Complete Algorithm Research Articles

GNN-RM: A trajectory completion algorithm based on graph neural networks and regeneration modules

Data about vehicle trajectories assumes a crucial role in applications such as intelligent connected vehicles. However, missing values resulting from sensors and other factors frequently affect real trajectory data. Currently, it is challenging to utilize trajectory completion methods to generate accurate real-time results at an affordable computing cost. This paper proposes GNN-RM, a trajectory completion algorithm based on graph neural networks and regeneration modules, encompassing feature extraction, subgraph construction, spatial interaction graph, and trajectory regeneration modules. The feature extraction algorithm extracts influential data as feature vectors based on certain conditions and organizes these feature vectors into different subgraphs according to categories. The spatial interaction graph constructed through graph neural networks extracts spatial interaction features between vehicles and the environment, while the regeneration modules constructed by multi-head attention mechanisms extract temporal features of vehicles, thereby completing the missing trajectories. The experimental results demonstrate that GNN-RM can achieve higher trajectory completion accuracy with fewer input parameters than multiple baseline models.

Tensor Completion Algorithm and Its Applications to Wireless Edge Caching and Hyper- Spectral Imaging

Tensor Completion Algorithm and Its Applications to Wireless Edge Caching and Hyper- Spectral Imaging

Image completion algorithm of anthurium spathes based on multi-scale feature learning.

Machine vision has been used to grade the potted anthurium plant in large-scale production recently. Images are taken to measure the number and size of anthurium spathes. However, due to the limitation of the shooting angle, the occlusion problem reduces the accuracy of measurement. It is necessary to segment the overlapping spathes and repair the incomplete ones. The traditional image completion model has good performance on missing small areas, but it is not satisfactory for missing large areas. In this article, a multi-scale fusion Recurrent Feature Reasoning (RFR) network was proposed to repair the spathe images. Unlike the traditional RFR, a multi-layer component was used in the feature reasoning module. This network can combine multi-scale features to complete the learning task and obtain more details of the spathe, which makes the network more advantageous in image completion when missing large areas of spathes. In this study, a comparison experiment between this network and the widely used image completion network was performed, and the results showed that this network performed well in all types of image completion, especially with large-area incomplete images.

TAMNR: a network embedding learning algorithm using text attention mechanism.

Because many existing algorithms are mainly trained based on the structural features of the networks, the results are more inclined to the structural commonality of the networks. These algorithms ignore the rich external information and node attributes (such as node text content, community and labels, etc.) that have important implications for network data analysis tasks. Existing network embedding algorithms considering text features usually regard the co-occurrence words in the node's text, or use an induced matrix completion algorithm to factorize the text feature matrix or the network structure feature matrix. Although this kind of algorithm can greatly improve the network embedding performance, they ignore the contribution rate of different co-occurrence words in the node's text. This article proposes a network embedding learning algorithm combining network structure and co-occurrence word features, also incorporating an attention mechanism to model the weight information of the co-occurrence words in the model. This mechanism filters out unimportant words and focuses on important words for learning and training tasks, fully considering the impact of the different co-occurrence words to the model. The proposed network representation algorithm is tested on three open datasets, and the experimental results demonstrate its strong advantages in node classification, visualization analysis, and case analysis tasks.

High-precision reconstruction method based on MTS-GAN for electromagnetic environment data in SAGIoT

Equipment failures and communication interruptions of satellites, aircraft and ground devices lead to data loss in Space-Air-Ground Integrated Internet of Things (SAGIoT). The incomplete data affect the accuracy of data modeling, decision-making and spectrum prediction. Reconstructing the incomplete data of electromagnetic environment is a significant task in the SAGIoT. Most spectral data completion algorithms have the problem of limited accuracy and slow iterative optimization. In light of these challenges, a novel high-precision reconstruction method for electromagnetic environment data based on multi-component time series generation adversarial network (MTS-GAN) is proposed in this paper. MTS-GAN transforms the reconstruction method of electromagnetic environment data into the data generation problem of multiple time series. It extracts the time–frequency joint features and the overall distribution of electromagnetic environment data. To improve the reconstruction precision, MTS-GAN simulates the time irregularity of incomplete time series by applying a gate recursive element to adapt to the attenuation effect of discontinuous time series observations. Experimental results show that the proposed MTS-GAN provides high completion accuracy and achieves better results than competitive data completion algorithms.

