Journal articles: '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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Hameed, Marawan Gamal Abdel, Marzieh S. Tahaei, Ali Mosleh, and Vahid Partovi Nia. "Convolutional Neural Network Compression through Generalized Kronecker Product Decomposition." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 1 (June 28, 2022): 771–79. http://dx.doi.org/10.1609/aaai.v36i1.19958.

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Modern Convolutional Neural Network (CNN) architectures, despite their superiority in solving various problems, are generally too large to be deployed on resource constrained edge devices. In this paper, we reduce memory usage and floating-point operations required by convolutional layers in CNNs. We compress these layers by generalizing the Kronecker Product Decomposition to apply to multidimensional tensors, leading to the Generalized Kronecker Product Decomposition (GKPD). Our approach yields a plug-and-play module that can be used as a drop-in replacement for any convolutional layer. Experimental results for image classification on CIFAR-10 and ImageNet datasets using ResNet, MobileNetv2 and SeNet architectures substantiate the effectiveness of our proposed approach. We find that GKPD outperforms state-of-the-art decomposition methods including Tensor-Train and Tensor-Ring as well as other relevant compression methods such as pruning and knowledge distillation.

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Yuan, Longhao, Chao Li, Danilo Mandic, Jianting Cao, and Qibin Zhao. "Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 9151–58. http://dx.doi.org/10.1609/aaai.v33i01.33019151.

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In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure of the TR latent space, we propose a novel tensor completion method which is robust to model selection. In contrast to imposing the low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in the optimization step using singular value decomposition (SVD) being performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm is shown to effectively alleviate the burden of TR-rank selection, thereby greatly reducing the computational cost. The extensive experimental results on both synthetic and real-world data demonstrate the superior performance and efficiency of the proposed approach against the state-of-the-art algorithms.

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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 (July 26, 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-spectral structure information when stacking the 3D data structure of a hyperspectral image into a matrix form. Moreover, the spectral, spatial, or their joint structural features have to be imposed from the outside as a constraint to well pose the matrix factorization problem. The proposed method has the advantage of preserving the spatio-spectral structure of hyperspectral images. In this paper, the NTD is directly imposed on the coupled tensors of the HSI and MSI. Hence, the intrinsic spatio-spectral structure of the HSI is represented without loss, and spatial and spectral information can be interdependently exploited. Furthermore, multilinear interactions of different modes of the HSIs can be exactly modeled with the core tensor of the Tucker tensor decomposition. The proposed method is straightforward and easy to implement. Unlike other state-of-the-art approaches, the complexity of the proposed approach is linear with the size of the HSI cube. Experiments on two well-known datasets give promising results when compared with some recent methods from the literature.

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Chen, Zitai, Chuan Chen, Zibin Zheng, and Yi Zhu. "Tensor Decomposition for Multilayer Networks Clustering." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 3371–78. http://dx.doi.org/10.1609/aaai.v33i01.33013371.

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Clustering on multilayer networks has been shown to be a promising approach to enhance the accuracy. Various multilayer networks clustering algorithms assume all networks derive from a latent clustering structure, and jointly learn the compatible and complementary information from different networks to excavate one shared underlying structure. However, such an assumption is in conflict with many emerging real-life applications due to the existence of noisy/irrelevant networks. To address this issue, we propose Centroid-based Multilayer Network Clustering (CMNC), a novel approach which can divide irrelevant relationships into different network groups and uncover the cluster structure in each group simultaneously. The multilayer networks is represented within a unified tensor framework for simultaneously capturing multiple types of relationships between a set of entities. By imposing the rank-(Lr,Lr,1) block term decomposition with nonnegativity, we are able to have well interpretations on the multiple clustering results based on graph cut theory. Numerically, we transform this tensor decomposition problem to an unconstrained optimization, thus can solve it efficiently under the nonlinear least squares (NLS) framework. Extensive experimental results on synthetic and real-world datasets show the effectiveness and robustness of our method against noise and irrelevant data.

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Dogariu, Laura-Maria, Cristian-Lucian Stanciu, Camelia Elisei-Iliescu, Constantin Paleologu, Jacob Benesty, and Silviu Ciochină. "Tensor-Based Adaptive Filtering Algorithms." Symmetry 13, no. 3 (March 15, 2021): 481. http://dx.doi.org/10.3390/sym13030481.

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Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and the channels can be grouped in the form of rank-1 tensors. Nevertheless, the approach could be further extended for single-input/single-output system identification scenarios, where the impulse responses (of more general forms) can be modeled as higher-rank tensors. As compared to the conventional adaptive filters, which involve a single (usually long) filter for the estimation of the global impulse response, the tensor-based algorithms achieve faster convergence rate and tracking, while also providing better accuracy of the solution. Simulation results support the theoretical findings and indicate the advantages of the tensor-based algorithms over the conventional ones, in terms of the main performance criteria.

