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1

Novototsky-Vlasov, V., V. Kovalev, and V. Tikhonov. "ON THE CORRECTNESS OF THE APPLICATION OF TENSOR DECOMPOSITION FOR EEG SPECTRA ANALYSIS." Znanstvena misel journal, no. 78 (May 29, 2023): 12–15. https://doi.org/10.5281/zenodo.7980556.

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In our previous work, it was suggested that the subject's EEG spectra in different functional states have a third-order tensor structure, and the PARAFAC tensor decomposition can be used to isolate physically and physiologically meaningful components from them. However, the correctness of using tensor decomposition to analyze EEG spectra in different physiological states has been substantiated neither experimentally nor theoretically. In this paper, we used the residual of data approximation by a low-rank tensor and proved the correctness of the application of the PARAFAC tensor decomposit
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Yokota, Tatsuya, Qibin Zhao, and Andrzej Cichocki. "Smooth PARAFAC Decomposition for Tensor Completion." IEEE Transactions on Signal Processing 64, no. 20 (2016): 5423–36. http://dx.doi.org/10.1109/tsp.2016.2586759.

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Mørup, Morten, Lars Kai Hansen, and Sidse M. Arnfred. "Algorithms for Sparse Nonnegative Tucker Decompositions." Neural Computation 20, no. 8 (2008): 2112–31. http://dx.doi.org/10.1162/neco.2008.11-06-407.

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There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as generalizations of the regular factor analysis to data of more than two modalities. Nonnegative matrix factorization (NMF), in conjunction with sparse coding, has recently been given much attention due to
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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 (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
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Phan, Anh-Huy, Petr Tichavsky, and Andrzej Cichocki. "CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping." IEEE Transactions on Signal Processing 61, no. 19 (2013): 4847–60. http://dx.doi.org/10.1109/tsp.2013.2269046.

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Sunil, Kumar Jyothula, and Chandra Prasad Talari Jaya. "An Efficient Transform based Low Rank Tensor Completion to Extreme Visual Recovery." Indian Journal of Science and Technology 15, no. 14 (2022): 608–18. https://doi.org/10.17485/IJST/v15i14.264.

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Abstract <strong>Objective:</strong>&nbsp;To propose an optimization approach in recovering of the corrupted tensors in the high dimensional real time data.&nbsp;<strong>Methods:</strong>&nbsp;The recovering of corrupted tensors is performed by low-rank tensor completion methods. The tensor decomposition methods are used in tensor completion methods. These Tensor decomposition methods; candecomp / parafac (CP), tucker and higher-order Singular Value Decomposition (HoSVD) are used to minimize the rank of a tensor data. The limitations are in finding the rank of a tensor.&nbsp;<strong>Findings:<
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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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Favier, Gérard, and Alain Kibangou. "Tensor-Based Approaches for Nonlinear and Multilinear Systems Modeling and Identification." Algorithms 16, no. 9 (2023): 443. http://dx.doi.org/10.3390/a16090443.

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Nonlinear (NL) and multilinear (ML) systems play a fundamental role in engineering and science. Over the last two decades, active research has been carried out on exploiting the intrinsically multilinear structure of input–output signals and/or models in order to develop more efficient identification algorithms. This has been achieved using the notion of tensors, which are the central objects in multilinear algebra, giving rise to tensor-based approaches. The aim of this paper is to review such approaches for modeling and identifying NL and ML systems using input–output data, with a reminder o
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9

Yang, Hye-Kyung, and Hwan-Seung Yong. "S-PARAFAC: Distributed Tensor Decomposition using Apache Spark." Journal of KIISE 45, no. 3 (2018): 280–87. http://dx.doi.org/10.5626/jok.2018.45.3.280.

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Rošt’áková, Zuzana, Roman Rosipal, Saman Seifpour, and Leonardo Jose Trejo. "A Comparison of Non-negative Tucker Decomposition and Parallel Factor Analysis for Identification and Measurement of Human EEG Rhythms." Measurement Science Review 20, no. 3 (2020): 126–38. http://dx.doi.org/10.2478/msr-2020-0015.