Graph-Tensor Neural Networks for Network Traffic Data Imputation

It is important to estimate the global network traffic data from partial traffic measurements for many network management tasks, including status monitoring and fault detection. However, existing estimation approaches cannot well handle the topological correlations hidden in network traffic and suffer from limited imputation performance. This paper proposes a deep learning approach for network traffic imputation, which well exploits the topological structure of network traffic. We first model the network traffic as a novel graph-tensor and derive a theoretical recovery guarantee. Then we develop an iterative graph-tensor completion algorithm and propose a graph neural network for network traffic imputation by unfolding the iterative algorithm. The proposed graph neural network well captures the topological correlations of network traffic and achieves accurate imputation. Extensive experiments on real-world datasets show that the proposed graph neural network achieves about one-half lower relative square error while at least ten times faster imputation speed than the existing methods.

Structural-Missing Tensor Completion for Robust DOA Estimation with Sensor Failure

Array sensor failure poses a serious challenge to robust direction-of-arrival (DOA) estimation in complicated environments. Although existing matrix completion methods can successfully recover the damaged signals of an impaired sensor array, they cannot preserve the multi-way signal characteristics as the dimension of arrays expands. In this paper, we propose a structural-missing tensor completion algorithm for robust DOA estimation with uniform rectangular array (URA), which exhibits a high robustness to non-ideal sensor failure conditions. Specifically, the signals received at the impaired URA are represented as a three-dimensional incomplete tensor, which contains whole fibers or slices of missing elements. Due to this structural-missing pattern, the conventional low-rank tensor completion becomes ineffective. To resolve this issue, a spatio-temporal dimension augmentation method is developed to transform the structural-missing tensor signal into a six-dimensional Hankel tensor with dispersed missing elements. The augmented Hankel tensor can then be completed with a low-rank regularization by solving a Hankel tensor nuclear norm minimization problem. As such, the inverse Hankelization on the completed Hankel tensor recovers the tensor signal of an unimpaired URA. Accordingly, a completed covariance tensor can be derived and decomposed for robust DOA estimation. Simulation results verify the effectiveness of the proposed algorithm.

An image inpainting algorithm using exemplar matching and low-rank sparse prior

Image inpainting is a challenging problem with a wide range of applications such as object removal and old photo restoration. The methods based on low-rank sparse prior have been used for regular or nearly regular texture inpainting. However, since such inpainting results do not synthesize the original pixels, they are usually not sharp especially when the area to be recovered is large. One remedy is to use an exemplar-based method. However, it often produces false matches and cannot obtain globally consistent inpainting results. In this paper, we give a new model to promote low rankness and sparsity and solve this model with a recently proposed Riemannian optimization algorithm. Furthermore, we propose a novel two-stage algorithm by integrating the low-rank sparse model with an exemplar-based method. Numerical experiments demonstrate that the proposed low-rank sparsity-based method and the two-stage algorithm achieve encouraging results compared to state-of-the-art image completion algorithms.

Hybrid deconvolution separation methods based on matrix completion for multi-motion modes sound sources

Beamforming techniques cannot effectively separate the mixed field of stationary and rotating sound sources. The issue becomes even more challenging when strong out-of-focus sources, e.g., stationary sources with rotating beamforming, are present, leading to a smearing effect and false localization results. The current algorithms for separating multiple moving sound sources have problems such as weak separation ability and complex computation. To more effectively address this challenge, two frequency domain hybrid deconvolution methods based on the virtual rotating array (VRA) and a matrix completion algorithm are proposed in this work. A matrix completion algorithm is used to establish the completed cross point spread function (C-PSF) matrix. Afterward, a linear equation system is constructed to separate the sound sources of different motion modes. Finally, the sound source separation localization problem is solved by Non-Negative Least-Squares (NNLS) and sparsity constraints deconvolution, respectively. The simulation and experimental results demonstrate that the proposed method can accurately locate and separate stationary and moving sound sources.

