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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 decomposition for the analysis of human EEG spectra.
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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 its part-based and easy interpretable representation. While NMF has been extended to the PARAFAC model, no such attempt has been done to extend NMF to the Tucker model. However, if the tensor data analyzed are nonnegative, it may well be relevant to consider purely additive (i.e., nonnegative) Tucker decompositions). To reduce ambiguities of this type of decomposition, we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse nonnegative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms for Tucker decompositions when the data and interactions can be considered nonnegative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is more appropriate for the data as well as to select the number of components by turning off excess components. The algorithms for SN-TUCKER can be downloaded from Mørup (2007).
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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 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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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> To propose an optimization approach in recovering of the corrupted tensors in the high dimensional real time data. <strong>Methods:</strong> 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. <strong>Findings:</strong> The recovered data using the lifting transform induced tensor- Singular Value Decomposition (t-SVD) technique were assessed utilizing the Peak Signal to Noise Ratio (PSNR), Structural Similarity (SSIM), Naturalness Image Quality Evaluator (NIQE), and Perceptual Image Quality Evaluator (PIQE). When compared to state-of-the-art approaches, the low rank assumption condition with the lifting transform consideration gave good data recovery for every missing ratio. <strong>Novelty:</strong> The missing data is calculated by lifting polyphase structures by utilizing the available data. The polyphase structures are splitting the value into equivalent multiple triangular matrices, these are processed with the t-SVD to have the better approximation tensor rank. <strong>Keywords:</strong> Tensor Completion; Transformbased Optimization; 5/3 Lifting Wavelet Transform; Lowrank tensor completion; tSVD
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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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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 of the tensor operations and decompositions needed to render the presentation as self-contained as possible. In the case of NL systems, two families of models are considered: the Volterra models and block-oriented ones. Volterra models, frequently used in numerous fields of application, have the drawback to be characterized by a huge number of coefficients contained in the so-called Volterra kernels, making their identification difficult. In order to reduce this parametric complexity, we show how Volterra systems can be represented by expanding high-order kernels using the parallel factor (PARAFAC) decomposition or generalized orthogonal basis (GOB) functions, which leads to the so-called Volterra–PARAFAC, and Volterra–GOB models, respectively. The extended Kalman filter (EKF) is presented to estimate the parameters of a Volterra–PARAFAC model. Another approach to reduce the parametric complexity consists in using block-oriented models such as those of Wiener, Hammerstein and Wiener–Hammerstein. With the purpose of estimating the parameters of such models, we show how the Volterra kernels associated with these models can be written under the form of structured tensor decompositions. In the last part of the paper, the notion of tensor systems is introduced using the Einstein product of tensors. Discrete-time memoryless tensor-input tensor-output (TITO) systems are defined by means of a relation between an Nth-order tensor of input signals and a Pth-order tensor of output signals via a (P+N)th-order transfer tensor. Such systems generalize the standard memoryless multi-input multi-output (MIMO) system to the case where input and output data define tensors of order higher than two. The case of a TISO system is then considered assuming the system transfer is a rank-one Nth-order tensor viewed as a global multilinear impulse response (IR) whose parameters are estimated using the weighted least-squares (WLS) method. A closed-form solution is proposed for estimating each individual IR associated with each mode-n subsystem.
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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 alternative tensor decomposition method – the Tucker model. We analyze situations, where in comparison to the PARAFAC solution, the Tucker model provides a more parsimonious representation of the EEG data decomposition. We show that this more parsimonious representation of EEG is achieved without reducing the ability to explain variance. We analyze EEG records of two patients after ischemic stroke and we focus on the extraction of specific sensorimotor oscillatory sources associated with motor imagery during neurorehabilitation training. Both models provided consistent results. The advantage of the Tucker model was a compact structure with only two spatial signatures reflecting the expected lateralized activation of the detected subject-specific sensorimotor rhythms.
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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 improve the stability and effect of the tensor CPD algorithm, this paper proposes a linear Radon transform–constrained tensor CPD method (RCPD) by using the sparsity of factor matrix in the Radon domain after high-dimensional seismic signal tensor CPD and uses alternating direction multiplier method (ADMM) to solve the established optimization problem. This proposed method is an essential realization of the high-dimensional linear Radon transform, and the results of synthetic and field data reconstruction prove the effectiveness of the proposed method.
