Efficient MATLAB Computations with Sparse and Factored Tensors

By Brett W. Bader, Tamara G. Kolda. SIAM Journal on Scientific Computing, 2007

509 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mathematics, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/0072eb224991ada6fc8a4e2d3465e4a51c0b26bc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Mathematics

In Hardware and Architecture

Citations in the corpus

Krylov-type methods for tensor computations I (2013, methodology): “The calculations were performed using Matlab and the TensorToolbox, which supports computation with sparse tensors [2, 3].”
Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions (2009, methodology): “This algorithm for the computation of the Tucker factors from the canonical decomposition based on Gram matrices is known [1].”
TT-cross approximation for multidimensional arrays (2010, background): “This includes sparse tensors [2] and tensors with shift-invariant (Toeplitz or Hankel) structure [1].”
Distributed large-scale tensor decomposition (2014, background): “Note that the data explosion problem can also be handled by exploiting sparseness of both data and latent factors as in [11, 12, 13].”
Tensors for Data Mining and Data Fusion (2016, background): “It is important to note that the kernel is also called Matricized Tensor Times Khatri-Rao Product or MTTKRP for short [Bader and Kolda 2007; Kolda and Bader 2009].”
Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case (2010, methodology): “We compare three methods: the Tucker-ALS [22, 7] (MATLAB implementation from Tensor Toolbox [1]), the minimal Krylov recursion (Alg.”
Temporal Link Prediction Using Matrix and Tensor Factorizations (2010, methodology): “We compute the CP model via an Alternating Least Squares (ALS) approach using the Tensor Toolbox for Matlab [Bader and Kolda 2007].”
COPA: Constrained PARAFAC2 for Sparse & Large Datasets (2018, unknown): “Matricized-Tensor-Times-Khatri-Rao-Product[3] (MTTKRP) is a multiplication which a naive construction of that for large and sparse tensors needs computational cost and enormous memory.”
MACH: Fast Randomized Tensor Decompositions (2009, methodology): “Experimental Setup We used the Tensor Toolbox [ 4 ], which contains MATLAB implementations of the HOSVD and the HOOI.”
Two-level Tucker-TT-QTT format for optimized tensor calculus (2012, background): “a tensor is (pointwise) sparse, the simplest approach is to store and use in computations only these elements [2, 3].”
SUSTain: Scalable Unsupervised Scoring for Tensors and its Application to Phenotyping (2018, methodology): “The Matricized-Tensor Times Khatri-Rao Product (MTTKRP) [3] w.”
Scalable Tensor Decompositions for Multi-aspect Data Mining (2008, methodology): “This calculation can be done with O(nnz(X)) memory and is described in detail in [6].”