Academic literature on the topic 'Tensor decomposition approach'

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Journal articles on the topic "Tensor decomposition approach"

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Hameduddin, Ismail, Charles Meneveau, Tamer A. Zaki, and Dennice F. Gayme. "Geometric decomposition of the conformation tensor in viscoelastic turbulence." Journal of Fluid Mechanics 842 (March 12, 2018): 395–427. http://dx.doi.org/10.1017/jfm.2018.118.

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This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
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Ouerfelli, Mohamed, Mohamed Tamaazousti, and Vincent Rivasseau. "Random Tensor Theory for Tensor Decomposition." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 7 (June 28, 2022): 7913–21. http://dx.doi.org/10.1609/aaai.v36i7.20761.

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We propose a new framework for tensor decomposition based on trace invariants, which are particular cases of tensor networks. In general, tensor networks are diagrams/graphs that specify a way to "multiply" a collection of tensors together to produce another tensor, matrix or scalar. The particularity of trace invariants is that the operation of multiplying copies of a certain input tensor that produces a scalar obeys specific symmetry constraints. In other words, the scalar resulting from this multiplication is invariant under some specific transformations of the involved tensor. We focus our study on the O(N)-invariant graphs, i.e. invariant under orthogonal transformations of the input tensor. The proposed approach is novel and versatile since it allows to address different theoretical and practical aspects of both CANDECOMP/PARAFAC (CP) and Tucker decomposition models. In particular we obtain several results: (i) we generalize the computational limit of Tensor PCA (a rank-one tensor decomposition) to the case of a tensor with axes of different dimensions (ii) we introduce new algorithms for both decomposition models (iii) we obtain theoretical guarantees for these algorithms and (iv) we show improvements with respect to state of the art on synthetic and real data which also highlights a promising potential for practical applications.
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Zhu, Ben-Chao, and Xiang-Song Chen. "Tensor gauge condition and tensor field decomposition." Modern Physics Letters A 30, no. 35 (October 28, 2015): 1550192. http://dx.doi.org/10.1142/s0217732315501928.

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We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin [Formula: see text]. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
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Sucharitha, B., and Dr K. Anitha Sheela. "Compression of Hyper Spectral Images using Tensor Decomposition Methods." International Journal of Circuits, Systems and Signal Processing 16 (October 7, 2022): 1148–55. http://dx.doi.org/10.46300/9106.2022.16.138.

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Tensor decomposition methods have beenrecently identified as an effective approach for compressing high-dimensional data. Tensors have a wide range of applications in numerical linear algebra, chemo metrics, data mining, signal processing, statics, and data mining and machine learning. Due to the huge amount of information that the hyper spectral images carry, they require more memory to store, process and send. We need to compress the hyper spectral images in order to reduce storage and processing costs. Tensor decomposition techniques can be used to compress the hyper spectral data. The primary objective of this work is to utilize tensor decomposition methods to compress the hyper spectral images. This paper explores three types of tensor decompositions: Tucker Decomposition (TD_ALS), CANDECOMP/PARAFAC (CP) and Tucker_HOSVD (Higher order singular value Decomposition) and comparison of these methods experimented on two real hyper spectral images: the Salinas image (512 x 217 x 224) and Indian Pines corrected (145 x 145 x 200). The PSNR and SSIM are used to evaluate how well these techniques work. When compared to the iterative approximation methods employed in the CP and Tucker_ALS methods, the Tucker_HOSVD method decomposes the hyper spectral image into core and component matrices more quickly. According to experimental analysis, Tucker HOSVD's reconstruction of the image preserves image quality while having a higher compression ratio than the other two techniques.
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Fossati, Caroline, Salah Bourennane, Romuald Sabatier, and Antonio Di Giacomo. "Tensorial Model for Photolithography Aerial Image Simulation." Advances in OptoElectronics 2009 (December 6, 2009): 1–9. http://dx.doi.org/10.1155/2009/457549.