Joint tensor completion anchor selection and coordinate transformation for high precision cooperative positioning in device-to-device systems

The synergistic amalgamation of device-to-device (D2D) communication between mobile terminals (MT) and ultra-dense networks in 5G systems enables cooperative positioning. In this paper, we propose a joint tensor completion, anchor selection, and coordinate transformation (JTCASCT) for high precision cooperative positioning in D2D systems. The positioning is achieved by mitigating the challenging issue of recovering the missing values from the corrupted distance between nodes and determining the global positions of unknown stationary nodes. Initially, a hankelized distance tensor structure called Euclidean distance tensor (EDT) is constructed from incomplete EDM. The missing values are recovered as tensor completion by exploiting its latent low rank structure. The optimization problem is solved using simple low rank tensor completion (SiLRTC) and high accuracy low rank tensor completion (HaLRTC) algorithms. The relative position of nodes is determined after applying multidimensionality scaling (MDS). To reduce the data dimension for coordinate transformation and to select the optimal combination of anchor nodes, we propose a low complex Kruskal–Wallis (KW) test. Finally, the global position of unknown nodes is computed using Helmert transformation (HT). Numerical evaluations demonstrate that the cooperative positioning accuracy is significantly improved with the proposed JTCASCT approach compared to the state-of-the-art techniques.

Squarefree normal representation of zeros of zero-dimensional polynomial systems

For any zero-dimensional polynomial ideal I and any nonzero polynomial F, this paper shows that the union of the multi-set of zeros of the ideal sum I+〈F〉 and that of the ideal quotient I:〈F〉 is equal to the multi-set of zeros of I, where zeros are counted with multiplicities. Based on this zero relation and the computation of Gröbner bases, a complete multiplicity-preserved algorithm is proposed to decompose any zero-dimensional polynomial set into finitely many squarefree normal triangular sets, resulting in a squarefree normal representation for the zeros of the polynomial set. In the representation the multiplicities of the zeros of the triangular sets can be read out directly. Examples and experiments are presented to illustrate the algorithm and its performance.

Face Image Recognition Algorithm Based on Label Complementation

<p>In face image recognition, labels play a fairly important role in recognition and classification, and rich and perfect labels can greatly improve the accuracy rate. However, it is almost impossible for the labels in the image to be recognized to describe the image completely and accurately. At the same time, the data obtained when feature extraction is performed on an image inevitably extracts a large amount of redundant and useless information at the same time, which affects the generalization performance of the model. Accordingly, we propose a face image recognition algorithm based on label completion in multi label learning. First, the SVD algorithm is used to remove redundant and useless information from the features of the original data by dimensionality reduction operation to obtain simplified sample attribute information, and the label completion algorithm is used to supplement the labels of the images using the extracted feature information. Finally the obtained label data as complete as possible is put into the extreme learning machine to construct the face recognition model and give the prediction results of the images. Experiments on the ORL dataset demonstrate that the algorithm can achieve good recognition results.</p> <p> </p>

On Ext1 for Drinfeld modules

Let A=Fq[t] be the polynomial ring over a finite field Fq and let ϕ and ψ be A-Drinfeld modules. In this paper we consider the group Ext1(ϕ,ψ) with the Baer addition. We show that if rankϕ>rankψ then Ext1(ϕ,ψ) has the structure of a t-module. We give complete algorithm describing this structure. We generalize this to the cases: Ext1(Φ,ψ) where Φ is a t-module and ψ is a Drinfeld module and Ext1(Φ,C⊗e) where Φ is a t-module and C⊗e is the e-th tensor product of Carlitz module. We also establish duality between Ext groups for t-modules and the corresponding adjoint tσ-modules. Finally, we prove the existence of “Hom−Ext” six-term exact sequences for t-modules and dual t-motives. As the category of t-modules is only additive (not abelian) this result is nontrivial.