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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 is composed by using compressing the third-order real-valued signal tensor. After that, PARAFAC decomposition is applied to obtain the direction matrix. Lastly, the angle and range are estimated by employing the least square (LS) fitting. The estimation error of the proposed method is about 10% lower than that of the traditional PARAFAC method under the low number of snapshots. When the number of snapshots is high, the performance of the two methods is close. Moreover, the computational complexity of the proposed method is nearly 96% less than those of the traditional PARAFAC methods in the case of low snapshots, while the gap is larger in the case of high snapshots. The superiority and effectiveness of the method are proved by complexity analysis and simulation experiments.
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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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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 symbols. To reduce the computational load, we adopt a recursive singular value decomposition method for tensor decomposition; then, the channel parameters can be estimated adaptively. Simulation results validate the effectiveness of the proposed algorithm under diverse signalling conditions.
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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 linear algebra algorithm is applied to obtain the DOA estimation via utilizing the rotational invariance between two submatrices. Compared with some existing algorithms, the proposed method has a better DOA estimation performance. Meanwhile, the proposed method consistently has a higher estimation accuracy and a much lower computational complexity than the trilinear alternating least square- (TALS-) based PARAFAC algorithm. Finally, numerical examples are conducted to demonstrate the effectiveness of the proposed approach in terms of estimation accuracy and computational complexity.
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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, involving e.g., repeated measures over time or multiple treatments (tensor data), requires new methods. Methods We developed a workflow for detecting metabotypes from experimental tensor data. The workflow is based on tensor decomposition, specifically PARAFAC which is conceptually similar to PCA but extended to multidimensional data. Metabotypes, based on metabolomics data were identified from PARAFAC scores using k-means clustering and validated by their association to anthropometric and clinical baseline data. Additionally, we evaluated the robustness of the metabotypes using bootstrapping. Furthermore, we applied the workflow to identify metabotypes using data from a crossover acute post-prandial dietary intervention study on 17 overweight males (BMI 25–30 kg/m2, 41–67 y of age) undergoing three dietary interventions (pickled herring, baked herring and baked beef), measuring 80 metabolites (from GC-MS metabolomics) at 8 time points (0–7h). Results We identified two metabotypes characterized by differences in amino acid levels, predominantly in the beef diet, that were also associated with creatinine (p = 0.007). The metabotype with higher postprandial amino acid levels was also associated with higher fasting creatinine compared to the other metabotype. Conclusions The results stress the potential of PARAFAC to discover metabotypes from complex study designs. The workflow is not restricted to our data structure and can be applied to any type of tensor data. However, PARAFAC is sensitive to data pre-processing and further studies where differential metabotypes are related to clinical endpoints are highly warranted. Funding Sources This work has been supported by the Swedish Foundation for Strategic Research and Formas, which is gratefully acknowledged.
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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 framework by introducing the L1-norm penalty and Graph Laplacian penalty to model the weakly dependency on graph. We further propose an efficient optimization algorithm based on the Block Coordinate Descent for efficient estimation. A case study based on the metro passenger flow data in Hong Kong is conducted to demonstrate an improved performance over the regular tensor completion methods.
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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 colored noise is considered in terms of co-channel interference (CCI) and front-end interference (FEI). In contrast to conventional algorithms that filter out interference, the proposed method jointly estimates the channel and interference parameters in the time–frequency domain. Simulation results validate the correctness of the proposed method by the evidence lower bound (ELBO) and reveal the fact that the proposed method outperforms traditional information-theoretic methods, tensor decomposition models, and robust model based on CP (RCP) in terms of estimation accuracy. Further, the interference parameter estimation technique has profound implications for anti-interference applications and dynamic spectrum allocation.
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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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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 Adam's optimization, which reduces the imputation error. This chaotic perturbed exponentially update in the learning rate replaces the fixed learning rate in the bias update by Adam optimization. The idea has experimented with Netflix and traffic datasets from Guangzhou, China
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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 construct the general form of a new predictor and we propose an optimization algorithm formulated as a quadratic programming (QP) algorithm under linear and nonlinear constraints. The performance of the proposed third-order S-PARAFAC Volterra model and the developed NMBPC algorithm are illustrated on a numerical simulation and validated on a benchmark such as a continuous stirred-tank reactor system.
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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) decomposition to analyse three mode characteristics of the data, which are location, vessel and time. For incomplete data, we exploit the link prediction technique based on tensor factorisation to recover vessel tracks in a specified area. A variant of temporal link prediction based on CP is presented. We illustrate the usefulness of exploiting the three-mode structure of AIS data by simulation, and demonstrate that the track recovery result has acceptable precision.
