A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
A Projection Method for Least Squares Problems with a Quadratic Equality Constraint
SIAM Journal on Matrix Analysis and Applications
Facial Expression Decomposition
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Multilinear Independent Components Analysis
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Separating Style and Content with Bilinear Models
Neural Computation
Journal of Cognitive Neuroscience
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Facial images change appearance due to multiple factors such as poses, lighting variations, facial expressions, etc. Tensor approach, an extension of conventional matrix, is appropriate to analyze facial factors since we can construct multilinear models consisting of multiple factors using tensor framework. However, given a test image, tensor factorization, i.e., decomposition of mixing factors, is a difficult problem especially when the factor parameters are unknown or are not in the training set. In this paper, we propose a novel tensor factorization method to decompose the mixing factors of a test image. We set up a tensor factorization problem as a least squares problem with a quadratic equality constraint, and solve it using numerical optimization techniques. The novelty in our approach compared to previous work is that our tensor factorization method does not require any knowledge or assumption of test images. We have conducted several experiments to show the versatility of the method for both face recognition and face synthesis.