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Yuan, Longhao, Chao Li, Jianting Cao, and Qibin Zhao. "Rank minimization on tensor ring: an efficient approach for tensor decomposition and completion." Machine Learning 109, no. 3 (November 4, 2019): 603–22. http://dx.doi.org/10.1007/s10994-019-05846-7.

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Krishnaswamy, Sriram, and Mrinal Kumar. "Tensor Decomposition Approach to Data Association for Multitarget Tracking." Journal of Guidance, Control, and Dynamics 42, no. 9 (September 2019): 2007–25. http://dx.doi.org/10.2514/1.g004122.

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Fan, Hongbiao, Jun-e. Feng, Min Meng, and Biao Wang. "General decomposition of fuzzy relations: Semi-tensor product approach." Fuzzy Sets and Systems 384 (April 2020): 75–90. http://dx.doi.org/10.1016/j.fss.2018.12.012.

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Rakhuba, M. V., and I. V. Oseledets. "Grid-based electronic structure calculations: The tensor decomposition approach." Journal of Computational Physics 312 (May 2016): 19–30. http://dx.doi.org/10.1016/j.jcp.2016.02.023.

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Nair, Nikhitha K., and S. Asharaf. "Tensor Decomposition Based Approach for Training Extreme Learning Machines." Big Data Research 10 (December 2017): 8–20. http://dx.doi.org/10.1016/j.bdr.2017.07.002.

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Misaghian, Negin, and Homayun Motameni. "An approach for requirements prioritization based on tensor decomposition." Requirements Engineering 23, no. 2 (December 7, 2016): 169–88. http://dx.doi.org/10.1007/s00766-016-0262-6.

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Lu, Wenqi, Ziwei Yi, Dongyu Luo, Yikang Rui, Bin Ran, Jianqing Wu, and Tao Li. "Urban Traffic State Estimation with Online Car-Hailing Data: A Dynamic Tensor-Based Bayesian Probabilistic Decomposition Approach." Journal of Advanced Transportation 2022 (April 26, 2022): 1–16. http://dx.doi.org/10.1155/2022/1793060.

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Timely and precise traffic state estimation of urban roads is significant for urban traffic management and operation. However, most of the advanced studies focus on building complex deep learning structures to learn the spatiotemporal feature of the urban traffic flow, ignoring improving the efficiency of the traffic state estimation. Considering the benefit of the tensor decomposition, we present a novel urban traffic state estimation based on dynamic tensor and Bayesian probabilistic decomposition. Firstly, the real-time traffic speed data are organized in the form of a dynamic tensor which contains the spatiotemporal characteristics of the traffic state. Then, a dynamic tensor Bayesian probabilistic decomposition (DTBPD) approach is built by decomposing the dynamic tensor into the outer product of several vectors. Afterward, the Gibbs sampling method is introduced to calibrate the parameters of the DTBPD models. Finally, the real-world traffic speeds data extracted from online car-hailing trajectories are employed to validate the model performance. Experimental results indicate that the proposed model can greatly reduce computational time while maintaining relatively high accuracy. Meanwhile, the DTBPD model outperforms the state-of-the-art models in terms of both single-step-ahead and multistep-ahead traffic state estimation.

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Lu, Wenqi, Ziwei Yi, Dongyu Luo, Yikang Rui, Bin Ran, Jianqing Wu, and Tao Li. "Urban Traffic State Estimation with Online Car-Hailing Data: A Dynamic Tensor-Based Bayesian Probabilistic Decomposition Approach." Journal of Advanced Transportation 2022 (April 26, 2022): 1–16. http://dx.doi.org/10.1155/2022/1793060.

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Timely and precise traffic state estimation of urban roads is significant for urban traffic management and operation. However, most of the advanced studies focus on building complex deep learning structures to learn the spatiotemporal feature of the urban traffic flow, ignoring improving the efficiency of the traffic state estimation. Considering the benefit of the tensor decomposition, we present a novel urban traffic state estimation based on dynamic tensor and Bayesian probabilistic decomposition. Firstly, the real-time traffic speed data are organized in the form of a dynamic tensor which contains the spatiotemporal characteristics of the traffic state. Then, a dynamic tensor Bayesian probabilistic decomposition (DTBPD) approach is built by decomposing the dynamic tensor into the outer product of several vectors. Afterward, the Gibbs sampling method is introduced to calibrate the parameters of the DTBPD models. Finally, the real-world traffic speeds data extracted from online car-hailing trajectories are employed to validate the model performance. Experimental results indicate that the proposed model can greatly reduce computational time while maintaining relatively high accuracy. Meanwhile, the DTBPD model outperforms the state-of-the-art models in terms of both single-step-ahead and multistep-ahead traffic state estimation.

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McNeice, Gary W., and Alan G. Jones. "Multisite, multifrequency tensor decomposition of magnetotelluric data." GEOPHYSICS 66, no. 1 (January 2001): 158–73. http://dx.doi.org/10.1190/1.1444891.