Comparison of machine learning models for MRI image-based brain tumor classification and segmentation

Brain tumors have a high-risk factor and are extremely harmful to the human body. With the development of science and technology in recent years, automatic segmentation has become popular in medical diagnosis because it provides higher accuracy than traditional hand segmentation. At present, more and more people start to study and improve it. Due to the non-invasive nature of MRI, MR images are often used to segment and classify brain tumors. However, limited by the inaccuracy and inoperability of manual segmentation, it is very necessary to have a complete and comprehensive automatic brain tumor segmentation and classification algorithm technology. This article discusses the benefits, drawbacks, and areas of application of several traditional algorithms as well as more modern, improved, and more advanced algorithms. Segmentation methods and classification methods can be used to classify these techniques. Convolutional neural networks (CNN), Support vector machines, and Transformers are examples of classification methods. Random forests, decision trees, and improved U-Net algorithms are examples of segmentation methods. To discuss the capability of classification and segmentation, there are three sections in the area used for segmenting brain tumors with three types, including Tumor Core, Enhance Tumor, and Whole Tumor, which could be abbreviated as TC, ET, and WT. Through the comparative analysis of these methods, useful insights for future research are provided.

An Ensemble Approach for Prioritizing Antivirals Against COVID-19 via Heterogeneous Network Inference-Based Inductive Matrix Completion

The global spread of COVID-19 caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) originated in Wuhan in December 2019, created a massive health crisis, and disrupted the world economy. Much research has been conducted to discover drugs, develop vaccines, and find repurposable drugs against the disease. Computational drug repurposing, the process of determining new uses for approved drugs through computational techniques, becomes an effective solution to fight the COVID-19 pandemic. This study aims to investigate and prioritize potential drugs against SARS-CoV-2 through an integrated network-based approach. We propose an ensemble approach based on network inference and inductive matrix completion (NIMCVDA) for virus–drug association prediction to identify antivirals against COVID-19. We constructed a heterogeneous drug–virus network using intra-similarities of virus genomic sequences and drug chemical structures and existing associations between viruses and drugs. A network inference method is used to infer missing drug–virus edges. Based on this, existing drug–virus association matrix is reconstructed. Finally, more accurate association scores between drugs and viruses are computed using the inductive matrix completion algorithm. The proposed method achieved an AUC of 0.9020 on five-fold cross-validation and 0.8786 on leave-one-out cross-validation. We compared the performance of the model with related approaches. In addition, we carried out case studies on the top-predicted drugs and implemented our model with other datasets to verify prediction performance. Our work prioritized repurposable drugs to battle with COVID-19 epidemic. The cross-validation results and case studies illustrate that the top-predicted drugs are strong candidates for further biological tests.

Deep learning-based identification of spine growth potential on EOS radiographs.

To develop an automatic computer-based method that can help clinicians in assessing spine growth potential based on EOS radiographs. We developed a deep learning-based (DL) algorithm that can mimic the human judgment process to automatically determine spine growth potential and the Risser sign based on full-length spine EOS radiographs. A total of 3383 EOS cases were collected and used for the training and test of the algorithm. Subsequently, the completed DL algorithm underwent clinical validation on an additional 440 cases and was compared to the evaluations of four clinicians. Regarding the Risser sign, the weighted kappa value of our DL algorithm was 0.933, while that of the four clinicians ranged from 0.909 to 0.930. In the assessment of spine growth potential, the kappa value of our DL algorithm was 0.944, while the kappa values of the four clinicians were 0.916, 0.934, 0.911, and 0.920, respectively. Furthermore, our DL algorithm obtained a slightly higher accuracy (0.973) and Youden index (0.952) compared to the best values achieved by the four clinicians. In addition, the speed of our DL algorithm was 15.2 ± 0.3 s/40 cases, much faster than the inference speeds of the clinicians, ranging from 177.2 ± 28.0 s/40 cases to 241.2 ± 64.1 s/40 cases. Our algorithm demonstrated comparable or even better performance compared to clinicians in assessing spine growth potential. This stable, efficient, and convenient algorithm seems to be a promising approach to assist doctors in clinical practice and deserves further study. This method has the ability to quickly ascertain the spine growth potential based on EOS radiographs, and it holds promise to provide assistance to busy doctors in certain clinical scenarios. • In the clinic, there is no available computer-based method that can automatically assess spine growth potential. • We developed a deep learning-based method that could automatically ascertain spine growth potential. • Compared with the results of the clinicians, our algorithm got comparable results.