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In this paper, we propose to adapt the multilinear algebra tools to the tensor of Transmission Cross-Coefficients (TCC) values for aerial image simulation in order to keep the data tensor as a whole entity. This new approach implicitly extends the singular value decomposition (SVD) to tensors, that is, Higher Order SVD or TUCKER3 tensor decomposition which is used to obtain lower rank- tensor approximation (LRTA ). This model requires an Alternating Least Square (ALS) process known as TUCKALS3 algorithm. The needed number of kernels is estimated using two adapted criteria, well known in signal processing and information theory. For runtime improvement, we use the fixed point algorithm to calculate only the needed eigenvectors. This new approach leads to a fast and accurate algorithm to compute aerial images.
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Khoromskij, B. N. "Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D." Computational Methods in Applied Mathematics 6, no. 2 (2006): 194–220. http://dx.doi.org/10.2478/cmam-2006-0010.

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AbstractThe structured tensor-product approximation of multidimensional nonlocal operators by a two-level rank-(r1, . . . , rd) decomposition of related higher-order tensors is proposed and analysed. In this approach, the construction of the desired approximant to a target tensor is a reminiscence of the Tucker-type model, where the canonical components are represented in a fixed (uniform) basis, while the core tensor is given in the canonical format. As an alternative, the multilevel nested canonical decomposition is presented. The complexity analysis of the corresponding multilinear algebra shows an almost linear cost in the one-dimensional problem size. The existence of a low Kronecker rank two-level representation is proven for a class of function-related tensors.
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Sobolev, Konstantin, Dmitry Ermilov, Anh-Huy Phan, and Andrzej Cichocki. "PARS: Proxy-Based Automatic Rank Selection for Neural Network Compression via Low-Rank Weight Approximation." Mathematics 10, no. 20 (October 14, 2022): 3801. http://dx.doi.org/10.3390/math10203801.

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Low-rank matrix/tensor decompositions are promising methods for reducing the inference time, computation, and memory consumption of deep neural networks (DNNs). This group of methods decomposes the pre-trained neural network weights through low-rank matrix/tensor decomposition and replaces the original layers with lightweight factorized layers. A main drawback of the technique is that it demands a great amount of time and effort to select the best ranks of tensor decomposition for each layer in a DNN. This paper proposes a Proxy-based Automatic tensor Rank Selection method (PARS) that utilizes a Bayesian optimization approach to find the best combination of ranks for neural network (NN) compression. We observe that the decomposition of weight tensors adversely influences the feature distribution inside the neural network and impairs the predictability of the post-compression DNN performance. Based on this finding, a novel proxy metric is proposed to deal with the abovementioned issue and to increase the quality of the rank search procedure. Experimental results show that PARS improves the results of existing decomposition methods on several representative NNs, including ResNet-18, ResNet-56, VGG-16, and AlexNet. We obtain a 3× FLOP reduction with almost no loss of accuracy for ILSVRC-2012ResNet-18 and a 5.5× FLOP reduction with an accuracy improvement for ILSVRC-2012 VGG-16.
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Schultz, T., and H. P. Seidel. "Estimating Crossing Fibers: A Tensor Decomposition Approach." IEEE Transactions on Visualization and Computer Graphics 14, no. 6 (November 2008): 1635–42. http://dx.doi.org/10.1109/tvcg.2008.128.

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Fernandes, Sofia, Hadi Fanaee-T, and João Gama. "Dynamic graph summarization: a tensor decomposition approach." Data Mining and Knowledge Discovery 32, no. 5 (July 12, 2018): 1397–420. http://dx.doi.org/10.1007/s10618-018-0583-9.

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Shi, Qiquan, Jiaming Yin, Jiajun Cai, Andrzej Cichocki, Tatsuya Yokota, Lei Chen, Mingxuan Yuan, and Jia Zeng. "Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 5758–66. http://dx.doi.org/10.1609/aaai.v34i04.6032.

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This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same time, the generalized tensor Autoregressive Integrated Moving Average (ARIMA) is explicitly used on consecutive core tensors to predict future samples. In this manner, the proposed approach tactically incorporates the unique advantages of MDT tensorization (to exploit mutual correlations) and tensor ARIMA coupled with low-rank Tucker decomposition into a unified framework. This framework exploits the low-rank structure of block Hankel tensors in the embedded space and captures the intrinsic correlations among multiple TS, which thus can improve the forecasting results, especially for multiple short time series. Experiments conducted on three public datasets and two industrial datasets verify that the proposed BHT-ARIMA effectively improves forecasting accuracy and reduces computational cost compared with the state-of-the-art methods.
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Dissertations / Theses on the topic "Tensor decomposition approach"

