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1

Wang, Hai Jun, Fei Yun Xu, and Fei Wang. "Tensor Factorization and Clustering for the Feature Extraction Based on Tucker3 with Updating Core." Advanced Materials Research 308-310 (August 2011): 2517–22. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.2517.

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Aiming at the problems of Tucker3 to large-scale tensor when applied to feature extraction, a new factorization based on Tucker3 is proposed to extract feature from the tensors. First, the large-scale tensor is divided into multiple sub-tensors so as to conveniently compute cores of sub-tensors in parallel mode with Matlab Parallel Computing Toolbox; Then, the cores of each sub-tensor are updated for reducing deviation in calculating and the similar characteristics of sub-tensors are clustered to obtain the features. Experiment results show that this methods is able to extract features rapidly
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Zhou, Ruofei, Gang Wang, Bo Li, Jinlong Wang, Tianzhu Liu, and Chungang Liu. "Key-Frame Detection and Super-Resolution of Hyperspectral Video via Sparse-Based Cumulative Tensor Factorization." Mathematical Problems in Engineering 2020 (July 14, 2020): 1–20. http://dx.doi.org/10.1155/2020/9548749.

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Thanks to the rapid development of hyperspectral sensors, hyperspectral videos (HSV) can now be collected with high temporal and spectral resolutions and utilized to handle invisible dynamic monitoring missions, such as chemical gas plume tracking. However, using such sequential large-scale data effectively is challenged, because the direct process of these data requires huge demands in terms of computational loads and memory. This paper presents a key-frame and target-detecting algorithm based on cumulative tensor CANDECOMP/PARAFAC (CP) factorization (CTCF) to select the frames where the targ
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Chen, Zhengyu, Ziqing Xu, and Donglin Wang. "Deep Transfer Tensor Decomposition with Orthogonal Constraint for Recommender Systems." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 5 (2021): 4010–18. http://dx.doi.org/10.1609/aaai.v35i5.16521.

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Tensor decomposition is one of the most effective techniques for multi-criteria recommendations. However, it suffers from data sparsity when dealing with three-dimensional (3D) user-item-criterion ratings. To mitigate this issue, we consider effectively incorporating the side information and cross-domain knowledge in tensor decomposition. A deep transfer tensor decomposition (DTTD) method is proposed by integrating deep structure and Tucker decomposition, where an orthogonal constrained stacked denoising autoencoder (OC-SDAE) is proposed for alleviating the scale variation in learning effectiv
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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
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Shi, Qiquan, Jiaming Yin, Jiajun Cai, et al. "Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (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 cor
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Tang, Tao, and Gangyao Kuang. "SAR Image Reconstruction of Vehicle Targets Based on Tensor Decomposition." Electronics 11, no. 18 (2022): 2859. http://dx.doi.org/10.3390/electronics11182859.

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Due to the imaging mechanism of Synthetic Aperture Radars (SARs), the target shape on an SAR image is sensitive to the radar incidence angle and target azimuth, but there is strong correlation and redundancy between adjacent azimuth images of SAR targets. This paper studies multi-angle SAR image reconstruction based on non-negative Tucker decomposition using adjacent azimuth images reconstructed to form a sparse tensor. Sparse tensors are used to perform non-negative Tucker decomposition, resulting in non-negative core tensors and factor matrices. The reconstruction tensor is obtained by calcu
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Maruszewski, B. "On a Dislocation Core Tensor." physica status solidi (b) 168, no. 1 (1991): 59–66. http://dx.doi.org/10.1002/pssb.2221680105.

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Arora, Jai, Sirui Lu, Devansh Jain, et al. "TensorRight: Automated Verification of Tensor Graph Rewrites." Proceedings of the ACM on Programming Languages 9, POPL (2025): 832–63. https://doi.org/10.1145/3704865.

