A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Compact Representation of Multidimensional Data Using Tensor Rank-One Decomposition
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Discriminant Analysis with Tensor Representation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Face transfer with multilinear models
ACM SIGGRAPH 2005 Papers
Out-of-core tensor approximation of multi-dimensional matrices of visual data
ACM SIGGRAPH 2005 Papers
Non-negative tensor factorization with applications to statistics and computer vision
ICML '05 Proceedings of the 22nd international conference on Machine learning
Separating Style and Content with Bilinear Models
Neural Computation
Applying Ensembles of Multilinear Classifiers in the Frequency Domain
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
A comparison of algorithms for fitting the PARAFAC model
Computational Statistics & Data Analysis
Separable linear discriminant classification
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
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This paper presents an extension of linear discriminant analysis to higher order tensors that enables robust color object recognition. Given a labeled sample of training images, the basic idea is to consider a parallel factor model of a corresponding projection tensor. In contrast to other recent approaches, we do not compute a higher order singular value decomposition of the optimal projection. Instead, we directly derive a suitable approximation from the training data. Applying an alternating least squares procedure to repeated tensor contractions allows us to compute templates or binary classifiers alike. Moreover, we show how to incorporate a regularization method and the kernel trick in order to better cope with variations in the data. Experiments on face recognition from color images demonstrate that our approach performs very reliably, even if just a few examples are available for training.