A Novel Tensor Decomposition-Based Efficient Detector for Low-Altitude Aerial Objects With Knowledge Distillation Scheme

Unmanned aerial vehicles(UAVs) have gained significant attention in practical applications, especially the low-altitude aerial(LAA) object detection imposes stringent requirements on recognition accuracy and computational resources. In this paper, the LAA images-oriented tensor decomposition and knowledge distillation-based network(TDKD-Net) is proposed,where the TT-format TD(tensor decomposition) and equalweighted response-based KD(knowledge distillation) methods are designed to minimize redundant parameters while ensuring comparable performance. Moreover, some robust network structures are developed, including the small object detection head and the dual-domain attention mechanism, which enable the model to leverage the learned knowledge from small-scale targets and selectively focus on salient features. Considering the imbalance of bounding box regression samples and the inaccuracy of regression geometric factors, the focal and efficient IoU(intersection of union) loss with optimal transport assignment(F-EIoU-OTA)mechanism is proposed to improve the detection accuracy. The proposed TDKD-Net is comprehensively evaluated through extensive experiments, and the results have demonstrated the effectiveness and superiority of the developed methods in comparison to other advanced detection algorithms, which also present high generalization and strong robustness. As a resource-efficient precise network, the complex detection of small and occluded LAA objects is also well addressed by TDKD-Net, which provides useful insights on handling imbalanced issues and realizing domain adaptation.

Multi-Aspect Incremental Tensor Decomposition Based on Distributed In-Memory Big Data Systems

Purpose:We propose In Par Ten2,a multi-aspect parallel factor analysis three-dimensional tensor decomposition algorithm based on the Apache Spark framework.The proposed method reduces re-decomposition cost and can handle large tensors.Design/methodology/approach:Considering that tensor addition increases the size of a given tensor along all axes,the proposed method decomposes incoming tensors using existing decomposition results without generating sub-tensors.Additionally,In Par Ten2 avoids the calculation of Khari–Rao products and minimizes shuffling by using the Apache Spark platform.Findings:The performance of In Par Ten2 is evaluated by comparing its execution time and accuracy with those of existing distributed tensor decomposition methods on various datasets.The results confirm that In Par Ten2 can process large tensors and reduce the re-calculation cost of tensor decomposition.Consequently,the proposed method is faster than existing tensor decomposition algorithms and can significantly reduce re-decomposition cost.Research limitations:There are several Hadoop-based distributed tensor decomposition algorithms as well as MATLAB-based decomposition methods.However,the former require longer iteration time,and therefore their execution time cannot be compared with that of Spark-based algorithms,whereas the latter run on a single machine,thus limiting their ability to handle large data.Practical implications:The proposed algorithm can reduce re-decomposition cost when tensors are added to a given tensor by decomposing them based on existing decomposition results without re-decomposing the entire tensor.Originality/value:The proposed method can handle large tensors and is fast within the limited-memory framework of Apache Spark.Moreover,In Par Ten2 can handle static as well as incremental tensor decomposition.

A multispectral image compression and encryption algorithm based on tensor decomposition and chaos

A multi spectral image compression and encryption algorithm that combines Karhunen-Loeve(KL) transform,tensor decomposition and chaos is proposed for solving the security problem of multi-spectral image compression and transmission.Firstly,in order to eliminate residual spatial redundancy and most of the spectral redundancy,the image is performed by KL transform.Secondly,to further eliminate spatial redundancy and reduce block effects in the compression process,two-dimensional discrete 9/7 wavelet transform is performed,and then Arnold transform and encryption processing on the transformed coefficients are performed.Subsequently,the tensor is decomposed to keep its intrinsic structure intact and eliminate residual space redundancy.Finally,differential pulse filters are used to encode the coefficients,and Tent mapping is used to implement confusion diffusion encryption on the code stream.The experimental results show that the method has high signal-to-noise ratio,fast calculation speed,and large key space,and it is sensitive to keys and plaintexts with a positive effect in spectrum assurance at the same time.

Key Exchange Protocol Based on Tensor Decomposition Problem

The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.

Efficient tensor decomposition method for noncircular source in colocated coprime MIMO radar

An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing the transmitter and receiver into two sparse subarrays,noncircular property of source can be used to construct new extended received signal model for two sparse subarrays.The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero.To further exploit the multidimensional structure of the noncircular received model,we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor,respectively.Thus,the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained.Then,the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship.Specifically,the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property.Furthermore,a closed-form expression for the deterministic CRB under the NC sources scenario is also derived.Simulation results verify the superiority of the proposed estimator.