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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 reduces the imputation error. This chaotic perturbed exponentially update in the learning rate replaces the fixed learning rate in the bias update by Adam optimization. The idea has experimented with Netflix and traffic datasets from Guangzhou, China.
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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)<+∞ 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 in which the cost-function w is the constant function 1. In this case, the rank is a well-studied notion that covers the tensor rank of tensors of arbitrary formats (PARAFAC or CP decomposition) and the additive decomposition of forms. We also adapt to cost-functions the rank 1 decomposition of real tensors in which we allow pairs of complex conjugate rank 1 tensors.
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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. Secondly, a constrained Cramér–Rao Bound (CRB) is also derived to provide a performance benchmark for the proposed approach. Simulation results verify the feasibility of our proposed approach in the case of low signal-to-noise (SNR) conditions.
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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 transmitting EMVS and receiving EMVS are placed in an arbitrary topology. Three tensor-aware spatial smoothing estimators are introduced. The core of the proposed estimators is to de-correlate the coherent targets via the spatial smoothing technique and then formulate the covariance matrix into a third-order parallel factor (PARAFAC) tensor. After the PARAFAC decomposition of the tensor, the factor matrices can be obtained. Thereafter, the 2D direction finding can be accomplished via the normalized vector cross-product technique. Finally, the 2D polarization parameter can be estimated via the least squares method. Unlike the state-of-the-art PARAFAC estimator, the proposed estimators are suitable for arbitrary sensor geometries, and they are robust to coherent targets as well as sensor position errors. In addition, they have better estimation performance than the current matrix-based estimators. Moreover, they are computationally efficient than the current subspace methods, especially in the presence of a large-scale sensor array. In addition, the proposed estimators are analyzed in detail. Numerical experiments coincide with our theoretical findings.
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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) communication systems. In a semi-blind system, a transmission symbol matrix and two channel matrices are coupled within the received signals at the base station (BS). We decouple them by building two parallel factor (PARAFAC) tensor models. Leveraging PARAFAC tensor decomposition, we transform the joint channel and symbol estimation problem into least square (LS) problems, which can be solved by Alternating Least Squares (ALSs). Our proposed scheme allows duplex communication. Compared to recently proposed pilot-based methods and semi-blind receivers, our results demonstrate the superior performance of our proposed algorithm in estimation accuracy and speed.
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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 obtained, which corresponds to a longer vector-sensor ULA and includes all of the measurements of the difference co-array constructed from the original nested vector-sensor array. Analyses show that the proposed PARAFAC model can fully use all of the measurements of the difference co-array, instead of its partial measurements as the reported models do in literature. It implies that all of the measurements of the difference co-array can be fully exploited to do the 2-D direction of arrival (DOA) and polarization parameter estimation effectively by a PARAFAC decomposition method so that both the better estimation performance and slightly improved identifiability are achieved. Simulation results confirm the efficiency of the proposed model.
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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 (PARAFAC) decomposition, and the range and angle are calculated by employing least square fitting. As contrasted with the classic PARAFAC method, the proposed method can estimate more targets and provide better estimation performance, and requires less computational complexity. The availability and excellence of the proposed method are reflected by numerical simulations and complexity analysis.
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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 receivers compute singular value decomposition (SVD) for each new sample, implying into a high computational complexity, being, therefore, prohibitive for real-time applications. Therefore, in order to reduce the computational complexity of the parameter estimates, subspace tracking algorithms are essential. In this work, we propose a tensor-based subspace tracking framework to reduce the overall computational complexity of the highly accurate tensor-based time-delay estimation process.
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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 decomposition based on batch processing cannot deal with few newly acquired interferograms filtering directly. The filtering of dynamic InSAR tensor is the inevitable challenge when processing InSAR stack data, where dynamic InSAR tensor denotes the size of InSAR tensor increases continuously due to the acquisition of new interferograms. Therefore, based on the online CANDECAMP/PARAFAC (CP) decomposition, we propose an online filter to fuse data and process the dynamic InSAR tensor, named OLCP-InSAR, which performs well especially for the urban area. In this method, CP rank is utilized to measure the tensor sparsity, which can maintain the structural features of the InSAR tensor. Additionally, CP rank estimation is applied as an important step to improve the robustness of Online CP decomposition - InSAR(OLCP-InSAR). Importing CP rank and outlier’s position as prior information, the filter fuses the noisy interferograms and decomposes the InSAR tensor to acquire the low rank information, i.e., filtered result. Moreover, this method can not only operate on tensor model, but also efficiently filter the new acquired interferogram as matrix model with the assistance of chosen low rank information. Compared with other tensor-based filters, e.g., high order robust principal component analysis (HoRPCA) and Kronecker-basis-representation multi-pass SAR interferometry (KBR-InSAR), and the widespread traditional filters operating on a single interferometric pair, e.g., Goldstein, non-local synthetic aperture radar (NL-SAR), non-local InSAR (NL-InSAR), and InSAR nonlocal block-matching 3-D (InSAR-BM3D), the effectiveness and robustness of OLCP-InSAR are proved in simulated and real InSAR stack data. Especially, OLCP-InSAR can maintain the fringe details at the regular building top with high noise intensity and high outlier ratio.
