Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
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
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The equivalence of two-dimensional PCA to line-based PCA
Pattern Recognition Letters
Generalized Low Rank Approximations of Matrices
Machine Learning
Equivalence of Non-Iterative Algorithms for Simultaneous Low Rank Approximations of Matrices
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
ACM Transactions on Mathematical Software (TOMS)
Is two-dimensional PCA equivalent to a special case of modular PCA?
Pattern Recognition Letters
Representing image matrices: eigenimages versus eigenvectors
ISNN'05 Proceedings of the Second international conference on Advances in neural networks - Volume Part II
MPCA: Multilinear Principal Component Analysis of Tensor Objects
IEEE Transactions on Neural Networks
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We propose simultaneous low rank approximation of tensors (SLRAT) for the dimensionality reduction of tensors and modify it to the robust one, i.e., the robust SLRAT. For both the SLRAT and the robust SLRAT, we propose iterative algorithms for solving them. It is experimentally shown that the robust SLRAT achieves lower reconstruction error than the SLRAT when a dataset contains noise data. We also propose a method for classifying sets of tensors and call it the subspace matching, where both training data and testing data are represented by their subspaces, and each testing datum is classified on the basis of the similarity between subspaces. It is experimentally verified that the robust SLRAT achieves higher recognition rate than the SLRAT when the testing data contain noise data.