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Tensor compilers, essential for generating efficient code for deep learning models across various applications, employ tensor graph rewrites as one of the key optimizations. These rewrites optimize tensor computational graphs with the expectation of preserving semantics for tensors of arbitrary rank and size. Despite this expectation, to the best of our knowledge, there does not exist a fully automated verification system to prove the soundness of these rewrites for tensors of arbitrary rank and size. Previous works, while successful in verifying rewrites with tensors of concrete rank, do not
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Jin, Hongwei, Mengyu He, and Yuzhen Wang. "The expressions of the generalized inverses of the block tensor via the C-product." Filomat 37, no. 26 (2023): 8909–26. http://dx.doi.org/10.2298/fil2326909j.

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In this paper, we present the expressions of the generalized inverses of the third-order 2 ? 2 block tensor under the C-Product. Firstly, we give the necessary and sufficient conditions to present some generalized inverses and the Moore-Penrose inverse of the block tensor in Banachiewicz-Schur forms. Next, some results are generalized to the group inverse and the Drazin inverse. Moreover, equivalent conditions for the existence as well as the expressions for the core inverse of the block tensor are obtained. Finally, the results are applied to express the quotient property and the first Sylsve
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Yang, Chuhong, Bin Li, and Nan Wu. "SPAC: Sparse Partitioning and Adaptive Core Tensor Pruning Model for Knowledge Graph Completion." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 14 (2025): 15230–38. https://doi.org/10.1609/aaai.v39i14.33671.

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Tensor decomposition (TD) models are promising solutions for knowledge graph completion due to their simple structures but powerful representation capacities. The TD models typically adopt Tucker decomposition with a structured core tensor. Some models with a sparse core tensor, such as DistMult and ComplEx, are too simple and thus limit the interaction between embedding components, while other models with a dense core tensor are too complex and may lead to significant overfitting. To address these issues, we propose a new TD model called SPAC (Sparse Partitioning and Adaptive Core tensor prun
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Zhou, Yajian, Zongqian Yue, and Zhe Chen. "A Two-Level Parallel Incremental Tensor Tucker Decomposition Method with Multi-Mode Growth (TPITTD-MG)." Mathematics 13, no. 7 (2025): 1211. https://doi.org/10.3390/math13071211.

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With the rapid growth of streaming data, traditional tensor decomposition methods can hardly handle real-time, high-dimensional data of massive amounts in this scenario. In this paper, a two-level parallel incremental tensor Tucker decomposition method with multi-mode growth (TPITTD-MG) is proposed to address the low parallelism issue of the existing Tucker decomposition methods on large-scale, high-dimensional, dynamically growing data. TPITTD-MG involves two mechanisms, i.e., a parallel sub-tensor partitioning mechanism based on the dynamic programming (PSTPA-DP) and a two-level parallel upd
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Li, Yang, Guangcan Liu, Yubao Sun, Qingshan Liu, and Shengyong Chen. "3D Tensor Auto-encoder with Application to Video Compression." ACM Transactions on Multimedia Computing, Communications, and Applications 17, no. 2 (2021): 1–18. http://dx.doi.org/10.1145/3431768.

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Auto-encoder has been widely used to compress high-dimensional data such as the images and videos. However, the traditional auto-encoder network needs to store a large number of parameters. Namely, when the input data is of dimension n , the number of parameters in an auto-encoder is in general O ( n ). In this article, we introduce a network structure called 3D Tensor Auto-Encoder (3DTAE). Unlike the traditional auto-encoder, in which a video is represented as a vector, our 3DTAE considers videos as 3D tensors to directly pass tensor objects through the network. The weights of each layer are
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Mangngiri, Itsar, Qonita Qurrota A’yun, and Wasono Wasono. "AN ORDER-P TENSOR MULTIPLICATION WITH CIRCULANT STRUCTURE." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 4 (2023): 2293–304. http://dx.doi.org/10.30598/barekengvol17iss4pp2293-2304.