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Accurate interpretation of magnetotelluric data requires an understanding of the directionality and dimensionality inherent in the data, and valid implementation of an appropriate method for removing the effects of shallow, small‐scale galvanic scatterers on the data to yield responses representative of regional‐scale structures. The galvanic distortion analysis approach advocated by Groom and Bailey has become the most adopted method, rightly so given that the approach decomposes the magnetotelluric impedance tensor into determinable and indeterminable parts, and tests statistically the validity of the galvanic distortion assumption. As proposed by Groom and Bailey, one must determine the appropriate frequency‐independent telluric distortion parameters and geoelectric strike by fitting the seven‐parameter model on a frequency‐by‐frequency and site‐by‐site basis independently. Although this approach has the attraction that one gains a more intimate understanding of the data set, it is rather time‐consuming and requires repetitive application. We propose an extension to Groom‐Bailey decomposition in which a global minimum is sought to determine the most appropriate strike direction and telluric distortion parameters for a range of frequencies and a set of sites. Also, we show how an analytically‐derived approximate Hessian of the objective function can reduce the required computing time. We illustrate application of the analysis to two synthetic data sets and to real data. Finally, we show how the analysis can be extended to cover the case of frequency‐dependent distortion caused by the magnetic effects of the galvanic charges.

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Keylock, Christopher J. "The Schur decomposition of the velocity gradient tensor for turbulent flows." Journal of Fluid Mechanics 848 (June 13, 2018): 876–905. http://dx.doi.org/10.1017/jfm.2018.344.

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The velocity gradient tensor for turbulent flow contains crucial information on the topology of turbulence, vortex stretching and the dissipation of energy. A Schur decomposition of the velocity gradient tensor (VGT) is introduced to supplement the standard decomposition into rotation and strain tensors. Thus, the normal parts of the tensor (represented by the eigenvalues) are separated explicitly from non-normality. Using a direct numerical simulation of homogeneous isotropic turbulence, it is shown that the norm of the non-normal part of the tensor is of a similar magnitude to the normal part. It is common to examine the second and third invariants of the characteristic equation of the tensor simultaneously (the$\unicode[STIX]{x1D64C}{-}\unicode[STIX]{x1D64D}$diagram). With the Schur approach, the discriminant function separating real and complex eigenvalues of the VGT has an explicit form in terms of strain and enstrophy: where eigenvalues are all real, enstrophy arises from the non-normal term only. Re-deriving the evolution equations for enstrophy and total strain highlights the production of non-normality and interaction production (normal straining of non-normality). These cancel when considering the evolution of the VGT in terms of its eigenvalues but are important for the full dynamics. Their properties as a function of location in$\unicode[STIX]{x1D64C}{-}\unicode[STIX]{x1D64D}$space are characterized. The Schur framework is then used to explain two properties of the VGT: the preference to form disc-like rather than rod-like flow structures, and the vorticity vector and strain alignments. In both cases, non-normality is critical for explaining behaviour in vortical regions.

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Dogariu, Laura-Maria, Silviu Ciochină, Jacob Benesty, and Constantin Paleologu. "System Identification Based on Tensor Decompositions: A Trilinear Approach." Symmetry 11, no. 4 (April 17, 2019): 556. http://dx.doi.org/10.3390/sym11040556.

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The theory of nonlinear systems can currently be encountered in many important fields, while the nonlinear behavior of electronic systems and devices has been studied for a long time. However, a global approach for dealing with nonlinear systems does not exist and the methods to address this problem differ depending on the application and on the types of nonlinearities. An interesting category of nonlinear systems is one that can be regarded as an ensemble of (approximately) linear systems. Some popular examples in this context are nonlinear electronic devices (such as acoustic echo cancellers, which are used in applications for two-party or multi-party voice communications, e.g., videoconferencing), which can be modeled as a cascade of linear and nonlinear systems, similar to the Hammerstein model. Multiple-input/single-output (MISO) systems can also be regarded as separable multilinear systems and be treated using the appropriate methods. The high dimension of the parameter space in such problems can be addressed with methods based on tensor decompositions and modelling. In recent work, we focused on a particular type of multilinear structure—namely the bilinear form (i.e., two-dimensional decompositions)—in the framework of identifying spatiotemporal models. In this paper, we extend the work to the decomposition of more complex systems and we propose an iterative Wiener filter tailored for the identification of trilinear forms (where third-order tensors are involved), which can then be further extended to higher order multilinear structures. In addition, we derive the least-mean-square (LMS) and normalized LMS (NLMS) algorithms tailored for such trilinear forms. Simulations performed in the context of system identification (based on the MISO system approach) indicate the good performance of the proposed solution, as compared to conventional approaches.

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Karami, Kiana, and David Westwick. "Initialization Approach for Decoupling Polynomial NARX Models Using Tensor Decomposition." IFAC-PapersOnLine 53, no. 2 (2020): 328–33. http://dx.doi.org/10.1016/j.ifacol.2020.12.181.