Recommender Systems Based on Tensor Decomposition

Recommender system is an effective tool to solve the problems of information overload.The traditional recommender systems,especially the collaborative filtering ones,only consider the two factors of users and items.While social networks contain abundant social information,such as tags,places and times.Researches show that the social information has a great impact on recommendation results.Tags not only describe the characteristics of items,but also reflect the interests and characteristics of users.Since the traditional recommender systems cannot parse multi-dimensional information,in this paper,a tensor decomposition model based on tag regularization is proposed which incorporates social information to benefit recommender systems.The original Singular Value Decomposition(SVD)model is optimized by mining the co-occurrence and mutual exclusion of tags,and their features are constrained by the relationship between tags.Experiments on real dataset show that the proposed algorithm achieves superior performance to existing algorithms.

TdBrnn:An Approach to Learning Users’Intention to Legal Consultation with Normalized Tensor Decomposition and Bi-LSTM

With the development of Internet technology and the enhancement of people’s concept of the rule of law,online legal consultation has become an important means for the general public to conduct legal consultation.However,different people have different language expressions and legal professional backgrounds.This phenomenon may lead to the phenomenon of different descriptions of the same legal consultation.How to accurately understand the true intentions behind different users’legal consulting statements is an important issue that needs to be solved urgently in the field of legal consulting services.Traditional intent understanding algorithms rely heavily on the lexical and semantic information between the original data,and are not scalable,and often require taxing manual annotation work.This article proposes a new approach TdBrnn which is based on the normalized tensor decomposition method and Bi-LSTM to learn users’intention to legal consulting.First,we present the users’legal consulting statements as a tensor.And then we use the normalized tensor decomposition layer proposed by this article to extract the tensor elements and structural information of the original tensor which can best represent users’intention of legal consultation,namely the core tensor.The core tensor relies less on the lexical and semantic information of the original users’legal consulting statements data,it reduces the dimension of the original tensor,and greatly reduces the computational complexity of the subsequent Bi-LSTM algorithm.Furthermore,we use a large number of core tensors obtained by the tensor decomposition layer with users’legal consulting statements tensors as inputs to continuously train Bi-LSTM,and finally derive the users’legal consultation intention classification model which can comprehensively understand the user’s legal consultation intention.Experiments show that our method has faster convergence speed and higher accuracy than traditional recurrent neural networks.

Detection of T-wave Alternans in ECG Signals Using FRFT and Tensor Decomposition

T-wave alternans(TWA)refers to the periodic beat-to-beat variation in the amplitude of T-wave in the electrocardiogram(ECG)signal in an ABAB-pattern.TWA has been proven to be a very important indicator of malignant arrhythmia risk stratification.A new method to detect TWA by combining fractional Fourier transform(FRFT)and tensor decomposition is proposed.First,the T-wave vector is extracted from the ECG of each heartbeat,and its FRFT amplitudes at multiple orders are arranged to form a T-wave matrix.Then,a third-order tensor is composed of T-wave matrices of several consecutive heart beats.After tensor decomposition,projection matrices are obtained in three dimensions.The complexity of the projection matrix is measured by Shannon entropy to obtain feature vector to detect the presence of TWA.Results show that the sensitivity,specificity,and accuracy of the algorithm on the MIT-BIH database are 91.16%,94.25%,and 92.68%,respectively.This method effectively utilizes the fractional domain information of ECG,and shows the promising potential of the FRFT in ECG signal processing.

Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion

Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.

An Efficient Randomized Fixed-Precision Algorithm for Tensor Singular Value Decomposition

The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition.This paper proposes a new randomized fixed-precision algorithm which for a given third-order tensor and a prescribed approximation error bound,it automatically finds the tubal rank and corresponding low tubal rank approximation.The algorithm is based on the random projection technique and equipped with the power iteration method for achieving better accuracy.We conduct simulations on synthetic and real-world datasets to show the efficiency and performance of the proposed algorithm.

Schur Forms and Normal-Nilpotent Decompositions

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.

A Novel Multichannel Audio Signal Compression Method Based on Tensor Representation and Decomposition

Multichannel audio signal is more difficult to be compressed than mono and stereo ones.A novel multichannel audio signal compression method based on tensor representation and decomposition is proposed in this paper.The multichannel audio is represented with 3-order tensor space and is decomposed into core tensor with three factor matrices in the way of channel,time and frequency.Only the truncated core tensor is transmitted which will be multiplied by the pre-trained factor matrices to reconstruct the original tensor space.Objective and subjective experiments have been done to show a very noticeable compression capability with an acceptable output quality.The novelty of the proposed compression method is that it enables both high compression capability and backward compatibility with limited signal distortion to the hearing.