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Cavalcante, Ãtalo Vitor. "Tensor approach for channel estimation in MIMO multi-hop cooperative networks." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12442.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
In this dissertation the problem of channel estimation in cooperative MIMO systems is investigated. More specifically, channel estimation techniques have been developed for a communication system assisted by relays with amplify-and-forward (AF) processing system in a three-hop scenario. The techniques developed use training sequences and enable, at the receiving node, the estimation of all the channels involved in the communication process. In an initial scenario, we consider a communication system with N transmit antennas and M receive antennas and between these nodes we have two relay groups with R1 and R2 antennas each. We propose protocols based on temporal multiplexing to coordinate the retransmission of the signals. At the end of the training phase, the receiving node estimates the channel matrices by combining the received data. By exploiting the multilinear (tensorial) structure of the sets of signals, we can model the received data through tensor models, such as PARAFAC and PARATUCK2 . This work proposes the combined use of these models and algebraic techniques to explore the spatial diversity. Secondly, we consider that the number of transmit and receive antennas at the relays may be different and that the data can travel in a bidirectional scheme (two-way). In order to validate the algorithms we use Monte-Carlo simulations in which we compare our proposed models with competing channel estimation algorithms, such as, the PARAFAC and Khatri-Rao factorization based algorithms in terms of NMSE and bit error rate.
Nesta dissertaÃÃo o problema de estimaÃÃo de canal em sistemas MIMO cooperativos à investigado. Mais especificamente, foram desenvolvidas tÃcnicas para estimaÃÃo de canal em um sistema de comunicaÃÃo assistida por relays com processamento do tipo amplifica-e-encaminha (do inglÃs, amplify-and-forward) em um cenÃrio de 3 saltos. As tÃcnicas desenvolvidas utilizam sequÃncia de treinamento e habilitam, no nà receptor, a estimaÃÃo de todos os canais envolvidos no processo de comunicaÃÃo. Em um cenÃrio inicial, consideramos um sistema de comunicaÃÃo com N antenas transmissoras e M antenas receptoras e entre esses nÃs temos dois grupos de relays com R1 e R2 antenas cada um. Foram desenvolvidos protocolos de transmissÃo baseado em multiplexaÃÃo temporal para coordenar as retransmissÃes dos sinais. Ao final da fase de treinamento, o nà receptor faz a estimaÃÃo das matrizes de canal atravÃs da combinaÃÃo dos dados recebidos. Explorando a estrutura multilinear (tensorial) dos diversos conjuntos de sinais, podemos modelar os dados recebidos atravÃs de modelos tensoriais, tais como: PARAFAC e PARATUCK2. Este trabalho propÃe a utilizaÃÃo combinada desses modelos e de tÃcnicas algÃbricas para explorar a diversidade espacial. Em um segundo momento, consideramos que o nÃmero de antenas transmissoras e receptoras dos relays podem ser diferentes e ainda que os dados podem trafegar em um esquema bidirecional (do inglÃs, two-way). Para fins de validaÃÃo dos algoritmos utilizamos simulaÃÃes de Monte-Carlo em que comparamos os modelos propostos com outros algoritmos de estimaÃÃo de canal, tais como os algoritmos baseados em PARAFAC e FatoraÃÃo de Khatri-Rao em termos de NMSE e taxa de erro de bit.
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Vu, Thi Thanh Xuan. "Optimisation déterministe et stochastique pour des problèmes de traitement d'images en grande dimension." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0540.