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Gao, Yuan, Guangming Zhang, Chunchun Zhang, Jinke Wang, Laurence T. Yang, and Yaliang Zhao. "Federated Tensor Decomposition-Based Feature Extraction Approach for Industrial IoT." IEEE Transactions on Industrial Informatics 17, no. 12 (December 2021): 8541–49. http://dx.doi.org/10.1109/tii.2021.3074152.

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Chen, Xinyu, Zhaocheng He, and Lijun Sun. "A Bayesian tensor decomposition approach for spatiotemporal traffic data imputation." Transportation Research Part C: Emerging Technologies 98 (January 2019): 73–84. http://dx.doi.org/10.1016/j.trc.2018.11.003.

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Liang, Zongwei, Junan Yang, Hui Liu, Keju Huang, Lingzhi Qu, Lin Cui, and Xiang Li. "SeAttE: An Embedding Model Based on Separating Attribute Space for Knowledge Graph Completion." Electronics 11, no. 7 (March 28, 2022): 1058. http://dx.doi.org/10.3390/electronics11071058.

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Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is the task of inferring missing facts based on existing ones. Knowledge graph embedding, representing entities and relations in the knowledge graphs with high-dimensional vectors, has made significant progress in link prediction. The tensor decomposition models are an embedding family with good performance in link prediction. The previous tensor decomposition models do not consider the problem of attribute separation. These models mainly explore particular regularization to improve performance. No matter how sophisticated the design of tensor decomposition models is, the performance is theoretically under the basic tensor decomposition model. Moreover, the unnoticed task of attribute separation in the traditional models is just handed over to the training. However, the amount of parameters for this task is tremendous, and the model is prone to overfitting. We investigate the design approaching the theoretical performance of tensor decomposition models in this paper. The observation that measuring the rationality of specific triples means comparing the matching degree of the specific attributes associated with the relations is well-known. Therefore, the comparison of actual triples needs first to separate specific attribute dimensions, which is ignored by existing models. Inspired by this observation, we design a novel tensor ecomposition model based on Separating Attribute space for knowledge graph completion (SeAttE). The major novelty of this paper is that SeAttE is the first model among the tensor decomposition family to consider the attribute space separation task. Furthermore, SeAttE transforms the learning of too many parameters for the attribute space separation task into the structure’s design. This operation allows the model to focus on learning the semantic equivalence between relations, causing the performance to approach the theoretical limit. We also prove that RESCAL, DisMult and ComplEx are special cases of SeAttE in this paper. Furthermore, we classify existing tensor decomposition models for subsequent researchers. Experiments on the benchmark datasets show that SeAttE has achieved state-of-the-art among tensor decomposition models.

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SHIMIZU, YUYA. "TENSOR RENORMALIZATION GROUP APPROACH TO A LATTICE BOSON MODEL." Modern Physics Letters A 27, no. 06 (February 28, 2012): 1250035. http://dx.doi.org/10.1142/s0217732312500356.

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A method to apply the tensor renormalization group to a lattice boson model is proposed. It is based on the truncated singular value decomposition of a compact operator. We demonstrate it using the (1+1)-dimensional ϕ4 model. The evaluated critical points on the lattice are consistent with the Monte Carlo result.

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Lee, Geunseop. "An Efficient Compressive Hyperspectral Imaging Algorithm Based on Sequential Computations of Alternating Least Squares." Remote Sensing 11, no. 24 (December 6, 2019): 2932. http://dx.doi.org/10.3390/rs11242932.

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Hyperspectral imaging is widely used to many applications as it includes both spatial and spectral distributions of a target scene. However, a compression, or a low multilinear rank approximation of hyperspectral imaging data, is required owing to the difficult manipulation of the massive amount of data. In this paper, we propose an efficient algorithm for higher order singular value decomposition that enables the decomposition of a tensor into a compressed tensor multiplied by orthogonal factor matrices. Specifically, we sequentially compute low rank factor matrices from the Tucker-1 model optimization problems via an alternating least squares approach. Experiments with real world hyperspectral imaging revealed that the proposed algorithm could compute the compressed tensor with a higher computational speed, but with no significant difference in accuracy of compression compared to the other tensor decomposition-based compression algorithms.

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Hached, Mustapha, Khalide Jbilou, Christos Koukouvinos, and Marilena Mitrouli. "A Multidimensional Principal Component Analysis via the C-Product Golub–Kahan–SVD for Classification and Face Recognition." Mathematics 9, no. 11 (May 29, 2021): 1249. http://dx.doi.org/10.3390/math9111249.