An inexact alternating proximal gradient algorithm for nonnegative CP tensor decomposition

Nonnegative tensor decomposition has become increasingly important for multiway data analysis in recent years. The alternating proximal gradient(APG) is a popular optimization method for nonnegative tensor decomposition in the block coordinate descent framework. In this study, we propose an inexact version of the APG algorithm for nonnegative CANDECOMP/PARAFAC decomposition, wherein each factor matrix is updated by only finite inner iterations. We also propose a parameter warm-start method that can avoid the frequent parameter resetting of conventional APG methods and improve convergence performance.By experimental tests, we find that when the number of inner iterations is limited to around 10 to 20, the convergence speed is accelerated significantly without losing its low relative error. We evaluate our method on both synthetic and real-world tensors.The results demonstrate that the proposed inexact APG algorithm exhibits outstanding performance on both convergence speed and computational precision compared with existing popular algorithms.

Link Prediction based on Tensor Decomposition for the Knowledge Graph of COVID-19 Antiviral Drug

Due to the large-scale spread of COVID-19,which has a significant impact on human health and social economy,developing effective antiviral drugs for COVID-19 is vital to saving human lives.Various biomedical associations,e.g.,drug-virus and viral protein-host protein interactions,can be used for building biomedical knowledge graphs.Based on these sources,large-scale knowledge reasoning algorithms can be used to predict new links between antiviral drugs and viruses.To utilize the various heterogeneous biomedical associations,we proposed a fusion strategy to integrate the results of two tensor decomposition-based models(i.e.,CP-N3 and Compl Ex-N3).Sufficient experiments indicated that our method obtained high performance(MRR=0.2328).Compared with CP-N3,the mean reciprocal rank(MRR)is increased by 3.3%and compared with Compl Ex-N3,the MRR is increased by 3.5%.Meanwhile,we explored the relationship between the performance and relationship types,which indicated that there is a negative correlation(PCC=0.446,P-value=2.26 e-194)between the performance of triples predicted by our method and edge betweenness.

Verification of neutron-induced fission product yields evaluated by a tensor decompsition model in transport-burnup simulations

Neutron-induced fission is an important research object in basic science.Moreover,its product yield data are an indispensable nuclear data basis in nuclear engineering and technology.The fission yield tensor decomposition(FYTD)model has been developed and used to evaluate the independent fission product yield.In general,fission yield data are verified by the direct comparison of experimental and evaluated data.However,such direct comparison cannot reflect the impact of the evaluated data on application scenarios,such as reactor transport-burnup simulation.Therefore,this study applies the evaluated fission yield data in transport-burnup simulation to verify their accuracy and possibility of application.Herein,the evaluated yield data of235U and239Pu are applied in the transport-burnup simulation of a pressurized water reactor(PWR)and sodium-cooled fast reactor(SFR)for verification.During the reactor operation stage,the errors in pin-cell reactivity caused by the evaluated fission yield do not exceed 500 and 200 pcm for the PWR and SFR,respectively.The errors in decay heat and135Xe and149Sm concentrations during the short-term shutdown of the PWR are all less than 1%;the errors in decay heat and activity of the spent fuel of the PWR and SFR during the temporary storage stage are all less than 2%.For the PWR,the errors in important nuclide concentrations in spent fuel,such as90Sr,137Cs,85Kr,and99Tc,are all less than 6%,and a larger error of 37%is observed on129I.For the SFR,the concentration errors of ten important nuclides in spent fuel are all less than 16%.A comparison of various aspects reveals that the transport-burnup simulation results using the FYTD model evaluation have little difference compared with the reference results using ENDF/B-Ⅷ.0 data.This proves that the evaluation of the FYTD model may have application value in reactor physical analysis.