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AbstractAnalysis of changes in the brain neural electrical activity measured by the electroencephalogram (EEG) plays a crucial role in the area of brain disorder diagnostics. The elementary latent sources of the brain neural activity can be extracted by a tensor decomposition of continuously recorded multichannel EEG. Parallel factor analysis (PARAFAC) is a powerful approach for this purpose. However, the assumption of the same number of factors in each dimension of the PARAFAC model may be restrictive when applied to EEG data. In this article we discuss the potential benefits of an alternativ
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Ouyang, Zhiyuan, Liqi Zhang, Huazhong Wang, and Kai Yang. "High-Dimensional Seismic Data Reconstruction Based on Linear Radon Transform–Constrained Tensor CANDECOM/PARAFAC Decomposition." Remote Sensing 14, no. 24 (2022): 6275. http://dx.doi.org/10.3390/rs14246275.

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Random noise and missing seismic traces are common in field seismic data, which seriously affects the subsequent seismic processing flow. The complete noise-free high-dimensional seismic dataset in the frequency–space (f-x) domain under the local linear assumption are regarded as a low-rank tensor, and each high dimensional seismic dataset containing only one linear event is a rank-1 tensor. The tensor CANDECOM/PARAFAC decomposition (CPD) method estimates complete noise-free seismic signals by characterizing high-dimensional seismic signals as the sum of several rank-1 tensors. In order to imp
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12

Wang, Wenshuai, Xianpeng Wang, Jinmei Shi, and Xiang Lan. "Joint Angle and Range Estimation in Monostatic FDA-MIMO Radar via Compressed Unitary PARAFAC." Remote Sensing 14, no. 6 (2022): 1398. http://dx.doi.org/10.3390/rs14061398.

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In this paper, we study the joint range and angle estimation problem based in monostatic frequency diverse-array multiple-input multiple-output (FDA-MIMO) radar, and propose a method for range and angle estimation base on compressed unitary parallel factor (PARAFAC). First, the received complex signal matrix is stacked into a third-order complex signal tensor. Then, we can transform the obtained third-order complex signal tensor into a third-order real-valued signal tensor by employing forward–backward and unitary transformation techniques. Next, a smaller third-order real-valued signal tensor
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13

Tichavsky, Petr, Anh Huy Phan, and Zbyněk Koldovsky. "Cramér-Rao-Induced Bounds for CANDECOMP/PARAFAC Tensor Decomposition." IEEE Transactions on Signal Processing 61, no. 8 (2013): 1986–97. http://dx.doi.org/10.1109/tsp.2013.2245660.

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14

Yang, Ruo-Nan, Wei-Tao Zhang, and Shun-Tian Lou. "Adaptive Blind Channel Estimation for MIMO-OFDM Systems Based on PARAFAC." Wireless Communications and Mobile Computing 2020 (October 24, 2020): 1–17. http://dx.doi.org/10.1155/2020/8396930.

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In order to track the changing channel in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, it is prior to estimate channel impulse response adaptively. In this paper, we proposed an adaptive blind channel estimation method based on parallel factor analysis (PARAFAC). We used an exponential window to weight the past observations; thus, the cost function can be constructed via a weighted least squares criterion. The minimization of the cost function is equivalent to the decomposition of third-order tensor which consists of the weighted OFDM data symb
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15

Lin, Heyun, Chaowei Yuan, Jianhe Du, and Zhongwei Hu. "Estimation of DOA for Noncircular Signals via Vandermonde Constrained Parallel Factor Analysis." International Journal of Antennas and Propagation 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/4612583.

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We provide a complete study on the direction-of-arrival (DOA) estimation of noncircular (NC) signals for uniform linear array (ULA) via Vandermonde constrained parallel factor (PARAFAC) analysis. By exploiting the noncircular property of the signals, we first construct an extended matrix which contains two times sampling number of the received signal. Then, taking the Vandermonde structure of the array manifold matrix into account, the extended matrix can be turned into a tensor model which admits the Vandermonde constrained PARAFAC decomposition. Based on this tensor model, an efficient linea
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16

Skantze, Viktor, Mikael Wallman, Ann-Sofie Sandberg, Rikard Landberg, Mats Jirstrand, and Carl Brunius. "Identifying Metabotypes From Complex Biological Data Using PARAFAC." Current Developments in Nutrition 5, Supplement_2 (2021): 882. http://dx.doi.org/10.1093/cdn/nzab048_017.

