Tensor Decompositions and Applications

Kolda, Tamara G.; Bader, Brett W.

doi:10.1137/07070111x

Cited by 8,408 publications

(7,657 citation statements)

References 204 publications

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“…This leads to the NTD model with many potential applications in neuroscience, bioinformatics, chemometrics and text mining [1,16,25]. For three-dimensional data the basic Tucker-3 model of a tensor Y is represented with three factors A = A (1) , B = A (2) , C = A (3)…”

Section: Nonnegative Tucker Decompositionmentioning

confidence: 99%

“…Most algorithms for the nonnegative matrix and tensor factorizations are based on the ALS minimization of the squared Euclidean distance (Frobenius norm) [2,25,35,37] used as the global cost function subject to nonnegativity constraints, that is…”

Section: Standard Als Algorithm For Nonnegative Tucker Decompositionmentioning

confidence: 99%

“…The performance of the new algorithm is compared with wellknown existing algorithms (HOOI [2], HONMF [16], and standard ALS [29]). …”

Section: Introductionmentioning

confidence: 99%

“…Tensor decompositions are emerging as novel and promising tools for exploratory analysis of multidimen-sional data in diverse disciplines including text mining, neuroscience, computer vision, and social networks analysis [1][2][3][4]. Tensor decompositions capture multilinear structures in higher-order data-sets, where the data have more than two modes [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Phan

Cichocki

2011

Neurocomputing

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Section: Nonnegative Tucker Decompositionmentioning

confidence: 99%

Section: Standard Als Algorithm For Nonnegative Tucker Decompositionmentioning

confidence: 99%

“…The performance of the new algorithm is compared with wellknown existing algorithms (HOOI [2], HONMF [16], and standard ALS [29]). …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Phan

Cichocki

2011

Neurocomputing

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“…Section 6 concludes the work. [33]. The multi-way structure of tensor provides a natural way to encode the underlying multiple dependencies in the sequential multivariate data.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Large-Scale Traffic Dynamics in an Urban Transportation Network Using Non-Negative Tensor Factorization

Han

Moutarde

2014

Int. J. ITS Res.

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In this paper, we present our work on clustering and prediction of temporal evolution of global congestion configurations in a large-scale urban transportation network. Instead of looking into temporal variations of traffic flow states of individual links, we focus on temporal evolution of the complete spatial configuration of congestions over the network. In our work, we pursue to describe the typical temporal patterns of the global traffic states and achieve long-term prediction of the large-scale traffic evolution in a unified data-mining framework. To this end, we formulate this joint task using regularized Non-negative Tensor Factorization, which has been shown to be a useful analysis tool for spatio-temporal data sequences. Clustering and prediction are performed based on the compact tensor factorization results. The validity of the proposed spatio-temporal traffic data analysis method is shown on experiments using simulated realistic traffic data.

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An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies

Afonso

Zlotnik

Dı́ez

2015

Geochem Geophys Geosyst

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Abstract. We present a flexible, general and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on multi-dimensional decomposition methods, which transform the original multi-dimensional discrete information into a separated representation that contains significantly less terms, thus drastically reducing the amount of information to be stored in memory during a numerical simulation or geophysical inversion. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g. preliminary runs vs full resolution runs). We illustrate the benefits, generality and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies. MAT-LAB implementations of the method and examples can be downloaded from [link].

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Tensor Decompositions and Applications

Cited by 8,408 publications

References 204 publications

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Analysis of Large-Scale Traffic Dynamics in an Urban Transportation Network Using Non-Negative Tensor Factorization

An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies

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