Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Hierarchical Latent Variable Model for Data Visualization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Human Motion Signatures: Analysis, Synthesis, Recognition
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 3 - Volume 3
Facial Expression Decomposition
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
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
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
A Tensor Decomposition for Geometric Grouping and Segmentation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Generalized Low Rank Approximations of Matrices
Machine Learning
Multilinear Discriminant Analysis for Face Recognition
IEEE Transactions on Image Processing
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In this corespondence, we study the extra-factor estimation problem with the assumption that the training image ensemble is expressed as an n th-order tensor with the nth-dimension characterizing all features for an image and other dimensions for different extra factors, such as illuminations, poses, and identities. To overcome the local minimum issue of conventional algorithms designed for this problem, we present a novel statistical learning framework called mode-kn Factor Analysis for obtaining a closed-form solution to estimating the extra factors of any test image. In the learning stage, for the kth (k ≠ n) dimension of the data tensor, the mode- Kn patterns are constructed by concatenating the feature dimension and the kth extra-factor dimension, and then a mode-kn factor analysis model is learnt based on the mode-kn patterns unfolded from the original data tensor. In the inference stage, for a test image, the mode classification of the kth dimension is performed within a probabilistic framework. The advantages of mode-kn factor analysis over conventional tensor analysis algorithms are twofold: 1) a closed-form solution, instead of iterative sub-optimal solution as conventionally, is derived for estimating the extra-factor mode of any test image; and 2) the classification capability is enhanced by interacting with the process of synthesizing data of all other modes in the kth dimension. Experiments on the Pointing'04 and CMUPIE databases for pose and illumination estimation both validate the superiority of the proposed algorithm over conventional algorithms for extra-factor estimation.