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Abstract Objectives Research have identified large individual variation in physiological response to diet, which has led to more focused investigations in precision nutrition. One approach towards personalized nutrition is to identify groups of differential responders, so called metabotypes (i.e., clusters of individuals with similar metabolic profiles and/or regulation). Metabotyping has previously been addressed using matrix decomposition tools like principal component analysis (PCA) on data organized in matrix form. However, metabotyping using data from more complex experimental designs, in
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Li, Ziyue, Nurettin Dorukhan Sergin, Hao Yan, Chen Zhang, and Fugee Tsung. "Tensor Completion for Weakly-Dependent Data on Graph for Metro Passenger Flow Prediction." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 4804–10. http://dx.doi.org/10.1609/aaai.v34i04.5915.

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Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular application that motivates this study is the spatiotemporal data analysis. As shown in the preliminary study, weakly dependencies can worsen the low-rank tensor completion performance. In this paper, we propose a novel low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion fr
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18

Sun, Yuzhe, Wei Wang, Yufan Wang, and Yuanfeng He. "A Bayesian Tensor Decomposition Method for Joint Estimation of Channel and Interference Parameters." Sensors 24, no. 16 (2024): 5284. http://dx.doi.org/10.3390/s24165284.

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Bayesian tensor decomposition has been widely applied in channel parameter estimations, particularly in cases with the presence of interference. However, the types of interference are not considered in Bayesian tensor decomposition, making it difficult to accurately estimate the interference parameters. In this paper, we present a robust tensor variational method using a CANDECOMP/PARAFAC (CP)-based additive interference model for multiple input–multiple output (MIMO) with orthogonal frequency division multiplexing (OFDM) systems. A more realistic interference model compared to traditional col
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19

Liu, Qing, Jian Xie, Zhaolin Zhang, Yanyun Gong, and Ling Wang. "Tensor-based passive localization of multiple wideband emitters using PARAFAC decomposition." Digital Signal Processing 164 (September 2025): 105290. https://doi.org/10.1016/j.dsp.2025.105290.

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20

Pooja, Choudhary, and Garg Kanwal. "Tensor Data Imputation by PARAFAC with Updated Chaotic Biases by Adam Optimizer." International Journal of Recent Technology and Engineering (IJRTE) 9, no. 6 (2021): 30–38. https://doi.org/10.35940/ijrte.E5291.039621.

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<strong>ABSTRACT:</strong> The big data pattern analysis suffers from incorrect responses due to missing data entries in the real world. Data collected for digital movie platforms like Netflix and intelligent transportation systems is Spatio-temporal data. Extracting the latent and explicit features from this data is a challenge. We present the high dimensional data imputation problem as a higher-order tensor decomposition. The regularized and biased PARAFAC decomposition is proposed to generate the missing data entries. The biases are created and updated by a chaotic exponential factor in Ada
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21

Khouaja, Anis, Tarek Garna, José Ragot, and Hassani Messaoud. "Constrained predictive control of a SISO nonlinear system based on third-order S-PARAFAC Volterra models." Transactions of the Institute of Measurement and Control 39, no. 6 (2016): 907–20. http://dx.doi.org/10.1177/0142331215627005.

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This paper is concerned with the identification and nonlinear predictive control approach for a nonlinear process based on a third-order reduced complexity, discrete-time Volterra model called the third-order S-PARAFAC Volterra model. The proposed model is given using the PARAFAC tensor decomposition that provides a parametric reduction compared with the conventional Volterra model. In addition, the symmetry property of the Volterra kernels allows us to further reduce the complexity of the model. These properties allow synthesizing a nonlinear model-based predictive control (NMBPC). Then we co
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Liu, Changqing, and Xiaoqian Chen. "Vessel Track Recovery With Incomplete AIS Data Using Tensor CANDECOM/PARAFAC Decomposition." Journal of Navigation 67, no. 1 (2013): 83–99. http://dx.doi.org/10.1017/s0373463313000398.

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Global analysis of vessel motion patterns has become possible using satellite-based Automatic Identification System (AIS). The concept of space-based AIS needs several satellites to provide complete coverage and high detection probability. However, in early development stages, often only one satellite is launched and due to its limitation of orbit and footprint, received AIS messages are discontinuous. In this paper, we have analysed real AIS data obtained by satellite to form a global maritime surveillance picture. Furthermore, we propose to take advantage of the tensor CANDECOMP/PARAFAC (CP)
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Choudhary, Pooja, and Kanwal Garg. "Tensor Data Imputation by PARAFAC with Updated Chaotic Biases by Adam Optimizer." International Journal of Recent Technology and Engineering 9, no. 6 (2021): 30–38. http://dx.doi.org/10.35940/ijrte.e5291.039621.