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Face recognition and identification are very important applications in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement. Moreover, the tensorial approaches are a natural choice, due to the mere structure of the databases, for example in the case of color images. Nevertheless, even though various authors proposed factorization strategies for tensors, the size of the considered tensors can pose some serious issues. Indeed, the most demanding part of the computational effort in recognition or identification problems resides in the training process. When only a few features are needed to construct the projection space, there is no need to compute a SVD on the whole data. Two versions of the tensor Golub–Kahan algorithm are considered in this manuscript, as an alternative to the classical use of the tensor SVD which is based on truncated strategies. In this paper, we consider the Tensor Tubal Golub–Kahan Principal Component Analysis method which purpose it to extract the main features of images using the tensor singular value decomposition (SVD) based on the tensor cosine product that uses the discrete cosine transform. This approach is applied for classification and face recognition and numerical tests show its effectiveness.

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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 extract the patterns of users’ consultation on different categories, which minimally depend on lexical, syntax, and sentence formatting. However, research in this area has rarely been conducted in previous legal advisory service studies. In this study, a classification approach for multiclass users’ intention based on pattern-oriented tensor decomposition and Bi-LSTM is proposed, and each user’s legal consulting statement is expressed as a tensor. Moreover, we propose a pattern-oriented tensor decomposition method that can obtain a core tensor that approximates the patterns of users’ consultation. These patterns can improve the accuracy of classifying users’ intention of legal consultation. We use Bi-LSTM to automatically learn and optimize these patterns. Evidently, Bi-LSTM with a pattern-oriented tensor decomposition layer performs better than a recurrent neural network only. Results show that our method is more accurate than the previous work, and the factor matrix and core tensor calculated by the pattern-oriented tensor decomposition are interpretable.

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Cheng, Jin Fang, Fu Qian, and Nan Li. "Direction of Arrival Estimation Based on a Tensor Approach." Applied Mechanics and Materials 530-531 (February 2014): 581–85. http://dx.doi.org/10.4028/www.scientific.net/amm.530-531.581.

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In this letter, we put forward a novel tensor-based Multiple Signal Classification (TB-MUSIC) applicable to a vector hydrophone array. For this purpose, the signal subspace is derived from the higher order singular value decomposition (HOSVD) of the third order tensor of the output model. Then the proposed method is achieved by signal subspace projection weighted with the reciprocal of principal singular values multiplying by the spatial spectrum based on TB-MUSIC. The synthetic spatial spectrum shows higher resolution and robustness under no-ideal scenarios. Monte Carlo experimental results are provided to illustrate the better performance of the proposed method.

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Li, Y. Q., and X. L. Gao. "Constitutive Equations for Hyperelastic Materials Based on the Upper Triangular Decomposition of the Deformation Gradient." Mathematics and Mechanics of Solids 24, no. 6 (December 24, 2018): 1785–99. http://dx.doi.org/10.1177/1081286518806950.

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The upper triangular decomposition has recently been proposed to multiplicatively decompose the deformation gradient tensor into a product of a rotation tensor and an upper triangular tensor called the distortion tensor, whose six components can be directly related to pure stretch and simple shear deformations, which are physically measurable. In the current paper, constitutive equations for hyperelastic materials are derived using strain energy density functions in terms of the distortion tensor, which satisfy the principle of material frame indifference and the first and second laws of thermodynamics. Being expressed directly as derivatives of the strain energy density function with respect to the components of the distortion tensor, the Cauchy stress components have simpler expressions than those based on the invariants of the right Cauchy-Green deformation tensor. To illustrate the new constitutive equations, strain energy density functions in terms of the distortion tensor are provided for unconstrained and incompressible isotropic materials, incompressible transversely isotropic composite materials, and incompressible orthotropic composite materials with two families of fibers. For each type of material, example problems are solved using the newly proposed constitutive equations and strain energy density functions, both in terms of the distortion tensor. The solutions of these problems are found to be the same as those obtained by applying the polar decomposition-based invariants approach, thereby validating and supporting the newly developed, alternative method based on the upper triangular decomposition of the deformation gradient tensor.

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Liu, Long, Ling Wang, Yuexian Wang, Jian Xie, and Zhaolin Zhang. "Coherent Signal Parameter Estimation by Exploiting Decomposition of Tensors." Mathematical Problems in Engineering 2019 (November 13, 2019): 1–8. http://dx.doi.org/10.1155/2019/5794791.

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The problem of parameter estimation of coherent signals impinging on an array with vector sensors is considered from a new perspective by means of the decomposition of tensors. Signal parameters to be estimated include the direction of arrival (DOA) and the state of polarization. In this paper, mild deterministic conditions are used for canonical polyadic decomposition (CPD) of the tensor-based signal model; i.e., the factor matrices can be recovered, as long as the matrices satisfy the requirement that at least one is full column rank. In conjoint with the estimation of signal parameters via the algebraic method, the DOAs and polarization parameters of coherent signals can be resolved by virtue of the first and second factor matrices. Hereinto, the key innovation of the proposed approach is that the proposed approach can effectively estimate the coherent signal parameters without sacrificing the array aperture. The superiority of the proposed algorithm is shown by comparing with the algorithms based on higher order singular value decomposition (HOSVD) and Toeplitz matrix. Theoretical and numerical simulations demonstrate the effectiveness of the proposed approach.