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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 complex signals created by pressure and flow information. The continuous wavelet transform was applied to analyze the high-dimensional multi-channel signals to construct the 3D tensor, which makes use of the advantages of the parallel factor decomposition to extract feature information of the complex system. The method was validated by diagnosing the nonstationary failure modes under the faulty conditions with impeller blade damage, impeller perforation damage and impeller edge damage. The correspondence between different fault characteristics of a centrifugal pump in a time and frequency information matrix was established. The characteristic frequency ranges of the fault modes are effectively presented. The optimization method for a PARAFAC-BP neural network is proposed using a genetic algorithm (GA) to significantly improve the accuracy of the centrifugal pump fault diagnosis.
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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 this work, we propose BS-CP, a quick and accurate structure to dynamically update the posterior of latent factors when a new observation tensor is received. We first present the BS-CP1 algorithm, which is an efficient implementation using assumed density filtering (ADF). In addition, we propose BS-CP2 algorithm, using Gauss–Laguerre quadrature method to integrate the noise effect which shows better empirical result. We tested BS-CP1 and BS-CP2 on generic real recommendation system datasets, including Beijing-15k, Beijing-20k, MovieLens-1m and Fit Record. Compared with state-of-the-art methods, BS-CP1 achieve 31.8% and 33.3% RMSE improvement in the last two datasets, with a similar trend observed for BS-CP2. This evidence proves that our algorithm has better results on large datasets and is more suitable for real-world scenarios. Compared with most other comparison methods, our approach has demonstrated an improvement of over 10% and exhibits superior stability.
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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-way tensor. Tucker and CANDECOMP/PARAFAC decomposition techniques are employed to decompose the tensor into temporal, spectral, spatial, and segmental factors. Finally, TF features of both IED and non-IED segments from scalp recordings are projected onto the temporal components for classification. Main results. The model performance is obtained in two different approaches: within- and between-subject classification approaches. Our proposed method is compared with four other methods, namely a tensor-based spatial component analysis method, TF-based method, linear regression mapping model, and asymmetric–symmetric autoencoder mapping model followed by convolutional neural networks. Our proposed method outperforms all these methods in both within- and between-subject classification approaches by respectively achieving 84.2% and 72.6% accuracy values. Significance. The findings show that mapping sEEG to iEEG improves the performance of the scalp-based IED detection model. Furthermore, the tensor-based mapping model outperforms the autoencoder- and regression-based mapping models.
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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 decomposition (CP decomposition) is proposed, which is called PCA-TensorDecomp. First, we use PCA to reduce the dimension of HSI signals by obtaining the first K principal components and get the principal composite components. The low-rank part corresponding to the first K principal components is considered the characteristic signal. Then, low-rank CP decomposition is carried out, to denoise the first principal components and the remaining minor components, the secondary composite components, which contain a large amount of noise. Finally, the inverse PCA is then used to restore the HSIs denoised, such that the effect of comprehensive denoising is achieved. To test the effectiveness of the improved algorithm introduced in this article, we compare it with several methods on simulated and real hyperspectral data. The results of the analysis herein indicate that the proposed algorithm possesses a good denoising effect.
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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 angle and range are achieved by utilizing the phase characteristic of the steering matrices. Due to exploiting the multidimensional structure of the received data to further suppress the effect of noise, the proposed method performs better in angle and range estimation than the existing algorithms based on ESPRIT, simulation results can prove the proposed method’s effectiveness.
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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 tensor form. Afterwards, we process the covariance matrix of the tensor structure by CANDECOMP/PARAFAC decomposition (CPD) to separate the respective signal subspaces of TD and AOA estimates. Finally, we conduct a one-dimensional (1-D) spectrum search to locate the TD estimates and a two-dimensional (2-D) spectrum search to locate the AOA estimates. The simulated performance demonstrates that the proposed algorithm offers precise estimates at low signal-to-noise ratios in a multipath environment and outperforms traditional vector-based algorithms with respect to computational complexity.
