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Temporal Link Prediction Using Matrix and Tensor Factorizations
ACM Transactions on Knowledge Discovery from Data (TKDD)
Krylov Subspace Methods for Linear Systems with Tensor Product Structure
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Effective hybrid recommendation combining users-searches correlations using tensors
APWeb'11 Proceedings of the 13th Asia-Pacific web conference on Web technologies and applications
Fast metadata-driven multiresolution tensor decomposition
Proceedings of the 20th ACM international conference on Information and knowledge management
Using tensor calculus for scenario modelling
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GigaTensor: scaling tensor analysis up by 100 times - algorithms and discoveries
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Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case
SIAM Journal on Scientific Computing
Fast similarity computation in factorized tensors
SISAP'12 Proceedings of the 5th international conference on Similarity Search and Applications
Tensor based sparse decomposition of 3D shape for visual detection of mirror symmetry
Computer Methods and Programs in Biomedicine
BTF compression via sparse tensor decomposition
EGSR'09 Proceedings of the Twentieth Eurographics conference on Rendering
Utilizing common substructures to speedup tensor factorization for mining dynamic graphs
Proceedings of the 21st ACM international conference on Information and knowledge management
ParCube: sparse parallelizable tensor decompositions
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Mixing and matching usage data: techniques for mining varied activity data sources
Proceedings of the 41st annual ACM SIGUCCS conference on User services
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In this paper, the term tensor refers simply to a multidimensional or $N$-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: A Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.