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Research on mathematical operations involving multidimensional arrays or tensors has increased along with the growing applications involving multidimensional data analysis. The -product of order- tensor is one of tensor multiplications. The -product is defined using two operations that transform the multiplication of two tensors into the multiplication of two block matrices, then the result is a block matrix which is further transformed back into a tensor. The composition of both operations used in the definition of -product can transform a tensor into a block circulant matrix. This research d
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Kuznetsov, Maxim A., and Ivan V. Oseledets. "Tensor Train Spectral Method for Learning of Hidden Markov Models (HMM)." Computational Methods in Applied Mathematics 19, no. 1 (2019): 93–99. http://dx.doi.org/10.1515/cmam-2018-0027.

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AbstractWe propose a new algorithm for spectral learning of Hidden Markov Models (HMM). In contrast to the standard approach, we do not estimate the parameters of the HMM directly, but construct an estimate for the joint probability distribution. The idea is based on the representation of a joint probability distribution as an N-th-order tensor with low ranks represented in the tensor train (TT) format. Using TT-format, we get an approximation by minimizing the Frobenius distance between the empirical joint probability distribution and tensors with low TT-ranks with core tensors normalization
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Somesh Nagalla. "Technical Review: Tensor-Decomposition Stream Codec." World Journal of Advanced Engineering Technology and Sciences 15, no. 3 (2025): 1051–59. https://doi.org/10.30574/wjaets.2025.15.3.0981.

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The Tensor-Decomposition Stream Codec represents a revolutionary advancement in data compression technology for high-dimensional event streams. This innovative solution transforms how clickstream and IoT data are processed by leveraging tensor mathematics and GPU acceleration to achieve exceptional compression ratios while preserving data fidelity. Unlike traditional compression techniques that focus solely on row-wise redundancy, this codec treats data as multi-dimensional tensors, enabling it to identify and exploit complex patterns across user IDs, item IDs, and temporal features simultaneo
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Gan, Chenquan, Junwei Mao, Zufan Zhang, and Qingyi Zhu. "A tensor compression algorithm using Tucker decomposition and dictionary dimensionality reduction." International Journal of Distributed Sensor Networks 16, no. 4 (2020): 155014772091640. http://dx.doi.org/10.1177/1550147720916408.

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Tensor compression algorithms play an important role in the processing of multidimensional signals. In previous work, tensor data structures are usually destroyed by vectorization operations, resulting in information loss and new noise. To this end, this article proposes a tensor compression algorithm using Tucker decomposition and dictionary dimensionality reduction, which mainly includes three parts: tensor dictionary representation, dictionary preprocessing, and dictionary update. Specifically, the tensor is respectively performed by the sparse representation and Tucker decomposition, from
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Wang, Hongxing, and Wei Wen. "T-BT Inverse and T-GC Partial Order via the T-Product." Axioms 12, no. 10 (2023): 929. http://dx.doi.org/10.3390/axioms12100929.

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In this paper, we extend the BT inverse to the set of third-order tensors, and we call it the T-BT inverse. We give characterizations and properties of the inverse by applying tensor decomposition. Based on the inverse, we introduce a new binary relation: T-BT order. Furthermore, by applying the T-BT order, we introduce a generalized core partial order (called T-GC partial order).
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Liu, Amanda, Gilbert Louis Bernstein, Adam Chlipala, and Jonathan Ragan-Kelley. "Verified tensor-program optimization via high-level scheduling rewrites." Proceedings of the ACM on Programming Languages 6, POPL (2022): 1–28. http://dx.doi.org/10.1145/3498717.

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We present a lightweight Coq framework for optimizing tensor kernels written in a pure, functional array language. Optimizations rely on user scheduling using series of verified, semantics-preserving rewrites. Unusually for compilation targeting imperative code with arrays and nested loops, all rewrites are source-to-source within a purely functional language. Our language comprises a set of core constructs for expressing high-level computation detail and a set of what we call reshape operators, which can be derived from core constructs but trigger low-level decisions about storage patterns an
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de Pinho, Pablo H. U., Maria de F. K. B. Couras, Gérard Favier, André L. F. de Almeida, and João Paulo J. da Costa. "Semi-Blind Receivers for Two-Hop MIMO Relay Systems with a Combined TSTF-MSMKron Coding." Sensors 23, no. 13 (2023): 5963. http://dx.doi.org/10.3390/s23135963.