A TRUST-REGION-BASED ALTERNATING LEAST-SQUARES ALGORITHM FOR TENSOR DECOMPOSITIONS

Tensor canonical decomposition （shorted as CANDECOMP/PARAFAC or CP） decomposes a tensor as a sum of rank-one tensors, which finds numerous applications in signal processing, hypergraph analysis, data analysis, etc. Alternating least-squares （ALS） is one of the most popular numerical algorithms for solving it. While there have been lots of efforts for enhancing its efficiency, in general its convergence can not been guaranteed. In this paper, we cooperate the ALS and the trust-region technique from optimization field to generate a trust-region-based alternating least-squares （TRALS） method for CP. Under mild assumptions, we prove that the whole iterative sequence generated by TRALS converges to a stationary point of CP. This thus provides a reasonable way to alleviate the swamps, the notorious phenomena of ALS that slow down the speed of the algorithm. Moreover, the trust region itself, in contrast to the regularization alternating least-squares （RALS） method, provides a self-adaptive way in choosing the parameter, which is essential for the efficiency of the algorithm. Our theoretical result is thus stronger than that of RALS in [26], which only proved the cluster point of the iterative sequence generated by RALS is a stationary point. In order to accelerate the new algorithm, we adopt an extrapolation scheme. We apply our algorithm to the amino acid fluorescence data decomposition from chemometrics, BCM decomposition and rank-（Lr, Lr, 1） decomposition arising from signal processing, and compare it with ALS and RALS. The numerical results show that TRALS is superior to ALS and RALS, both from the number of iterations and CPU time perspectives.

Popularity Prediction of Social Media Post Using Tensor Factorization

The traditional method of doing business has been disrupted by socialmedia. In order to develop the enterprise, it is essential to forecast the level ofinteraction that a new post would receive from social media users. It is possiblefor the user’s interest in any one social media post to be impacted by external factors or to dwindle as a result of changes in his behaviour. The popularity detectionstrategies that are user-based or population-based are unable to keep up with theseshifts, which leads to inaccurate forecasts. This work makes a prediction abouthow popular the post will be and addresses any anomalies caused by factors outside of the study. A novel improved PARAFAC (A-PARAFAC) method that istensor factorization-based has been presented in order to cope with the user criteria that will be used in the future to rate any project. We consolidated the information on the historically popular content, and we accelerated the computation bychoosing the top contents that were most like each other. The tensor is factorisedwith the application of the Adam optimization. It has been modified such that thebias is now included in the gradient function of A-PARAFAC, and the value ofthe bias is updated after each iteration. The prediction accuracy is improved by32.25% with this strategy compared to other state of the art methods.

Tensor Decomposition and High-Performance Computing for Solving High-Dimensional Stochastic Control System Numerically

The paper presents a numerical method for solving a class of high-dimensional stochastic control systems based on tensor decomposition and parallel computing.The HJB solution provides a globally optimal controller to the associated dynamical system.Variable substitution is used to simplify the nonlinear HJB equation.The curse of dimensionality is avoided by representing the HJB equation using separated representation.Alternating least squares(ALS)is used to reduced the separation rank.The experiment is conducted and the numerical solution is obtained.A high-performance algorithm is designed to reduce the separation rank in the parallel environment,solving the high-dimensional HJB equation with high efficiency.

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work.In practical applications,such processes are used to model velocity fields,temperature distributions,response of vibrating systems,to name a few.Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations,for instance,in a computational mechanics problem.For a single-parameter process such as spatial or temporal process,the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Lo`eve(KL)decomposition.However,for multiparameter processes such as a spatio-temporal process,the covariance function itself can be defined in multiple ways.Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants.Then the spatial covariance matrix at different time instants are considered to define the covariance of the process.This set of square,symmetric,positive semi-definite matrices is then represented as a thirdorder tensor.A suitable decomposition of this tensor can identify the dominant components of the process,and these components are then used to define a closed-form representation of the process.The procedure is analogous to the KL decomposition for a single-parameter process,however,the decompositions and interpretations vary significantly.The tensor decompositions are successfully applied on(i)a heat conduction problem,(ii)a vibration problem,and(iii)a covariance function taken from the literature that was fitted to model a measured wind velocity data.It is observed that the proposed representation provides an efficient approximation to some processes.Furthermore,a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL,both in terms of computer memory and execution time.

Gradient Descent for Symmetric Tensor Decomposition

Symmetric tensor decomposition is of great importance in applications.Several studies have employed a greedy approach,where the main idea is to first find a best rank-one approximation of a given tensor,and then repeat the process to the residual tensor by subtracting the rank-one component.In this paper,we focus on finding a best rank-one approximation of a given orthogonally order-3 symmetric tensor.We give a geometric landscape analysis of a nonconvex optimization for the best rank-one approximation of orthogonally symmetric tensors.We show that any local minimizer must be a factor in this orthogonally symmetric tensor decomposition,and any other critical points are linear combinations of the factors.Then,we propose a gradient descent algorithm with a carefully designed initialization to solve this nonconvex optimization problem,and we prove that the algorithm converges to the global minimum with high probability for orthogonal decomposable tensors.This result,combined with the landscape analysis,reveals that the greedy algorithm will get the tensor CP low-rank decomposition.Numerical results are provided to verify our theoretical results.