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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 matrices. Our approach differs from most existing works that assume the number of channel paths is known and the proposed method is able to estimate channel parameters accurately without the prior knowledge of number of multipaths. The objective of this work is to estimate the tensor rank by a novel sparsity-promoting prior that is incorporated into a standard alternating least squares (ALS) function. We introduce a weighting parameter to control the impact of the previous estimate and the tensor rank estimation bias compensation in the regularized ALS. The channel information is then extracted from the estimated component matrices. Simulation results show that the proposed scheme outperforms the baseline l1 strategy in terms of accuracy and robustness. It also shows that this method significantly improves rank estimation success at the expense of slightly more iterations.
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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 introducing a simpler iterative optimization constraint and linear interpolation. Finally, we provide a strategy on the receiver design based on the feasibility conditions discussed in this paper, which can guarantee the uniqueness of the channel estimation problem. Simulation results show that the proposed algorithm can obtain a faster estimation speed and less iteration steps than the alternating least squares (ALS) algorithm, and the accuracy of the two algorithms is very close.
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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 of the signal. The dimensions of the three-dimensional matrix are reduced by parallel factor analysis, and the time characteristic matrix, frequency characteristic matrix, and spatial characteristic matrix are obtained with tensor decomposition. Through the comparative analysis of the simulation and the experiment, the time characteristic matrix and the frequency characteristic matrix can accurately characterize the normal and fault states of the mechanical equipment. On this basis, the authors established a probabilistic neural network classification model optimized by the improved particle swarm algorithm (IPSO). The parallel factor (PARAFAC) decomposition algorithm can extract features from the centrifugal pump experimental data for normal and multiple fault states, establish the mapping relationship of different fault features of the centrifugal pump in time, frequency, and space, and import the fault features into the model classification. The above measures can significantly improve the fault identification rate and accuracy for a centrifugal pump.
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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 symbols. By preserving the Khatri-Rao product, we used a recursive least squares solution to update the estimated subspace at each time instant, then the channel parameters can be estimated adaptively, and the algorithm achieves superior convergence performance. Simulation results validate the effectiveness of the proposed algorithm.
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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 imagined moving his hemiplegic hand with closed and open eyes to control an external robotic splint. In order to precisely identify the main profiles of neural activation affected by MI with eyes-open (MIEO) and eyes-closed (MIEC), a data-driven approach based on parallel factor analysis (PARAFAC) tensor decomposition was employed. Using the proposed framework, a set of narrow-band, subject-specific sensorimotor rhythms was identified; each of them had its own spatial and time signature. When MIEC trials were compared with MIEO trials, three key narrow-band rhythms whose peak frequencies centred at ∼8.0 Hz, ∼11.5 Hz, and ∼15.5 Hz, were identified with differently modulated oscillatory dynamics during movement preparation, initiation, and completion time frames. Furthermore, we observed that lower and higher sensorimotor oscillations represent different functional mechanisms within the MI paradigm, reinforcing the hypothesis that rhythmic activity in the human sensorimotor system is dissociated. Leveraging PARAFAC, this study achieves remarkable precision in estimating latent sensorimotor neural substrates, aiding the investigation of the specific functional mechanisms involved in the MI process.
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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 deficiency, and the algorithms of sparse NCP may not converge. In this paper, we proposed a novel model of sparse NCP with the proximal algorithm. The subproblems in the new model are strongly convex in the block coordinate descent (BCD) framework. Therefore, the new sparse NCP provides a full column rank condition and guarantees to converge to a stationary point. In addition, we proposed an inexact BCD scheme for sparse NCP, where each subproblem is updated multiple times to speed up the computation. In order to prove the effectiveness and efficiency of the sparse NCP with the proximal algorithm, we employed two optimization algorithms to solve the model, including inexact alternating nonnegative quadratic programming and inexact hierarchical alternating least squares. We evaluated the proposed sparse NCP methods by experiments on synthetic, real-world, small-scale, and large-scale tensor data. The experimental results demonstrate that our proposed algorithms can efficiently impose sparsity on factor matrices, extract meaningful sparse components, and outperform state-of-the-art methods.