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Dans cette thèse on s’intéresse au problème des décompositions canoniques polyadiques de tenseurs d’ordre $N$ potentiellement grands et sous différentes contraintes (non-négativité, aspect creux lié à une possible surestimation du rang du tenseur). Pour traiter ce problème, nous proposons trois nouvelles approches itératives différentes: deux approches déterministes dont une approche proximale, et une approche stochastique. La première approche étend les travaux de thèse de J-P. Royer au cas de tenseurs de dimension $N$. Dans l’approche stochastique, nous considérons pour la première fois dans le domaine des décompositions tensorielles, des algorithmes génétiques (mimétiques) dont principe général repose sur l’évolution d’une population de candidats. Dans le dernier type d’approche, nous avons considéré un algorithme proximal pré-conditionné (le Block-Coordinate Variable Metric Forward-Backward), algorithme fonctionnant par blocs de données avec une matrice de pré-conditionnement liée à chaque bloc et fondé sur deux étapes successives principales : une étape de gradient et une étape proximale. Finalement, les différentes méthodes suggérées sont comparées entre elles et avec d’autres algorithmes classiques de la littérature sur des données synthétiques (à la fois aléatoires ou proches des données observées en spectroscopie de fluorescence) et sur des données expérimentales réelles correspondant à une campagne de surveillance des eaux d’une rivière et visant à la détection d’apparition de polluants
In this PhD thesis, we consider the problem of the Canonical Polyadic Decomposition (CPD) of potentially large $N$-th order tensors under different constraints (non-negativity, sparsity due to a possible overestimation of the tensor rank, etc.). To tackle such a problem, we propose three new iterative methods: a standard gradient based deterministic approach, a stochastic approach (memetic) and finally a proximal approach (Block-Coordinate Variable Metric Forward-Backward). The first approach extends J-P. Royer's works to the case of non-negative N-th order tensors. In the stochastic approach, genetic (memetic) methods are considered for the first time to solve the CPD problem. Their general principle is based on the evolution of a family of candidates. In the third type of approaches, a proximal algorithm namely the Block-Coordinate Variable Metric Forward-Backward is presented. The algorithm relies on two main steps: a gradient step and a proximal step. The blocks of coordinates naturally correspond to latent matrices. We propose a majorant function as well as a preconditioner with regard to each block. All methods are compared with other popular algorithms of the literature on synthetic (fluorescence spectroscopy like or random) data and on real experimental data corresponding to a water monitoring campaign aiming at detecting the appearance of pollutants
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(9192548), Zongwei Li. "Autoregressive Tensor Decomposition for NYC Taxi Data Analysis." Thesis, 2020.

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Cities have adopted evolving urban digitization strategies, and most of those increasingly focus on data, especially in the field of public transportation. Transportation data have intuitively spatial and temporal characteristics, for they are often described with when and where the trips occur. Since a trip is often described with many attributes, the transportation data can be presented with a tensor, a container which can house data in $N$-dimensions. Unlike a traditional data frame, which only has column variables, tensor is intuitively more straightforward to explore spatio-temporal data-sets, which makes those attributes more easily interpreted. However, it requires unique techniques to extract useful and relatively correct information in attributes highly correlated with each other. This work presents a mixed model consisting of tensor decomposition combined with seasonal vector autoregression in time to find latent patterns within historical taxi data classified by types of taxis, pick-up and drop-off times of services in NYC, so that it can help predict the place and time where taxis are demanded. We validated the proposed approach using the experiment evaluation with real NYC tax data. The proposed method shows the best prediction among alternative models without geographical inference, and captures the daily patterns of taxi demands for business and entertainment needs.
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Book chapters on the topic "Tensor decomposition approach"

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Vu, Xuan, Caroline Chaux, Nadège Thirion-Moreau, and Sylvain Maire. "A Proximal Approach for Nonnegative Tensor Decomposition." In Latent Variable Analysis and Signal Separation, 201–10. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53547-0_20.

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Fan, Jianchao, and Jun Wang. "A Collective Neurodynamic Optimization Approach to Nonnegative Tensor Decomposition." In Advances in Neural Networks - ISNN 2017, 207–13. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59081-3_25.

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Colace, Francesco, Dajana Conte, Brij Gupta, Domenico Santaniello, Alfredo Troiano, and Carmine Valentino. "A Novel Context-Aware Recommendation Approach Based on Tensor Decomposition." In Proceedings of Seventh International Congress on Information and Communication Technology, 453–62. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1610-6_39.

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Phan, Anh Huy, Andrzej Cichocki, Petr Tichavský, Danilo P. Mandic, and Kiyotoshi Matsuoka. "On Revealing Replicating Structures in Multiway Data: A Novel Tensor Decomposition Approach." In Latent Variable Analysis and Signal Separation, 297–305. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28551-6_37.

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Mironov, Rumen, and Ivo Draganov. "Multidimensional Graphic Objects Filtration Using HoSVD Tensor Decomposition." In New Approaches for Multidimensional Signal Processing, 255–66. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4676-5_21.