Algorithm of differential diagnosis of anemia involving laboratory medicine specialists to advance diagnostic excellence.

Anemia is a severe global public health issue. Testing practices for anemia suggest overuse of screening laboratory tests and misinterpretation of studies even in "easy-to-diagnose" underlying causes, leading to late diagnoses and missed treatment opportunities. We aimed to develop a complete and efficient algorithm for clinical pathologists and laboratory medicine physicians for the differential diagnosis of anemia. Comprehensive literature search encompassing original articles, studies, reviews, gold standard books, and other evidence. We created a complex algorithm, primarily for clinical pathology/laboratory use, that explores all major and several rare causes of anemia in an efficient and evidence-based manner. The algorithm includes gold-standard diagnostic laboratory tests available in most clinical laboratories and indices that can be easily calculated to provide an evidence-based differential diagnosis of anemia. The diagnostic strategy combines previously available diagnostic tests and protocols in an efficient order. Clinical pathologists following the algorithm can independently provide valuable diagnostic support for healthcare providers. Clinical pathologists providing complete differential diagnostic services with the proposed algorithm may create an opportunity for an advanced diagnostic service that supports diagnostic excellence and helps patients receive a timely diagnosis and early treatment opportunities.

Tensor completion algorithm-aided structural color design.

In recent years, structural color has developed rapidly due to its distinct advantages, such as low loss, high spatial resolution and environmental friendliness. Various inverse design methods have been extensively investigated to efficiently design optical structures. However, the optimization method for the inverse design of structural color remains a formidable challenge. Traditional optimization approaches, such as genetic algorithms require time-consuming repetitions of structural simulations. Deep learning-assisted design necessitates prior simulations and large amounts of data, making it less efficient for systems with a small number of features. This study proposes a tensor completion algorithm capable of swiftly and accurately predicting missing datasets based on partially obtained datasets to assist in structural color design. Transforming the complex physical problem of structural color design into a spatial structure relationship problem linking geometric parameters and spectral data. The method utilizes tensor multilinear data analysis to effectively capture the complex relationships associated with geometric parameters and spectral data in higher-order data. Numerical and experimental results demonstrate that the algorithm exhibits high reliability in terms of speed and accuracy for diverse structures, datasets of varying sizes, and different materials, significantly enhancing design efficiency. The proposed algorithm offers a viable solution for inverse design problems involving complex physical systems, thereby introducing a novel approach to the design of photonic devices. Additionally, numerical experiments illustrate that the structural color of cruciform resonators with diamond can overcome the high loss issues observed in traditional dielectric materials within the blue wavelength region and enhance the corrosion resistance of the structure. We achieve a wide color gamut and a high-narrow reflection spectrum nearing 1 by this structure, and the theoretical analysis further verifies that diamond holds great promise in the realm of optics.

Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the “t-matrix” model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This “t-matrix” model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and publicly available images. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts.

Computing the Non-properness Set of Real Polynomial Maps in the Plane

AbstractWe introduce novel mathematical and computational tools to develop a complete algorithm for computing the set of non-properness of polynomials maps in the plane. In particular, this set, which we call the Jelonek set, is a subset of $$\mathbb {K}^2$$ K 2 , where a dominant polynomial map $$f: \mathbb {K}^2 \rightarrow \mathbb {K}^2$$ f : K 2 → K 2 is not proper; $$\mathbb {K}$$ K could be either $$\mathbb {C}$$ C or $$\mathbb {R}$$ R . Unlike all the previously known approaches we make no assumptions on f whenever $$\mathbb {K} = \mathbb {R}$$ K = R ; this is the first algorithm with this property. The algorithm takes into account the Newton polytopes of the polynomials. As a byproduct we provide a finer representation of the set of non-properness as a union of semi-algebraic curves, that correspond to edges of the Newton polytopes, which is of independent interest. Finally, we present a precise Boolean complexity analysis of the algorithm and a prototype implementation in maple.