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Due to the increase in the number of mobile stations in recent years, cooperative relaying systems have emerged as a promising technique for improving the quality of fifth-generation (5G) wireless networks with an extension of the coverage area. In this paper, we propose a two-hop orthogonal frequency division multiplexing and code-division multiple-access (OFDM-CDMA) multiple-input multiple-output (MIMO) relay system, which combines, both at the source and relay nodes, a tensor space–time–frequency (TSTF) coding with a multiple symbol matrices Kronecker product (MSMKron), called TSTF-MSMKron
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Harada, Akira, Shota Nishikawa, and Shoichi Yamada. "Deep Learning of the Eddington Tensor in Core-collapse Supernova Simulation." Astrophysical Journal 925, no. 2 (2022): 117. http://dx.doi.org/10.3847/1538-4357/ac3998.

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Abstract We trained deep neural networks (DNNs) as a function of the neutrino energy density, flux, and the fluid velocity to reproduce the Eddington tensor for neutrinos obtained in our first-principles core-collapse supernova simulation. Although the moment method, which is one of the most popular approximations for neutrino transport, requires a closure relation, none of the analytical closure relations commonly employed in the literature capture all aspects of the neutrino angular distribution in momentum space. In this paper, we develop a closure relation by using DNNs that take the neutr
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Cai, Yunfeng, and Ping Li. "A Blind Block Term Decomposition of High Order Tensors." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 6868–76. http://dx.doi.org/10.1609/aaai.v35i8.16847.

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Tensor decompositions have found many applications in signal processing, data mining, machine learning, etc. In particular, the block term decomposition (BTD), which is a generalization of CP decomposition and Tucker decomposition/HOSVD, has been successfully used for the compression and acceleration of neural networks. However, computing BTD is NP-hard, and optimization based methods usually suffer from slow convergence or even fail to converge, which limits the applications of BTD. This paper considers a “blind” block term decomposition (BBTD) of high order tensors, in which the block diagon
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Yadav, Rohan, Michael Garland, Alex Aiken, and Michael Bauer. "Task-Based Tensor Computations on Modern GPUs." Proceedings of the ACM on Programming Languages 9, PLDI (2025): 396–420. https://doi.org/10.1145/3729262.

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Domain-specific, fixed-function units are becoming increasingly common in modern processors. As the computational demands of applications evolve, the capabilities and programming interfaces of these fixed-function units continue to change. NVIDIA’s Hopper GPU architecture contains multiple fixed-function units per compute unit, including an asynchronous data movement unit (TMA) and an asynchronous matrix multiplication unit (Tensor Core). Efficiently utilizing these units requires a fundamentally different programming style than previous architectures; programmers must now develop warp-special
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Choquette, Jack, Wishwesh Gandhi, Olivier Giroux, Nick Stam, and Ronny Krashinsky. "NVIDIA A100 Tensor Core GPU: Performance and Innovation." IEEE Micro 41, no. 2 (2021): 29–35. http://dx.doi.org/10.1109/mm.2021.3061394.

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Oster, T., C. Rössl, and H. Theisel. "Core Lines in 3D Second-Order Tensor Fields." Computer Graphics Forum 37, no. 3 (2018): 327–37. http://dx.doi.org/10.1111/cgf.13423.

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Jiang, Bo, Fan Yang, and Shuzhong Zhang. "Tensor and its tucker core: The invariance relationships." Numerical Linear Algebra with Applications 24, no. 3 (2017): e2086. http://dx.doi.org/10.1002/nla.2086.

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Chen, Yanping, Mingdao Zhao, Hong Xia, Xiaodong Jin, Zhongmin Wang, and Zhong Yu. "A Method for Extracting High-Quality Core Data from Edge Computing Nodes." Mathematical Problems in Engineering 2019 (June 12, 2019): 1–10. http://dx.doi.org/10.1155/2019/3834846.