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Draganov, Ivo, and Rumen Mironov. "Tracking of Domestic Animals in Thermal Videos by Tensor Decompositions." In New Approaches for Multidimensional Signal Processing, 57–71. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4676-5_4.

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Sewe, Erik, Georg Pangalos, and Gerwald Lichtenberg. "Approaches to Fault Detection for Heating Systems Using CP Tensor Decompositions." In Advances in Intelligent Systems and Computing, 128–52. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01470-4_8.

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Kountchev, Roumen, and Roumiana Kountcheva. "Hierarchical Decomposition of Third-Order Tensor Through Adaptive Branched Inverse Difference Pyramid Based on 3D-WHT." In New Approaches for Multidimensional Signal Processing, 49–61. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-8558-3_3.

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Ding, Yue, Dong Wang, and Xin Xin. "Novel Approaches for Shop Recommendation in Large Shopping Mall Scenario: From Matrix Factorization to Tensor Decomposition." In Knowledge Science, Engineering and Management, 471–82. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25159-2_42.

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Chikitkin, Aleksandr V., and Egor K. Kornev. "Different Approaches to Numerical Solution of the Boltzmann Equation with Model Collision Integral Using Tensor Decompositions." In Smart Modelling for Engineering Systems, 105–16. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4619-2_9.

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Conference papers on the topic "Tensor decomposition approach"

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Krishnaswamy, Sriram, and Mrinal Kumar. "A Tensor Decomposition Approach to Data Association." In 2018 AIAA Guidance, Navigation, and Control Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-1134.

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Marmin, Arthur, Marc Castella, and Jean-Christophe Pesquet. "A Moment-Based Approach for Guaranteed Tensor Decomposition." In ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2020. http://dx.doi.org/10.1109/icassp40776.2020.9054186.

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Sofuoglu, Seyyid Emre, and Selin Aviyente. "A Two-Stage Approach to Robust Tensor Decomposition." In 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2018. http://dx.doi.org/10.1109/ssp.2018.8450832.

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Pimentel-Alarcon, Daniel L. "A simpler approach to low-rank tensor canonical polyadic decomposition." In 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2016. http://dx.doi.org/10.1109/allerton.2016.7852269.

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Li, Yang, Peng Yu, Luolei Zhang, Jialin Wang, and Jiansheng Wu. "An improved approach on distortion decomposition of magnetotelluric impedance tensor." In SEG Technical Program Expanded Abstracts 2010. Society of Exploration Geophysicists, 2010. http://dx.doi.org/10.1190/1.3513907.

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Sun, Yifei, and Mrinal Kumar. "A tensor decomposition approach to high dimensional stationary Fokker-Planck equations." In 2014 American Control Conference - ACC 2014. IEEE, 2014. http://dx.doi.org/10.1109/acc.2014.6859175.

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Zhang, Guoyong, Xiao Fu, Kejun Huang, and Jun Wang. "Hyperspectral Super-Resolution: A Coupled Nonnegative Block-Term Tensor Decomposition Approach." In 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2019. http://dx.doi.org/10.1109/camsap45676.2019.9022476.

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Shukla, Sparsh, Ishita Kalsi, Ayush Jain, and Ankita Verma. "A Tensor Decomposition Based Approach for Context-Aware Recommender Systems (CARS)." In IC3 '21: 2021 Thirteenth International Conference on Contemporary Computing. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3474124.3474191.

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Schnur, Jennifer J., Ryan Karl, Angelica Garcia-Martinez, Meng Jiang, and Nitesh V. Chawla. "Imputing Growth Snapshot Similarity in Early Childhood Development: A Tensor Decomposition Approach." In 2020 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). IEEE, 2020. http://dx.doi.org/10.1109/bibm49941.2020.9313188.

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Ribeiro, Lucas N., Antonio R. Hidalgo-Munoz, and Vicente Zarzoso. "Atrial signal extraction in atrial fibrillation electrocardiograms using a tensor decomposition approach." In 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE, 2015. http://dx.doi.org/10.1109/embc.2015.7320000.

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Reports on the topic "Tensor decomposition approach"

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Dunlavy, Daniel M., Evrim Acar, and Tamara Gibson Kolda. An optimization approach for fitting canonical tensor decompositions. Office of Scientific and Technical Information (OSTI), February 2009. http://dx.doi.org/10.2172/978916.

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