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Yin, Miao, Huy Phan, Xiao Zang, Siyu Liao, and Bo Yuan. "BATUDE: Budget-Aware Neural Network Compression Based on Tucker Decomposition." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (June 28, 2022): 8874–82. http://dx.doi.org/10.1609/aaai.v36i8.20869.

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Model compression is very important for the efficient deployment of deep neural network (DNN) models on resource-constrained devices. Among various model compression approaches, high-order tensor decomposition is particularly attractive and useful because the decomposed model is very small and fully structured. For this category of approaches, tensor ranks are the most important hyper-parameters that directly determine the architecture and task performance of the compressed DNN models. However, as an NP-hard problem, selecting optimal tensor ranks under the desired budget is very challenging and the state-of-the-art studies suffer from unsatisfied compression performance and timing-consuming search procedures. To systematically address this fundamental problem, in this paper we propose BATUDE, a Budget-Aware TUcker DEcomposition-based compression approach that can efficiently calculate optimal tensor ranks via one-shot training. By integrating the rank selecting procedure to the DNN training process with a specified compression budget, the tensor ranks of the DNN models are learned from the data and thereby bringing very significant improvement on both compression ratio and classification accuracy for the compressed models. The experimental results on ImageNet dataset show that our method enjoys 0.33% top-5 higher accuracy with 2.52X less computational cost as compared to the uncompressed ResNet-18 model. For ResNet-50, the proposed approach enables 0.37% and 0.55% top-5 accuracy increase with 2.97X and 2.04X computational cost reduction, respectively, over the uncompressed model.

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Cai, Shuting, Qilun Luo, Ming Yang, Wen Li, and Mingqing Xiao. "Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation." Applied Sciences 9, no. 7 (April 3, 2019): 1411. http://dx.doi.org/10.3390/app9071411.

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Tensor Robust Principal Component Analysis (TRPCA) plays a critical role in handling high multi-dimensional data sets, aiming to recover the low-rank and sparse components both accurately and efficiently. In this paper, different from current approach, we developed a new t-Gamma tensor quasi-norm as a non-convex regularization to approximate the low-rank component. Compared to various convex regularization, this new configuration not only can better capture the tensor rank but also provides a simplified approach. An optimization process is conducted via tensor singular decomposition and an efficient augmented Lagrange multiplier algorithm is established. Extensive experimental results demonstrate that our new approach outperforms current state-of-the-art algorithms in terms of accuracy and efficiency.

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Kountchev, Roumen, Rumen Mironov, and Roumiana Kountcheva. "Complexity Estimation of Cubical Tensor Represented through 3D Frequency-Ordered Hierarchical KLT." Symmetry 12, no. 10 (September 26, 2020): 1605. http://dx.doi.org/10.3390/sym12101605.

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In this work is introduced one new hierarchical decomposition for cubical tensor of size 2n, based on the well-known orthogonal transforms Principal Component Analysis and Karhunen–Loeve Transform. The decomposition is called 3D Frequency-Ordered Hierarchical KLT (3D-FOHKLT). It is separable, and its calculation is based on the one-dimensional Frequency-Ordered Hierarchical KLT (1D-FOHKLT) applied on a sequence of matrices. The transform matrix is the product of n sparse matrices, symmetrical at the point of their main diagonal. In particular, for the case in which the angles which define the transform coefficients for the couples of matrices in each hierarchical level of 1D-FOHKLT are equal to π/4, the transform coincides with this of the frequency-ordered 1D Walsh–Hadamard. Compared to the hierarchical decompositions of Tucker (H-Tucker) and the Tensor-Train (TT), the offered approach does not ensure full decorrelation between its components, but is close to the maximum. On the other hand, the evaluation of the computational complexity (CC) of the new decomposition proves that it is lower than that of the above-mentioned similar approaches. In correspondence with the comparison results for H-Tucker and TT, the CC decreases fast together with the increase of the hierarchical levels’ number, n. An additional advantage of 3D-FOHKLT is that it is based on the use of operations of low complexity, while the similar famous decompositions need large numbers of iterations to achieve the coveted accuracy.

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Miao, Jifei, and Kit Ian Kou. "Quaternion tensor singular value decomposition using a flexible transform-based approach." Signal Processing 206 (May 2023): 108910. http://dx.doi.org/10.1016/j.sigpro.2022.108910.

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Megherbi, T., M. Kachouane, F. Oulebsir-Boumghar, and R. Deriche. "Crossing Fibers Detection with an Analytical High Order Tensor Decomposition." Computational and Mathematical Methods in Medicine 2014 (2014): 1–18. http://dx.doi.org/10.1155/2014/476837.