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Intelligent factory has the characteristics of wide data sources, high data dimensions, and strong data relevance. Intelligent factories need to make different decisions for different needs, so they need to efficiently analyze these data and explore the inherent laws contained in them. At the same time, the increasing amount of data brings various burdens to the network infrastructure between users and smart devices. For the above needs, this paper proposes a tension-based heterogeneous data fusion model in the edge computing layer, which represents the multisource heterogeneous data in the in
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Alekseev, A. K., A. E. Bondarev, and Yu S. Pyatakova. "On Application of Canonical Decomposition for the Visualization of Results of Multiparameter Computations." Scientific Visualization 15, no. 4 (2023): 12–23. http://dx.doi.org/10.26583/sv.15.4.02.

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The approximation of the tensor appearing at a discretization of the multidimensional function is considered from the viewpoint of storing and treating of the results of parametric computations obtained in computational aerogasdynamics. The new algorithm for the computation of the canonical decomposition using gradient descent and approximately decomposable goal functional is described. This algorithm applies the random set of points on the hyperplane orthogonal to the computed core of the canonical decomposition (“umbrella”) that ensures its flexible application for an approximation of the te
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Li, Li, Rui Bai, Jianfeng Lu, Shanqing Zhang, and Ching-Chun Chang. "A Watermarking Scheme for Color Image Using Quaternion Discrete Fourier Transform and Tensor Decomposition." Applied Sciences 11, no. 11 (2021): 5006. http://dx.doi.org/10.3390/app11115006.

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To protect the copyright of the color image, a color image watermarking scheme based on quaternion discrete Fourier transform (QDFT) and tensor decomposition (TD) is presented. Specifically, the cover image is partitioned into non-overlapping blocks, and then QDFT is performed on each image block. Then, the three imaginary frequency components of QDFT are used to construct a third-order tensor. The third-order tensor is decomposed by Tucker decomposition and generates a core tensor. Finally, an improved odd–even quantization technique is employed to embed a watermark in the core tensor. Moreov
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Guo, Weihong, Yunmei Chen, and Qingguo Zeng. "A geometric flow-based approach for diffusion tensor image segmentation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1874 (2008): 2279–92. http://dx.doi.org/10.1098/rsta.2008.0042.

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Diffusion tensor magnetic resonance imaging (DT-MRI, shortened as DTI) produces, from a set of diffusion-weighted magnetic resonance images, tensor-valued images where each voxel is assigned a 3×3 symmetric, positive-definite matrix. This tensor is simply the covariance matrix of a local Gaussian process with zero mean, modelling the average motion of water molecules. We propose a three-dimensional geometric flow-based model to segment the main core of cerebral white matter fibre tracts from DTI. The segmentation is carried out with a front propagation algorithm. The front is a three-dimension
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Du, Hong-Mei, Bing-Xue Wang, and Hai-Feng Ma. "Perturbation theory for core and core-EP inverses of tensor via Einstein product." Filomat 33, no. 16 (2019): 5207–17. http://dx.doi.org/10.2298/fil1916207d.

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Guo, Xiaoding, Hongli Zhang, Lin Ye, and Shang Li. "Learning Users’ Intention of Legal Consultation through Pattern-Oriented Tensor Decomposition with Bi-LSTM." Wireless Communications and Mobile Computing 2019 (March 7, 2019): 1–16. http://dx.doi.org/10.1155/2019/2589784.

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Online legal consultation plays an increasingly important role in the modern rule-of-law society. This study aims to understand the intention of legal consultation of users with different language expressions and legal knowledge background. A critical issue is a method through which users’ legal consultation data are classified and the feature of each category is extracted. Traditional classification methods rely considerably on lexical and syntactic features and frequently require strict sentence formatting, which eliminates substantial energy and may not be universally applicable. We aim to
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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 prim
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López, Josué, Deni Torres, Stewart Santos, and Clement Atzberger. "Spectral Imagery Tensor Decomposition for Semantic Segmentation of Remote Sensing Data through Fully Convolutional Networks." Remote Sensing 12, no. 3 (2020): 517. http://dx.doi.org/10.3390/rs12030517.