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The big data pattern analysis suffers from incorrect responses due to missing data entries in the real world. Data collected for digital movie platforms like Netflix and intelligent transportation systems is Spatio-temporal data. Extracting the latent and explicit features from this data is a challenge. We present the high dimensional data imputation problem as a higher-order tensor decomposition. The regularized and biased PARAFAC decomposition is proposed to generate the missing data entries. The biases are created and updated by a chaotic exponential factor in Adam's optimization, which red
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Ballico, Edoardo. "Ranks with Respect to a Projective Variety and a Cost-Function." AppliedMath 2, no. 3 (2022): 457–65. http://dx.doi.org/10.3390/appliedmath2030026.

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Let X⊂Pr be an integral and non-degenerate variety. A “cost-function” (for the Zariski topology, the semialgebraic one, or the Euclidean one) is a semicontinuous function w:=[1,+∞)∪+∞ such that w(a)=1 for a non-empty open subset of X. For any q∈Pr, the rank rX,w(q) of q with respect to (X,w) is the minimum of all ∑a∈Sw(a), where S is a finite subset of X spanning q. We have rX,w(q)&lt;+∞ for all q. We discuss this definition and classify extremal cases of pairs (X,q). We give upper bounds for all rX,w(q) (twice the generic rank) not depending on w. This notion is the generalization of the case
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Li, Liangliang, Tao Liang, Huaguo Zhang, Songmao Du, and Lin Gao. "A Tensor-Based Approach to Blind Despreading of Long-Code Multiuser DSSS Signals." Electronics 12, no. 5 (2023): 1097. http://dx.doi.org/10.3390/electronics12051097.

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In this paper, a tensor-based approach to blind despreading of long-code multiuser DSSS signals is proposed. We aim to generalize the tensor-based methods originally developed for blind separation of short-code multiuser DSSS signals to long-code cases. Firstly, we model the intercepted long-code multiuser DSSS signals with an antenna-array receiver as a three-order tensor with missing values, and then, the blind separation problem can be formulated as a canonical or parallel factor (CANDECOMP/PARAFAC) decomposition problem of the missing-data tensor, which can be solved using optimum methods.
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Zhang, Lei, Han Wang, Fang-Qing Wen, and Jun-Peng Shi. "PARAFAC Estimators for Coherent Targets in EMVS-MIMO Radar with Arbitrary Geometry." Remote Sensing 14, no. 12 (2022): 2905. http://dx.doi.org/10.3390/rs14122905.

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In the past few years, multiple-input multiple-output (MIMO) radar with electromagnetic vector sensor (EMVS) array, or called EMVS-MIMO radar, has attracted extensive attention in target detection. Unlike the traditional scalar sensor-based MIMO radar, an EMVS-MIMO radar can not only provides a two-dimensional (2D) direction finding of the targets but also offers 2D polarization parameter estimation, which may be important for detecting weak targets. In this paper, we investigate into multiple parameter estimations for a bistatic EMVS-MIMO radar in the presence of coherent targets, whose trans
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Li, Ni, Honggui Deng, Fuxin Xu, et al. "Tensor Based Semi-Blind Channel Estimation for Reconfigurable Intelligent Surface-Aided Multiple-Input Multiple-Output Communication Systems." Sensors 24, no. 20 (2024): 6625. http://dx.doi.org/10.3390/s24206625.

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Reconfigurable intelligent surfaces (RISs) are a promising technology for sixth-generation (6G) wireless networks. However, a fully passive RIS cannot independently process signals. Wireless systems equipped with it often encounter the challenge of large channel matrix dimensions when acquiring channel state information using pilot-assisted algorithms, resulting in high pilot overhead. To address this issue, this article proposes a semi-blind joint channel and symbol estimation receiver without a pilot training stage for RIS-aided multiple-input multiple-output (MIMO) (including massive MIMO)
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Nion, D., and N. D. Sidiropoulos. "Adaptive Algorithms to Track the PARAFAC Decomposition of a Third-Order Tensor." IEEE Transactions on Signal Processing 57, no. 6 (2009): 2299–310. http://dx.doi.org/10.1109/tsp.2009.2016885.

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Rao, Wei, Dan Li, and Jian Zhang. "A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array." Sensors 18, no. 11 (2018): 3708. http://dx.doi.org/10.3390/s18113708.

