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Abstract: This work addresses the two class classification problem within the tensor-based large margin classification paradigm. To this end, we formulate the higher rank Support Tensor Machines (STMs), in which the parameters defining the separating hyperplane form a tensor (tensorplane) that is constrained to be the sum of rank one tensors. Subsequently, we propose two extensions in which the separating tensorplanes take into consideration the spread of the training data along the different tensor modes. More specifically, we first propose the higher rank STMs that use the total or the within-class covariance matrix in order to whiten the data and thus provide invariance to affine transformations. Second, we propose the higher rank Relative Margin Support Tensor Machines (RMSTMs) that bound from above the distance of the data samples from the separating tensorplane while maximizing the margin from it. The corresponding optimization problem is solved in an iterative manner utilizing the CANDECOMP/PARAFAC (CP) decomposition, where at each iteration the parameters corresponding to the projections along a single tensor mode are estimated by solving a typical Support Vector Machine (SVM)-type optimization problem. The efficiency of the proposed method is illustrated on the problems of gait and action recognition where we report results that improve, in some cases considerably, the state of the art. [Copyright &y& Elsevier]

Abstract: A novel method based on fusion of texture and shape information is proposed for facial expression and Facial Action Unit (FAU) recognition from video sequences. Regarding facial expression recognition, a subspace method based on Discriminant Non-negative Matrix Factorization (DNMF) is applied to the images, thus extracting the texture information. In order to extract the shape information, the system firstly extracts the deformed Candide facial grid that corresponds to the facial expression depicted in the video sequence. A Support Vector Machine (SVM) system designed on an Euclidean space, defined over a novel metric between grids, is used for the classification of the shape information. Regarding FAU recognition, the texture extraction method (DNMF) is applied on the differences images of the video sequence, calculated taking under consideration the neutral and the expressive frame. An SVM system is used for FAU classification from the shape information. This time, the shape information consists of the grid node coordinate displacements between the neutral and the expressed facial expression frame. The fusion of texture and shape information is performed using various approaches, among which are SVMs and Median Radial Basis Functions (MRBFs), in order to detect the facial expression and the set of present FAUs. The accuracy achieved using the Cohn–Kanade database is 92.3% when recognizing the seven basic facial expressions (anger, disgust, fear, happiness, sadness, surprise and neutral), and 92.1% when recognizing the 17 FAUs that are responsible for facial expression development. [Copyright &y& Elsevier]