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Diffusion magnetic resonance imaging (dMRI) is the only technique to probein vivoand noninvasively the fiber structure of human brain white matter. Detecting the crossing of neuronal fibers remains an exciting challenge with an important impact in tractography. In this work, we tackle this challenging problem and propose an original and efficient technique to extract all crossing fibers from diffusion signals. To this end, we start by estimating, from the dMRI signal, the so-called Cartesian tensor fiber orientation distribution (CT-FOD) function, whose maxima correspond exactly to the orientations of the fibers. The fourth order symmetric positive definite tensor that represents the CT-FOD is then analytically decomposed via the application of a new theoretical approach and this decomposition is used to accurately extract all the fibers orientations. Our proposed high order tensor decomposition based approach is minimal and allows recovering the whole crossing fibers without any a priori information on the total number of fibers. Various experiments performed on noisy synthetic data, on phantom diffusion, data and on human brain data validate our approach and clearly demonstrate that it is efficient, robust to noise and performs favorably in terms of angular resolution and accuracy when compared to some classical and state-of-the-art approaches.

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Filisbino, Tiene A., Gilson A. Giraldi, and Carlos Thomaz. "Ranking Tensor Subspaces in Weighted Multilinear Principal Component Analysis." International Journal of Pattern Recognition and Artificial Intelligence 31, no. 07 (April 10, 2017): 1751003. http://dx.doi.org/10.1142/s021800141751003x.

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Multilinear principal component analysis (MPCA) has been applied for tensor decomposition and dimensionality reduction in image databases modeled through higher order tensors. Despite the well-known attractive properties of MPCA, the traditional approach does not incorporate prior information in order to steer its subspace computation. In this paper, we propose a method to explicitly incorporate such semantics in the MPCA framework to allow an automatic selective treatment of the variables that compose the patterns of interest. The method relies on spatial weights calculated, in this work, by separating hyperplanes and Fisher criterion. In this way, we can perform feature extraction and dimensionality reduction taking advantage of high level information in the form of labeled data. Besides, the corresponding tensor components are ranked in order to identify the principal weighted tensor subspaces for classification tasks. In the computational results we consider gender and facial expression experiments to illustrate the capabilities of the method for dimensionality reduction, classification and reconstruction of face images.

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Li, Han, Qizhong Zhang, Ziying Lin, and Farong Gao. "Prediction of Epilepsy Based on Tensor Decomposition and Functional Brain Network." Brain Sciences 11, no. 8 (August 13, 2021): 1066. http://dx.doi.org/10.3390/brainsci11081066.

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Epilepsy is a chronic neurological disorder which can affect 65 million patients worldwide. Recently, network based analyses have been of great help in the investigation of seizures. Now graph theory is commonly applied to analyze functional brain networks, but functional brain networks are dynamic. Methods based on graph theory find it difficult to reflect the dynamic changes of functional brain network. In this paper, an approach to extracting features from brain functional networks is presented. Dynamic functional brain networks can be obtained by stacking multiple functional brain networks on the time axis. Then, a tensor decomposition method is used to extract features, and an ELM classifier is introduced to complete epilepsy prediction. In the prediction of epilepsy, the accuracy and F1 score of the feature extracted by tensor decomposition are higher than the degree and clustering coefficient. The features extracted from the dynamic functional brain network by tensor decomposition show better and more comprehensive performance than degree and clustering coefficient in epilepsy prediction.

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Oymak, Samet, and Mahdi Soltanolkotabi. "Learning a deep convolutional neural network via tensor decomposition." Information and Inference: A Journal of the IMA 10, no. 3 (February 1, 2021): 1031–71. http://dx.doi.org/10.1093/imaiai/iaaa042.

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Abstract In this paper, we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches. We develop an algorithm for simultaneously learning all the kernels from the training data. Our approach dubbed deep tensor decomposition (DeepTD) is based on a low-rank tensor decomposition. We theoretically investigate DeepTD under a realizable model for the training data where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to planted convolutional kernels. We show that DeepTD is sample efficient and provably works as soon as the sample size exceeds the total number of convolutional weights in the network.

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Zdunek, Rafał, and Tomasz Sadowski. "Image Completion with Hybrid Interpolation in Tensor Representation." Applied Sciences 10, no. 3 (January 22, 2020): 797. http://dx.doi.org/10.3390/app10030797.

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The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.

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Guo, Xiaoding, Hongli Zhang, Lin Ye, and Shang Li. "RnRTD: Intelligent Approach Based on the Relationship-Driven Neural Network and Restricted Tensor Decomposition for Multiple Accusation Judgment in Legal Cases." Computational Intelligence and Neuroscience 2019 (July 7, 2019): 1–18. http://dx.doi.org/10.1155/2019/6705405.