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In this paper, a novel parallel factor (PARAFAC) model for processing the nested vector-sensor array is proposed. It is first shown that a nested vector-sensor array can be divided into multiple nested scalar-sensor subarrays. By means of the autocorrelation matrices of the measurements of these subarrays and the cross-correlation matrices among them, it is then demonstrated that these subarrays can be transformed into virtual scalar-sensor uniform linear arrays (ULAs). When the measurement matrices of these scalar-sensor ULAs are combined to form a third-order tensor, a novel PARAFAC model is
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Wang, Wenshuai, Xiang Lan, Jinmei Shi, and Xianpeng Wang. "A Fast PARAFAC Algorithm for Parameter Estimation in Monostatic FDA-MIMO Radar." Remote Sensing 14, no. 13 (2022): 3093. http://dx.doi.org/10.3390/rs14133093.

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This paper studies the joint range and angle estimation of monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) radar and proposes a joint estimation algorithm. First, the transmit direction matrix is converted into real values by unitary transformation, and the Vandermonde-like matrix structure is used to construct an augmented output that doubles the aperture of the receive array. Then the augmented output is combined into a third-order tensor. Next, the factor matrices are initially estimated. Finally, the direction matrices are estimated utilizing parallel factor (P
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Garcez, Caio C. R., Daniel Valle de Lima, Ricardo Kehrle Miranda, et al. "Tensor-Based Subspace Tracking for Time-Delay Estimation in GNSS Multi-Antenna Receivers." Sensors 19, no. 23 (2019): 5076. http://dx.doi.org/10.3390/s19235076.

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Although Global Navigation Satellite Systems (GNSS) receivers currently achieve high accuracy when processing their geographic location under line of sight (LOS), multipath interference and noise degrades the accuracy considerably. In order to mitigate multipath interference, receivers based on multiple antennas became the focus of research and technological development. In this context, tensor-based approaches based on Parallel Factor Analysis (PARAFAC) models have been proposed in the literature, providing optimum performance. State-of-the-art techniques for antenna array based GNSS receiver
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You, Yanan, Rui Wang, and Wenli Zhou. "An Optimized Filtering Method of Massive Interferometric SAR Data for Urban Areas by Online Tensor Decomposition." Remote Sensing 12, no. 16 (2020): 2582. http://dx.doi.org/10.3390/rs12162582.

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The filtering of multi-pass synthetic aperture radar interferometry (InSAR) stack data is a necessary preprocessing step utilized to improve the accuracy of the object-based three-dimensional information inversion in urban area. InSAR stack data is composed of multi-temporal homogeneous data, which is regarded as a third-order tensor. The InSAR tensor can be filtered by data fusion, i.e., tensor decomposition, and these filters keep balance in the noise elimination and the fringe details preservation, especially with abrupt fringe change, e.g., the edge of urban structures. However, tensor dec
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Chen, Hanxin, Shaoyi Li, and Menglong Li. "Multi-Channel High-Dimensional Data Analysis with PARAFAC-GA-BP for Nonstationary Mechanical Fault Diagnosis." International Journal of Turbomachinery, Propulsion and Power 7, no. 3 (2022): 19. http://dx.doi.org/10.3390/ijtpp7030019.

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Conventional signal processing methods such as Principle Component Analysis (PCA) focus on the decomposition of signals in the 2D time–frequency domain. Parallel factor analysis (PARAFAC) is a novel method used to decompose multi-dimensional arrays, which focuses on analyzing the relevant feature information by deleting the duplicated information among the multiple measurement points. In the paper, a novel hybrid intelligent algorithm for the fault diagnosis of a mechanical system was proposed to analyze the multiple vibration signals of the centrifugal pump system and multi-dimensional comple
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Liu, Jiaqi, Qiwu Wu, Lingzhi Jiang, et al. "BS-CP: Efficient streaming Bayesian tensor decomposition method via assumed density filtering." PLOS ONE 19, no. 12 (2024): e0312723. https://doi.org/10.1371/journal.pone.0312723.