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This work aims at addressing two issues simultaneously: data compression at input space and semantic segmentation. Semantic segmentation of remotely sensed multi- or hyperspectral images through deep learning (DL) artificial neural networks (ANN) delivers as output the corresponding matrix of pixels classified elementwise, achieving competitive performance metrics. With technological progress, current remote sensing (RS) sensors have more spectral bands and higher spatial resolution than before, which means a greater number of pixels in the same area. Nevertheless, the more spectral bands and
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Feldmann, J., N. Youngblood, M. Karpov, et al. "Parallel convolutional processing using an integrated photonic tensor core." Nature 589, no. 7840 (2021): 52–58. http://dx.doi.org/10.1038/s41586-020-03070-1.

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Chua, Siew E., and Grainne McAlonan. "Is there core diffusion tensor imaging pathology in schizophrenia?" British Journal of Psychiatry 195, no. 1 (2009): 86–87. http://dx.doi.org/10.1192/bjp.195.1.86b.

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Zare, Marzieh, Mohammad Sadegh Helfroush, Kamran Kazemi, and Paul Scheunders. "Hyperspectral and Multispectral Image Fusion Using Coupled Non-Negative Tucker Tensor Decomposition." Remote Sensing 13, no. 15 (2021): 2930. http://dx.doi.org/10.3390/rs13152930.

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Fusing a low spatial resolution hyperspectral image (HSI) with a high spatial resolution multispectral image (MSI), aiming to produce a super-resolution hyperspectral image, has recently attracted increasing research interest. In this paper, a novel approach based on coupled non-negative tensor decomposition is proposed. The proposed method performs a tucker tensor factorization of a low resolution hyperspectral image and a high resolution multispectral image under the constraint of non-negative tensor decomposition (NTD). The conventional matrix factorization methods essentially lose spatio-s
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Kolosov, G. A., A. S. Shorokhov, and A. A. Fedyanin. "Numerical Simulation of a Photonic Tensor Core for the Hardware Acceleration of the Optical Matrix–Vector Multiplication." JETP Letters 120, no. 12 (2024): 932–38. https://doi.org/10.1134/s0021364024603956.

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A realistic numerical model of a photonic tensor core based on the crossbar architecture with absorbing GeSbTe chalcogenide glass films as weight elements of a photonic matrix has been developed. The performance of the model for the matrix–vector multiplication has been demonstrated. The possibility of using the tensor core based on the implemented architecture in convolutional neural networks for image recognition tasks has been shown. Numerical simulations have been used for the first time to estimate the potential performance and energy efficiency of a photonic hardware accelerator, taking
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Watanabe, N., A. Ishida, J. Murakami, and N. Yamamoto. "Solar Radiation and Weather Analysis of Meteorological Satellite Data by Tensor Decomposition." Journal of Image and Graphics 11, no. 3 (2023): 271–81. http://dx.doi.org/10.18178/joig.11.3.271-281.

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In this study, the data obtained from meteorological satellites were analyzed using tensor decomposition. The data used in this paper are meteorological image data observed by the Himawari-8 satellite and solar radiation data generated from Himawari Standard Data. First, we applied Higher-Order Singular Value Decomposition (HOSVD), a type of tensor decomposition, to the original image data and analyzed the features of the data, called the core tensor, obtained from the decomposition. As a result, it was found that the maximum value of the core tensor element is related to the cloud cover in th
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Gao, Tong, Hao Chen, and Junhong Lu. "Coupled Heterogeneous Tucker Decomposition: A Feature Extraction Method for Multisource Fusion and Domain Adaptation Using Multisource Heterogeneous Remote Sensing Data." Remote Sensing 14, no. 11 (2022): 2553. http://dx.doi.org/10.3390/rs14112553.

