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Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors.
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On the best rank-1 and rank- ( R 1 , R 2 , … , R N ) (R_{1},R_{2},...,R_{N}) approximation of higher-order tensors
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Parallel factor analysis in sensor array processing
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On the uniqueness of multilinear decomposition of N-way arrays
N.D. Sidiropoulos and R. Bro · 2000
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Data mining with sparse grids
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Generalizing Caratheodory’s uniqueness of harmonic parameterization to N dimensions
N.D. Sidiropoulos · 2001
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Multilinear analysis of image ensembles: Tensorfaces
M.A.O. Vasilescu and D. Terzopoulos · 2002
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Kernel independent component analysis
F.R. Bach and M.I. Jordan · 2003
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Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
A. Cichocki and S. Amari · 2003
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Efficient classical simulation of slightly entangled quantum computations
G. Vidal · 2003
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Multilayer formulation of the multiconfiguration time-dependent Hartree theory
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Sparse grids
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N.D. Sidiropoulos · 2004
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Independent component analysis of fMRI group studies by self-organizing clustering
F. Esposito, T. Scarabino, A. Hyvärinen, J. Himberg, E. Formisano, S. Comani, G. Tedeschi, R. Goebel, E. Seifritz, and F. Di Salle · 2005
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Robust iterative fitting of multilinear models
S.A. Vorobyov, Y. Rong, N.D. Sidiropoulos, and A.B. Gershman · 2005
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Out-of-core tensor approximation of multi-dimensional matrices of visual data
H. Wang, Q. Wu, L. Shi, Y. Yu, and N. Ahuja · 2005
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A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization
L. De Lathauwer · 2006
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Beyond streams and graphs: Dynamic tensor analysis
J. Sun, D. Tao, and C. Faloutsos · 2006
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A randomized algorithm for a tensor-based generalization of the singular value decomposition
P. Drineas and M.W. Mahoney · 2007
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Matrix product state representations
D. Perez-Garcia, F. Verstraete, M.M. Wolf, and J.I. Cirac · 2007
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General tensor discriminant analysis and Gabor features for gait recognition
D. Tao, X. Li, X. Wu, and S. Maybank · 2007
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Decompositions of a higher-order tensor in block terms — Part I and II
L. De Lathauwer · 2008
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Decompositions of a higher-order tensor in block terms – Part III: Alternating least squares algorithms
L. De Lathauwer and D. Nion · 2008
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Tensor rank and the ill-posedness of the best low-rank approximation problem
V. de Silva and L.-H. Lim · 2008
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Quantum multiscale entanglement renormalization ansatz channels
V. Giovannetti, S. Montangero, and R. Fazio · 2008
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Higher-order SVD based subspace estimation to improve the parameter estimation accuracy in multi-dimensional harmonic retrieval problems
M. Haardt, F. Roemer, and G. Del Galdo · 2008
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Simultaneous tensor subspace selection and clustering: The equivalence of high order SVD and K-means clustering
H. Huang, C. Ding, D. Luo, and T. Li · 2008
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Applied Multiway Data Analysis
P.M. Kroonenberg · 2008
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Tensor-CUR decompositions for tensor-based data
M.W. Mahoney, M. Maggioni, and P. Drineas · 2008
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Analytical advantages of multivariate data processing. One, two, three, infinity?
A.C. Olivieri · 2008
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Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
F. Verstraete, V. Murg, and I. Cirac · 2008
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Unsupervised multiway data analysis: A literature survey
E. Acar and B. Yener · 2009
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From sparse solutions of systems of equations to sparse modeling of signals and images
A. Bruckstein, D. Donoho, and M. Elad · 2009
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Anomaly detection: A survey
V. Chandola, A. Banerjee, and V. Kumar · 2009
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Probabilistic models for incomplete multi-dimensional arrays
W. Chu and Z. Ghahramani · 2009
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Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
A. Cichocki, R Zdunek, A.-H. Phan, and S. Amari · 2009
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Fast Newton-type methods for nonnegative matrix and tensor approximation
I.S. Dhillon · 2009
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Algorithms for entanglement renormalization
G. Evenbly and G. Vidal · 2009
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Tensor-product representations for string-net condensed states
Z.-C. Gu, M. Levin, B. Swingle, and X.-G. Wen · 2009
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A new scheme for the tensor representation
W. Hackbusch and S. Kühn · 2009
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Tensor decompositions and applications
T.G. Kolda and B.W. Bader · 2009
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CUR matrix decompositions for improved data analysis
M.W. Mahoney and P. Drineas · 2009
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Breaking the curse of dimensionality, or how to use SVD in many dimensions
I.V. Oseledets and E.E. Tyrtyshnikov · 2009
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Sequential unfolding SVD for tensors with applications in array signal processing
