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SIAM Journal on Matrix Analysis and Applications
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
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CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
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Grassmann Registration Manifolds for Face Recognition
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Canonical Correlation Analysis of Video Volume Tensors for Action Categorization and Detection
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Tensor Decompositions and Applications
SIAM Review
Canonical Stiefel quotient and its application to generic face recognition in illumination spaces
BTAS'09 Proceedings of the 3rd IEEE international conference on Biometrics: Theory, applications and systems
Gesture recognition under small sample size
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Action Recognition in Videos Using Nonnegative Tensor Factorization
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
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ICVS'11 Proceedings of the 8th international conference on Computer vision systems
Class consistent k-means: Application to face and action recognition
Computer Vision and Image Understanding
WACV '12 Proceedings of the 2012 IEEE Workshop on the Applications of Computer Vision
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Advances in matrix manifolds for computer vision
Image and Vision Computing
Online RGB-D gesture recognition with extreme learning machines
Proceedings of the 15th ACM on International conference on multimodal interaction
One-shot learning gesture recognition from RGB-D data using bag of features
The Journal of Machine Learning Research
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Action videos are multidimensional data and can be naturally represented as data tensors. While tensor computing is widely used in computer vision, the geometry of tensor space is often ignored. The aim of this paper is to demonstrate the importance of the intrinsic geometry of tensor space which yields a very discriminating structure for action recognition. We characterize data tensors as points on a product manifold and model it statistically using least squares regression. To this aim, we factorize a data tensor relating to each order of the tensor using Higher Order Singular Value Decomposition (HOSVD) and then impose each factorized element on a Grassmann manifold. Furthermore, we account for underlying geometry on manifolds and formulate least squares regression as a composite function. This gives a natural extension from Euclidean space to manifolds. Consequently, classification is performed using geodesic distance on a product manifold where each factor manifold is Grassmannian. Our method exploits appearance and motion without explicitly modeling the shapes and dynamics. We assess the proposed method using three gesture databases, namely the Cambridge hand-gesture, the UMD Keck body-gesture, and the CHALEARN gesture challenge data sets. Experimental results reveal that not only does the proposed method perform well on the standard benchmark data sets, but also it generalizes well on the one-shot-learning gesture challenge. Furthermore, it is based on a simple statistical model and the intrinsic geometry of tensor space.