Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
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
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
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
Facial Expression Decomposition
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
GPCA: an efficient dimension reduction scheme for image compression and retrieval
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
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
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Rank-R Approximation of Tensors: Using Image-as-Matrix Representation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Out-of-core tensor approximation of multi-dimensional matrices of visual data
ACM SIGGRAPH 2005 Papers
A Multi-Scale Hybrid Linear Model for Lossy Image Representation
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Generalized Low Rank Approximations of Matrices
Machine Learning
Separating Style and Content with Bilinear Models
Neural Computation
Journal of Cognitive Neuroscience
Tag recommendations based on tensor dimensionality reduction
Proceedings of the 2008 ACM conference on Recommender systems
A new implementation of common matrix approach using third-order tensors for face recognition
Expert Systems with Applications: An International Journal
Optimum subspace learning and error correction for tensors
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Incremental Tensor Subspace Learning and Its Applications to Foreground Segmentation and Tracking
International Journal of Computer Vision
A survey of multilinear subspace learning for tensor data
Pattern Recognition
Computers and Electrical Engineering
Feature Fusion Using Multiple Component Analysis
Neural Processing Letters
Higher-order SVD analysis for crowd density estimation
Computer Vision and Image Understanding
Tensor-SIFT Based Earth Mover's Distance for Contour Tracking
Journal of Mathematical Imaging and Vision
Modular discriminant analysis and its applications
Artificial Intelligence Review
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Dimensionality reduction has recently been extensively studied for computer vision applications. We present a novel multilinear algebra based approach to reduced dimensionality representation of multidimensional data, such as image ensembles, video sequences and volume data. Before reducing the dimensionality we do not convert it into a vector as is done by traditional dimensionality reduction techniques like PCA. Our approach works directly on the multidimensional form of the data (matrix in 2D and tensor in higher dimensions) to yield what we call a Datum-as-Is representation. This helps exploit spatio-temporal redundancies with less information loss than image-as-vector methods. An efficient rank-R tensor approximation algorithm is presented to approximate higher-order tensors. We show that rank-R tensor approximation using Datum-as-Is representation generalizes many existing approaches that use image-as-matrix representation, such as generalized low rank approximation of matrices (GLRAM) (Ye, Y. in Mach. Learn. 61:167---191, 2005), rank-one decomposition of matrices (RODM) (Shashua, A., Levin, A. in CVPR'01: Proceedings of the 2001 IEEE computer society conference on computer vision and pattern recognition, p. 42, 2001) and rank-one decomposition of tensors (RODT) (Wang, H., Ahuja, N. in ICPR '04: ICPR '04: Proceedings of the 17th international conference on pattern recognition (ICPR'04), vol. 1, pp. 44---47, 2004). Our approach yields the most compact data representation among all known image-as-matrix methods. In addition, we propose another rank-R tensor approximation algorithm based on slice projection of third-order tensors, which needs fewer iterations for convergence for the important special case of 2D image ensembles, e.g., video. We evaluated the performance of our approach vs. other approaches on a number of datasets with the following two main results. First, for a fixed compression ratio, the proposed algorithm yields the best representation of image ensembles visually as well as in the least squares sense. Second, proposed representation gives the best performance for object classification.