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Tensor data is common in real-world applications, such as recommendation system and air quality monitoring. But such data is often sparse, noisy, and fast produced. CANDECOMP/PARAFAC (CP) is a popular tensor decomposition model, which is both theoretically advantageous and numerically stable. However, learning the CP model in a Bayesian framework, though promising to handle data sparsity and noise, is computationally challenging, especially with fast produced data streams. The fundamental problem addressed by the paper is mainly tackles the efficient processing of streaming tensor data. In thi
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Abdi-Sargezeh, Bahman, Antonio Valentin, Gonzalo Alarcon, David Martin-Lopez, and Saeid Sanei. "Higher-order tensor decomposition based scalp-to-intracranial EEG projection for detection of interictal epileptiform discharges." Journal of Neural Engineering 18, no. 6 (2021): 066039. http://dx.doi.org/10.1088/1741-2552/ac3cc4.

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Abstract Objective. Interictal epileptiform discharges (IEDs) occur between two seizures onsets. IEDs are mainly captured by intracranial recordings and are often invisible over the scalp. This study proposes a model based on tensor factorization to map the time-frequency (TF) features of scalp EEG (sEEG) to the TF features of intracranial EEG (iEEG) in order to detect IEDs from over the scalp with high sensitivity. Approach. Continuous wavelet transform is employed to extract the TF features. Time, frequency, and channel modes of IED segments from iEEG recordings are concatenated into a four-
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Wu, Hao, Ruihan Yue, Ruixue Gao, Rui Wen, Jun Feng, and Youhua Wei. "Hyperspectral denoising based on the principal component low-rank tensor decomposition." Open Geosciences 14, no. 1 (2022): 518–29. http://dx.doi.org/10.1515/geo-2022-0379.

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Abstract Due to the characteristics of hyperspectral images (HSIs), such as their high spectral resolution and multiple continuous narrow bands, HSI technology has become widely used in fields such as target recognition, environmental detection, and agroforestry detection. HSIs are subject, for various reasons, to noise in the processes of data acquisition and transmission. Therefore, the denoising of HSIs is very necessary and important. In this article, according to the characteristics of HSIs, an HSI denoising model combining principal component analysis (PCA) and CANDECOMP/PARAFAC decompos
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Xu, Tengxian, Yongqin Yang, Mengxing Huang, Han Wang, Di Wu, and Qu Yi. "Tensor-Based Angle and Range Estimation Method in Monostatic FDA-MIMO Radar." Mathematical Problems in Engineering 2020 (August 12, 2020): 1–8. http://dx.doi.org/10.1155/2020/5720189.

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In the paper, joint angle and range estimation issue for monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) is proposed, and a tensor-based framework is addressed to solve it. The proposed method exploits the multidimensional structure of matched filters in FDA-MIMO radar. Firstly, stack the received data to form a third-order tensor so that the multidimensional structure information of the received data can be acquired. Then, the steering matrices contain the angle and rang information are estimated by using the parallel factor (PARAFAC) decomposition. Finally, the a
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Du, Jinzhi, Weijia Cui, Bin Ba, Chunxiao Jian, and Haiyun Xu. "Fast Tensor-Based Joint Estimation for Time Delay and Angle of Arrival in OFDM System." International Journal of Antennas and Propagation 2022 (September 27, 2022): 1–10. http://dx.doi.org/10.1155/2022/6856050.

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Nowadays, the joint estimation of time delay (TD) and angle of arrival (AOA) using conventional vector structure suffers from the considerable complexity of multidimensional spectrum search. Therefore, a fast estimation method using orthogonal frequency division multiplexing (OFDM) technology and uniform planar array (UPA) is proposed in this paper, which adopts low-complexity tensor-based operations and spatial-frequency features to reconfigure the channel frequency response. To begin with, the array response is integrated with the OFDM signal characteristics to build an extended array in ten
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He, Fei, Andrew Harms, and Lamar Yaoqing Yang. "Tensor Rank Regularization with Bias Compensation for Millimeter Wave Channel Estimation." Signals 3, no. 4 (2022): 664–81. http://dx.doi.org/10.3390/signals3040040.

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This paper presents a novel method of tensor rank regularization with bias compensation for channel estimation in a hybrid millimeter wave MIMO-OFDM system. Channel estimation is challenging due to the unknown number of multipath components that determines the channel rank. In general, finding the intrinsic rank of a tensor is a non-deterministic polynomial-time (NP) hard problem. However, by leveraging the sparse characteristics of millimeter wave channels, we propose a modified CANDECOMP/PARAFAC (CP) decomposition-based method that jointly estimates the tensor rank and channel component matr
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Xiao, Haoqi, Honggui Deng, Aimin Guo, Yuyan Qian, Chengzuo Peng, and Yinhao Zhang. "Accelerated PARAFAC-Based Channel Estimation for Reconfigurable Intelligent Surface-Assisted MISO Systems." Sensors 22, no. 19 (2022): 7463. http://dx.doi.org/10.3390/s22197463.