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The use of intelligent judgment technology to assist in judgment is an inevitable trend in the development of judgment in contemporary social legal cases. Using big data and artificial intelligence technology to accurately determine multiple accusations involved in legal cases is an urgent problem to be solved in legal judgment. The key to solving these problems lies in two points, namely, (1) characterization of legal cases and (2) classification and prediction of legal case data. Traditional methods of entity characterization rely on feature extraction, which is often based on vocabulary and syntax information. Thus, traditional entity characterization often requires extensive energy and has poor generality, thus introducing a large amount of computation and limitation to subsequent classification algorithms. This study proposes an intelligent judgment approach called RnRTD, which is based on the relationship-driven recurrent neural network (rdRNN) and restricted tensor decomposition (RTD). We represent legal cases as tensors and propose an innovative RTD method. RTD has low dependence on vocabulary and syntax and extracts the feature structure that is most favorable for improving the accuracy of the subsequent classification algorithm. RTD maps the tensors, which represent legal cases, into a specific feature space and transforms the original tensor into a core tensor and its corresponding factor matrices. This study uses rdRNN to continuously update and optimize the constraints in RTD so that rdRNN can have the best legal case classification effect in the target feature space generated by RTD. Simultaneously, rdRNN sets up a new gate and a similar case list to represent the interaction between legal cases. In comparison with traditional feature extraction methods, our proposed RTD method is less expensive and more universal in the characterization of legal cases. Moreover, rdRNN with an RTD layer has a better effect than the recurrent neural network (RNN) only on the classification and prediction of multiple accusations in legal cases. Experiments show that compared with previous approaches, our method achieves higher accuracy in the classification and prediction of multiple accusations in legal cases, and our algorithm is more interpretable.

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Kountcheva, Roumiana A., Rumen P. Mironov, and Roumen K. Kountchev. "MLTSP: New 3D Framework, Based on the Multilayer Tensor Spectrum Pyramid." Symmetry 14, no. 9 (September 12, 2022): 1909. http://dx.doi.org/10.3390/sym14091909.

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A tensor representation structure based on the multilayer tensor spectrum pyramid (MLTSP) is introduced in this work. The structure is “truncated”, i.e., part of the high-frequency spectrum coefficients is cut-off, and on the retained low-frequency coefficients, obtained at the output of each pyramid layer, a hierarchical tensor SVD (HTSVD) is applied. This ensures a high concentration of the input tensor energy into a small number of decomposition components of the tensors obtained at the coder output. The implementation of this idea is based on a symmetrical coder/decoder. An example structure for a cubical tensor of size 8 × 8 × 8, which is represented as a two-layer tensor spectrum pyramid, where 3D frequency-ordered fast Walsh–Hadamard transform and HTSVD are used, is given in this paper. The analysis of the needed mathematical operations proved the low computational complexity of the new approach, due to a lack of iterative calculations. The high flexibility of the structure in respect to the number of pyramid layers, the kind of used orthogonal transforms, the number of retained spectrum coefficients, and HTSVD components, permits us to achieve the desired accuracy of the restored output tensor, imposed by the application. Furthermore, this paper presents one possible application for 3D object searches in a tensor database. In this case, to obtain the invariant representation of the 3D objects, in the spectrum pyramid, the 3D modified Mellin–Fourier transform is embedded, and the corresponding algorithm is shown.

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Jamali, Ali Akbar, Yuting Tan, Anthony Kusalik, and Fang-Xiang Wu. "NTD-DR: Nonnegative tensor decomposition for drug repositioning." PLOS ONE 17, no. 7 (July 21, 2022): e0270852. http://dx.doi.org/10.1371/journal.pone.0270852.

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Computational drug repositioning aims to identify potential applications of existing drugs for the treatment of diseases for which they were not designed. This approach can considerably accelerate the traditional drug discovery process by decreasing the required time and costs of drug development. Tensor decomposition enables us to integrate multiple drug- and disease-related data to boost the performance of prediction. In this study, a nonnegative tensor decomposition for drug repositioning, NTD-DR, is proposed. In order to capture the hidden information in drug-target, drug-disease, and target-disease networks, NTD-DR uses these pairwise associations to construct a three-dimensional tensor representing drug-target-disease triplet associations and integrates them with similarity information of drugs, targets, and disease to make a prediction. We compare NTD-DR with recent state-of-the-art methods in terms of the area under the receiver operating characteristic (ROC) curve (AUC) and the area under the precision and recall curve (AUPR) and find that our method outperforms competing methods. Moreover, case studies with five diseases also confirm the reliability of predictions made by NTD-DR. Our proposed method identifies more known associations among the top 50 predictions than other methods. In addition, novel associations identified by NTD-DR are validated by literature analyses.

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Mahyari, Arash Golibagh, David M. Zoltowski, Edward M. Bernat, and Selin Aviyente. "A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG." IEEE Transactions on Biomedical Engineering 64, no. 1 (January 2017): 225–37. http://dx.doi.org/10.1109/tbme.2016.2553960.

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Journal articles on the topic 'Tensor decomposition approach'

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