive novel multiplicative update rules for its optimization. The usefulness of the developed algorithm is demonstrated for unsupervised facial behaviour dynamics analysis on MMI database.
Typically, the problems of spatial and temporal alignment of sequences are considered disjoint. That is, in order to align two sequences, a methodology that (non)-rigidly aligns the images is first applied, followed by temporal alignment of the obtained aligned images. In this paper, we propose the first, to the best of our knowledge, methodology that can jointly spatio-temporally align two sequences, which display highly deformable texture-varying objects. We show that by treating the problems of deformable spatial and temporal alignment jointly, we achieve better results than considering the problems independent. Furthermore, we show that deformable spatio-temporal alignment of faces can be performed in an unsupervised manner (i.e., without employing face trackers or building person-specific deformable models).
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