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To excavate adequately the rich information contained in multisource remote sensing data, feature extraction as basic yet important research has two typical applications: one of which is to extract complementary information of multisource data to improve classification; and the other is to extract shared information across sources for domain adaptation. However, typical feature extraction methods require the input represented as vectors or homogeneous tensors and fail to process multisource data represented as heterogeneous tensors. Therefore, the coupled heterogeneous Tucker decomposition (C-
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Szewczyk, Roman, Michał Nowicki, Anna Ostaszewska-Liżewska, and Mika Malinen. "Modeling the Influence of a Magnetomechanical Effect on the Permeability Tensor of a Tensductor Core." Materials 12, no. 24 (2019): 4023. http://dx.doi.org/10.3390/ma12244023.

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This paper presents a new method of modeling the influence of mechanical stresses on a magnetic permeability tensor of soft magnetic materials. The proposed method utilizes the principal stresses concept to compensate the influence of shear stresses. As a result, the stress dependence of a magnetic permeability tensor may be assessed with only the knowledge about the influence of axial stresses on magnetic properties of isotropic material. The proposed method was used for a finite element method based model of a tensductor designed for measurements of tensile forces. Due to the fact that 2D st
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Lemeshko, Oleksandr, Jozef Papan, Oleksandra Yeremenko, Maryna Yevdokymenko, and Pavel Segec. "Research and Development of Delay-Sensitive Routing Tensor Model in IoT Core Networks." Sensors 21, no. 11 (2021): 3934. http://dx.doi.org/10.3390/s21113934.

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In the article, we present the research and development of an improved delay-sensitive routing tensor model for the core of the IoT network. The flow-based tensor model is considered within the coordinate system of interpolar paths and internal node pairs. The advantage of the presented model is the application for IoT architectures to ensure the Quality of Service under the parameters of bandwidth, average end-to-end delay, and the probability of packet loss. Hence, the technical task of delay-sensitive routing is formulated as the optimization problem together with constraints and conditions
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42

Lihua, Gui, Zhao Xuyang, Zhao Qibin, and Cao Jianting. "Image and Video Completion by Using Bayesian Tensor Decomposition." International Journal of Computer Science Issues 15, no. 5 (2018): 1–8. https://doi.org/10.5281/zenodo.1467644.

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Reconstruction of image and video from sparse observations attract a great deal of interest in the filed of image/video compression, feature extraction and denoising. Since the color image and video data can be naturally expressed as a tensor structure, many methods based on tensor algebra have been studied together with promising predictive performance. However, one challenging problem in those methods is tuning parameters empirically which usually requires computational demanding cross validation or intuitive selection. In this paper, we introduce Bayesian Tucker decomposition to reconstruct
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43

Wei, Hong-Xuan, Pangfeng Liu, Ding-Yong Hong, Jan-Jan Wu, and An-Tai Chen. "CNN Models Acceleration Using Filter Pruning and Sparse Tensor Core." International Journal of Networking and Computing 12, no. 2 (2022): 270–94. http://dx.doi.org/10.15803/ijnc.12.2_270.

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44

Lu, Deyong, Wei An, Qiang Ling, et al. "LSTT: Long-Term Spatial–Temporal Tensor Model for Infrared Small Target Detection under Dynamic Background." Remote Sensing 16, no. 15 (2024): 2746. http://dx.doi.org/10.3390/rs16152746.

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Infrared small target detection is an important and core problem in infrared search and track systems. Many infrared small target detection methods work well under the premise of a static background; however, the detection effect decreases seriously when the background changes dynamically. In addition, the spatiotemporal information of the target and background of the image sequence are not fully developed and utilized, lacking long-term temporal characteristics. To solve these problems, a novel long-term spatial–temporal tensor (LSTT) model is proposed in this paper. The image registration te
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45

Karandas, Ya V., and A. V. Korotun. "Dielectric function and the absorption cross-section of the metal-graphene nanocylinders of the finite length." Himia, Fizika ta Tehnologia Poverhni 13, no. 4 (2022): 467–75. http://dx.doi.org/10.15407/hftp13.04.467.