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To achieve fast and accurate channel estimation of reconfigurable intelligent surface (RIS)-assisted multiple-input single-output (MISO) systems, we propose an accelerated bilinear alternating least squares algorithm (ABALS) based on parallel factor decomposition. Firstly, we build a tensor model of the received signal, and expand it to obtain the unfolded forms of the model. Secondly, we derive the expression of the estimation problem of two channels based on the unfolded forms to transform the problem into a cost function problem. Furthermore, we solve the cost function problem by introducin
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Chen, Hanxin, Yunwei Xiong, Shaoyi Li, Ziwei Song, Zhenyu Hu, and Feiyang Liu. "Multi-Sensor Data Driven with PARAFAC-IPSO-PNN for Identification of Mechanical Nonstationary Multi-Fault Mode." Machines 10, no. 2 (2022): 155. http://dx.doi.org/10.3390/machines10020155.

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Data analysis has wide applications in eliminating the irrelevant and redundant components in signals to reveal the important informational characteristics that are required. Conventional methods for multi-dimensional data analysis via the decomposition of time and frequency information that ignore the information in signal space include independent component analysis (ICA) and principal component analysis (PCA). We propose the processing of a signal according to the continuous wavelet transform and the construction of a three-dimensional matrix containing the time–frequency–space information
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42

Yang, Ruo-Nan, Wei-Tao Zhang, and Shun-Tian Lou. "Joint Adaptive Blind Channel Estimation and Data Detection for MIMO-OFDM Systems." Wireless Communications and Mobile Computing 2020 (July 2, 2020): 1–9. http://dx.doi.org/10.1155/2020/2508130.

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In order to track a changing channel in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems, it is a priority to estimate channel impulse response adaptively. In this paper, we propose an adaptive blind channel estimation method based on parallel factor analysis (PARAFAC). We used an exponential window to weigh the past observations; thus, the cost function can be constructed via a weighted least squares criterion. The minimization of the cost function is equivalent to the decomposition of a third-order tensor, which consists of the weighted OFDM data
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43

Seifpour, Saman, and Alexander Šatka. "Tensor Decomposition Analysis of Longitudinal EEG Signals Reveals Differential Oscillatory Dynamics in Eyes-Closed and Eyes-Open Motor Imagery BCI: A Case Report." Brain Sciences 13, no. 7 (2023): 1013. http://dx.doi.org/10.3390/brainsci13071013.

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Functional dissociation of brain neural activity induced by opening or closing the eyes has been well established. However, how the temporal dynamics of the underlying neuronal modulations differ between these eye conditions during movement-related behaviours is less known. Using a robotic-assisted motor imagery brain-computer interface (MI BCI), we measured neural activity over the motor regions with electroencephalography (EEG) in a stroke survivor during his longitudinal rehabilitation training. We investigated lateralized oscillatory sensorimotor rhythm modulations while the patient imagin
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Wang, Deqing, Zheng Chang, and Fengyu Cong. "Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme." Neural Computing and Applications 33, no. 24 (2021): 17369–87. http://dx.doi.org/10.1007/s00521-021-06325-8.

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AbstractNonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, the sparsity is only a side effect and cannot be explicitly controlled without additional regularization. In this paper, we investigated the nonnegative CANDECOMP/PARAFAC (NCP) decomposition with the sparse regularization item using $$l_1$$ l 1 -norm (sparse NCP). When high sparsity is imposed, the factor matrices will contain more zero components and will not be of full column rank. Thus, the sparse NCP is prone to rank de
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Zhong, Han, Geqi Qi, Wei Guan, and Xiaochen Hua. "Application of Nonnegative Tensor Factorization for Intercity Rail–Air Transport Supply Configuration Pattern Recognition." Sustainability 11, no. 6 (2019): 1803. http://dx.doi.org/10.3390/su11061803.

