A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
SIMPLIcity: Semantics-Sensitive Integrated Matching for Picture LIbraries
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
Quantifiable data mining using ratio rules
The VLDB Journal — The International Journal on Very Large Data Bases
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized low rank approximations of matrices
ICML '04 Proceedings of the twenty-first international conference on Machine learning
IEEE Transactions on Knowledge and Data Engineering
Beyond streams and graphs: dynamic tensor analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
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
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Extracting the optimal dimensionality for local tensor discriminant analysis
Pattern Recognition
Learning optimal ranking with tensor factorization for tag recommendation
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Higher-order SVD analysis for crowd density estimation
Computer Vision and Image Understanding
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Matrix factorizations and tensor decompositions are now widely used in machine learning and data mining. They decompose input matrix and tensor data into matrix factors by optimizing a least square objective function using iterative updating algorithms, e.g. HOSVD (High Order Singular Value Decomposition) and ParaFac (Parallel Factors). One fundamental problem of these algorithms remains unsolved: are the solutions found by these algorithms global optimal? Surprisingly, we provide a positive answer for HSOVD and negative answer for ParaFac by combining theoretical analysis and experimental evidence. Our discoveries of this intrinsic property of HOSVD assure us that in real world applications HOSVD provides repeatable and reliable results.