J. Salmi, A. Richter, and V. Koivunen · 2009
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Fast approximate joint diagonalization incorporating weight matrices
P. Tichavsky and A. Yeredor · 2009
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Variational learning of inducing variables in sparse Gaussian processes
M.K. Titsias · 2009
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Generalizing the column-row matrix decomposition to multi-way arrays
C. Caiafa and A. Cichocki · 2010
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Handbook of Blind Source Separation: Independent Component Analysis and Applications
P. Comon and C. Jutten · 2010
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Hierarchical singular value decomposition of tensors
L. Grasedyck · 2010
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Concatenated tensor network states
R. Hübener, V. Nebendahl, and W. Dür · 2010
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Multiarray signal processing: Tensor decomposition meets compressed sensing
L.H. Lim and P. Comon · 2010
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Approximation of 2 d × 2 d 2^{d}\times 2^{d} matrices using tensor decomposition
I.V. Oseledets · 2010
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TT cross–approximation for multidimensional arrays
I.V. Oseledets and E.E. Tyrtyshnikov · 2010
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Tensor decompositions for feature extraction and classification of high dimensional datasets
A.H. Phan and A. Cichocki · 2010
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PEPS as ground states: Degeneracy and topology
N. Schuch, I. Cirac, and D. Pérez-García · 2010
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Minimally entangled typical thermal state algorithms
E.M. Stoudenmire and Steven R. White · 2010
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Renormalization of tensor-network states
H.H. Zhao, Z.Y. Xie, Q.N. Chen, Z.C. Wei, J.W. Cai, and T. Xiang · 2010
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Quantum-information analysis of electronic states of different molecular structures
G. Barcza, Ö. Legeza, K.H. Marti, and M. Reiher · 2011
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Adaptive cross-approximation of multivariate functions
M. Bebendorf · 2011
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Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
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Tall and skinny QR factorizations in MapReduce architectures
P.G. Constantine and D.F. Gleich · 2011
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Population value decomposition, a framework for the analysis of image populations
C. Crainiceanu, B. Caffo, S. Luo, V. Zipunnikov, and N. Punjabi · 2011
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Blind separation of exponential polynomials and the decomposition of a tensor in rank- ( L r , L r , 1 ) ({L}_{r},{L}_{r},1) terms
L. De Lathauwer · 2011
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Linked independent component analysis for multimodal data fusion
A.R. Groves, C.F. Beckmann, S.M. Smith, and M.W. Woolrich · 2011
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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
N. Halko, P. Martinsson, and J. Tropp · 2011
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O ( d log N ) O(d\log N) -quantics approximation of N N - d d tensors in high-dimensional numerical modeling
B.N. Khoromskij · 2011
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Tensors-structured numerical methods in scientific computing: Survey on recent advances
B.N. Khoromskij · 2011
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A survey of multilinear subspace learning for tensor data
H. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos · 2011
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Randomized algorithms for matrices and data
M.W. Mahoney · 2011
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Applications of tensor (multiway array) factorizations and decompositions in data mining
M. Mørup · 2011
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Tensor-train decomposition
I.V. Oseledets · 2011
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NCON: A tensor network contractor for MATLAB
R. Pfeifer, G. Evenbly, S. Singh, and G. Vidal · 2014
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Group-PCA for very large fMRI datasets
S.M. Smith, A. Hyvärinen, G. Varoquaux, K.L. Miller, and C.F. Beckmann · 2014
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Breaking the curse of dimensionality using decompositions of incomplete tensors: Tensor-based scientific computing in big data analysis
N. Vervliet, O. Debals, L. Sorber, and L. De Lathauwer · 2014
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Learning multidimensional Fourier series with tensor trains
S. Wahls, V. Koivunen, H.V. Poor, and M. Verhaegen · 2014
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Spectral gap error bounds for improving CUR matrix decomposition and the Nyström method
D. Anderson, S. Du, M. Mahoney, C. Melgaard, K. Wu, and M. Gu · 2015
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Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification
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The density-matrix renormalization group in the age of matrix product states
U. Schollwöck · 2011
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A least-squares framework for component analysis
F. De la Torre · 2012
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TensorCalculus library, 2012
M Espig, M Schuster, A Killaitis, N Waldren, P Wähnert, S Handschuh, and H Auer · 2012
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Tensor Spaces and Numerical Tensor Calculus
W. Hackbusch · 2012
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W. Austin, G. Ballard, and T.G. Kolda · 2015
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MATLAB tensor toolbox version 2.6, February 2015
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Improving the numerical stability of fast matrix multiplication algorithms
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Brief announcement: Hypergraph partitioning for parallel sparse matrix-matrix multiplication
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A constructive arbitrary-degree Kronecker product decomposition of tensors
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