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With the rapid expansion of the railway represented by high-speed rail (HSR) in China, competition between railway and aviation will become increasingly common on a large scale. Beijing, Shanghai, and Guangzhou are the busiest cities and the hubs of railway and aviation transportation in China. Obtaining their supply configuration patterns can help identify defects in planning. To achieve that, supply level is proposed, which is a weighted supply traffic volume that takes population and distance factors into account. Then supply configuration can be expressed as the distribution of supply leve
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Wang, Ning, Hui Qi, Yong Deng, Weiwei Yu, and Zhong Chen. "Transmission and Drug Resistance Characteristics of Human Immunodeficiency Virus-1 Strain Using Medical Information Data Retrieval System." Computational and Mathematical Methods in Medicine 2022 (June 13, 2022): 1–10. http://dx.doi.org/10.1155/2022/2173339.

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This study was aimed at exploring the transmission and drug resistance characteristics of acquired immunodeficiency syndrome (AIDS) caused by human immunodeficiency virus-1 (HIV-1). The query expansion algorithm based on Candecomp Parafac (CP) decomposition was adopted to construct a data information retrieval system for semantic web and tensor decomposition. In the latent variable model based on tensor decomposition, the three elements in the triples generated feature vectors to calculate the training samples. The HIV patient data set was selected to evaluate the performance of the system, an
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Favier, Gérard, and Danilo Sousa Rocha. "Overview of Tensor-Based Cooperative MIMO Communication Systems—Part 2: Semi-Blind Receivers." Entropy 26, no. 11 (2024): 937. http://dx.doi.org/10.3390/e26110937.

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Cooperative MIMO communication systems play an important role in the development of future sixth-generation (6G) wireless systems incorporating new technologies such as massive MIMO relay systems, dual-polarized antenna arrays, millimeter-wave communications, and, more recently, communications assisted using intelligent reflecting surfaces (IRSs), and unmanned aerial vehicles (UAVs). In a companion paper, we provided an overview of cooperative communication systems from a tensor modeling perspective. The objective of the present paper is to provide a comprehensive tutorial on semi-blind receiv
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Guo, Yuehao, Xianpeng Wang, Jinmei Shi, Xiang Lan, and Liangtian Wan. "Tensor-Based Target Parameter Estimation Algorithm for FDA-MIMO Radar with Array Gain-Phase Error." Remote Sensing 14, no. 6 (2022): 1405. http://dx.doi.org/10.3390/rs14061405.

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As a new radar system, FDA-MIMO radar has recently developed rapidly, as it has broad prospects in angle-range estimation. Unfortunately, the performance of existing algorithms for FDA-MIMO radar is greatly degrading or even failing under the condition of array gain-phase error. This paper proposes an innovative solution to the joint angle and range estimation of FDA-MIMO radar under the condition of array gain-phase error and an estimation algorithm is developed. Moreover, the corresponding Cramér-Rao bound (CRB) is derived to evaluate the algorithm. The parallel factor (PARAFAC) decompositio
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Wang, Yingshu, Juanjuan Zhang, Shu Yuan, Weizhi Ren, Jilin Wang, and Hongwei Wang. "Joint Wideband Spectrum Sensing and Carrier Frequency Estimation in the Multi-Path Propagation Environment Based on Sub-Nyquist Sampling." Electronics 13, no. 21 (2024): 4282. http://dx.doi.org/10.3390/electronics13214282.

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We consider the wideband spectrum sensing within a multi-path propagation environment, where a multi-antenna base station (BS) is tasked with identifying the frequency positions of multiple narrowband transmissions distributed across a broad range of frequencies. To tackle this, we propose a sub-Nyquist sampling structure that incorporates a phased array system. Specifically, each antenna is connected to two separate sampling channels, i.e., one for direct sampling and another for delayed sampling, with the latter incorporating a specified time delay factor. The cross-correlation matrices asso
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Choudhary, Pooja, and Kanwal Garg. "A Novel Privacy Preservation Scheme by Matrix Factorized Deep Autoencoder." International Journal of Computer Network and Information Security 16, no. 3 (2024): 84–98. http://dx.doi.org/10.5815/ijcnis.2024.03.07.

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Data transport entails substantial security to avoid unauthorized snooping as data mining yields important and quite often sensitive information that must be and can be secured using one of the myriad Data Privacy Preservation methods. This study aspires to provide new knowledge to the study of protecting personal information. The key contributions of the work are an imputation method for filling in missing data before learning item profiles and the optimization of the Deep Auto-encoded NMF with a customizable learning rate. We used Bayesian inference to assess imputation for data with 13%, 26
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