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The behavior of the diagonal components of the dielectric tensor and the behavior of the absorption cross-section in the different frequency ranges for the composite cylindrical nanostructures “metallic core – graphene shell” have been studied. In order to obtain the calculation formulas one uses the relations for the longitudinal and transverse components of the dielectric tensors for metallic core and graphene shell, which are determined by Drude model and Cubo model correspondingly. The consideration is carried out in the frameworks of “equivalent” elongated spheroid approach, according to
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46

Simpson, Alex, and Matt Visser. "The eye of the storm: a regular Kerr black hole." Journal of Cosmology and Astroparticle Physics 2022, no. 03 (2022): 011. http://dx.doi.org/10.1088/1475-7516/2022/03/011.

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Abstract We analyse in some detail a highly tractable non-singular modification of the Kerr geometry, dubbed the “eye of the storm” — a rotating regular black hole with an asymptotically Minkowski core. This is achieved by “exponentially suppressing” the mass parameter in the Kerr spacetime: m → m e-ℓ/r . The single suppression parameter ℓ quantifies the deviation from the usual Kerr spacetime. Some of the classical energy conditions are globally satisfied, whilst certain choices for ℓ force any energy-condition-violating physics into the deep core. The geometry possesses the full “Killing tow
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Liu, Zhaoyu, Shi Liu, Minxin Chen, Yaofang Zhang, and Pengbo Yao. "Application of Tucker Decomposition in Temperature Distribution Reconstruction." Applied Sciences 12, no. 5 (2022): 2749. http://dx.doi.org/10.3390/app12052749.

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Constrained by cost, measuring conditions and excessive calculation, it is difficult to reconstruct a 3D real-time temperature field. For the purpose of solving these problems, a three-dimensional temperature distribution reconstruction algorithm based on Tucker decomposition algorithm is proposed. The Tucker decomposition algorithm is used to reduce the dimension of the measured data, and the processed core tensor is used for the temperature field reconstruction of sparse data. Theoretical analysis and simulations show that the proposed method is feasible; the overall optimization is realized
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Cao, Meng, Wenxing Bao, and Kewen Qu. "Hyperspectral Super-Resolution Via Joint Regularization of Low-Rank Tensor Decomposition." Remote Sensing 13, no. 20 (2021): 4116. http://dx.doi.org/10.3390/rs13204116.

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The hyperspectral image super-resolution (HSI-SR) problem aims at reconstructing the high resolution spatial–spectral information of the scene by fusing low-resolution hyperspectral images (LR-HSI) and the corresponding high-resolution multispectral image (HR-MSI). In order to effectively preserve the spatial and spectral structure of hyperspectral images, a new joint regularized low-rank tensor decomposition method (JRLTD) is proposed for HSI-SR. This model alleviates the problem that the traditional HSI-SR method, based on tensor decomposition, fails to adequately take into account the manif
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Yan, Tian, Yinan Li та Fang Liu. "Noise‐Augmented ℓ0 Regularization of Tensor Regression With Tucker Decomposition". Statistical Analysis and Data Mining: An ASA Data Science Journal 18, № 1 (2025). https://doi.org/10.1002/sam.70010.

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ABSTRACTTensor data are multi‐dimensional arrays. Low‐rank decomposition‐based regression methods with tensor predictors exploit the structural information in tensor predictors while significantly reducing the number of parameters in tensor regression. We propose a method named (Noise Augmentation for regularization on Core Tensor in Tucker decomposition) to regularize the parameters in tensor regression (TR), coupled with Tucker decomposition. We establish theoretically that achieves exact regularization on the core tensor from the Tucker decomposition in linear TR and generalized linear TR.
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Romein, J. W. "The Tensor-Core Correlator." Astronomy & Astrophysics, September 27, 2021. http://dx.doi.org/10.1051/0004-6361/202141896.

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