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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 level over time periods with different railway stations, airports, and city categories. Furthermore, nonnegative tensor factorization (NTF) is applied to pattern recognition by introducing CP (CANDECOMP/PARAFAC) decomposition and the block coordinate descent (BCD) algorithm for the selected data set. Numerical experiments show that the designed method has good performance in terms of computation speed and solution quality. Recognition results indicate the significant pattern characteristics of rail–air transport for Beijing, Shanghai, and Guangzhou are extracted, which can provide some theoretical references for practical policymakers.
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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, and then, the HIV gene resistance of 213 patients was retrospectively analyzed based on the electronic medical records. 43 cases showed failure of ribonucleic acid drug resistance, the ART virological failure rate was 24.43% (43/213), and one case was not reported. There was 1 case of RNA hemolysis that could not be detected. There were 50 resistant cases of nonnucleotide reverse transcriptase inhibitors (NNRTI), accounting for 29.94% (50/167), and there were 17 resistant cases of nucleotide reverse transcriptase inhibitors (NRTI), accounting for 10.18% (17/167) of all mutation cases. Among the HIV-1 strains, 19 cases failed the detection of drug resistance sites in the integrase region, and mutations in the integrase region were significantly more than those in the protease region. There were 12 types of HIV-1 strains with drug-resistant mutations. The fusion technical scheme constructed in this study showed excellent performance in medical information retrieval. In this study, the characteristics of HIV-1 of AIDS patients were analyzed from different directions, and effective treatment was performed for patients, so as to provide reference for clinical diagnosis of AIDS patients.
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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 receivers for MIMO one-way two-hop relay systems, allowing the joint estimation of transmitted symbols and individual communication channels with only a few pilot symbols. After a reminder of some tensor prerequisites, we present an overview of tensor models, with a detailed, unified, and original description of two classes of tensor decomposition frequently used in the design of relay systems, namely nested CPD/PARAFAC and nested Tucker decomposition (TD). Some new variants of nested models are introduced. Uniqueness and identifiability conditions, depending on the algorithm used to estimate the parameters of these models, are established. Two families of algorithms are presented: iterative algorithms based on alternating least squares (ALS) and closed-form solutions using Khatri–Rao and Kronecker factorization methods, which consist of SVD-based rank-one matrix or tensor approximations. In a second part of the paper, the overview of cooperative communication systems is completed before presenting several two-hop relay systems using different codings and configurations in terms of relaying protocol (AF/DF) and channel modeling. The aim of this presentation is firstly to show how these choices lead to different nested tensor models for the signals received at destination. Then, by capitalizing on these models and their correspondence with the generic models studied in the first part, we derive semi-blind receivers to jointly estimate the transmitted symbols and the individual communication channels for each relay system considered. In a third part, extensive Monte Carlo simulation results are presented to compare the performance of relay systems and associated semi-blind receivers in terms of the symbol error rate (SER) and channel estimate normalized mean-square error (NMSE). Their computation time is also compared. Finally, some perspectives are drawn for future research work.
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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) decomposition technique can be utilized to calculate transmitter and receiver direction matrices. Taking advantage of receiver direction matrix, the angle estimation can be obtained. The range estimation can be estimated by transmitter direction matrix and angle estimation. To eliminate the error accumulation effect of array gain-phase error, the gain error and phase error are obtained separately. In this algorithm, the impact of gain-phase error on parameter estimation is removed and so is the error accumulation effect. Therefore, the proposed algorithm can provide excellent performance of angle-range and gain-phase error estimation. Numerical experiments prove the validity and advantages of the proposed method.
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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.
Full textAbstract:
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 associated with the samples, which are characterized by different time lags, are calculated. These matrices are represented in tensor form, and the factor matrices are extracted through CANDECOMP/PARAFAC (CP) decomposition. By these factor matrices, the carrier frequencies and the power spectra of the far-field signals of interest are estimated. Numerical simulations are conducted to evaluate the performance of the proposed method, and the results reveal the feasibility and effectiveness of the approach, demonstrating its potential for accurate and efficient wideband spectrum sensing in complex multi-path propagation environments.
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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.
Full textAbstract:
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%, and 52% missing at random. By correcting any inherent biases, the results of decomposition problems may be enhanced. As the statistical analysis tool, MAPE is used. The proposed approach is evaluated on the Wiki dataset and the traffic dataset, against state-of-the-art techniques including BATF, BGCP, BCPF, and modified PARAFAC, all of which use a Bayesian Gaussian tensor factorization. Using this approach, the MAPE index is decreased for data which avails privacy safeguards than its corresponding original forms.