Wideband Spectrum Sensing via Derived Correlation Matrix Completion Based on Generalized Coprime Sampling

In this paper, we propose a method for predicting scores of mock examinations taken by high school students using the matrix completion method. In the proposed method, we adopt the matrix completion method to predict the scores from the results of the past mock examinations. The matrix completion method can solve the problem of missing information due to different mock examinations taken by each student. In practice, we adopt singular value decomposition and use the estimated pseudo-information to solve the problem. This is the first attempt to realize accurate prediction of scores of mock examinations using the matrix completion method with those of the past mock examinations, and this is the main contribution of this paper. The evaluation is performed by measuring the difference between the original information and the information predicted by using the proposed method.

Direction-of-arrival (DOA) estimation using nested linear array ignores the information from repeated sensors, thus involves the problem of losing accuracy. Moreover, non-circular feature of signals is rarely considered and it results in discontinuity of the virtual array, namely, holes appear. This paper first provide an improved data averaging method to increase the accuracy of DOA estimation by fusing data from covariance and elliptic covariance. And then an algorithm based on matrix completion theory in nested array that greatly extends the degrees of freedom (DOF) and is able to find more sources than number of physical sensors is presented. The algorithm reconstructs the covariance matrix of the virtual linear array, which exactly has the same shift invariance as the uniform linear array but a higher aperture. Considering about the missing elements of the virtual array covariance matrix, we apply matrix completion theory to solve the problem. Finally, true DOAs of multiple signals can be obtained through subspace algorithms. Numerical results demonstrate that the proposed algorithms can obtain high accuracy while underdetermined DOA estimation is realized.

Full-field displacement perception and digital twins for core components play a crucial role in the precision manufacturing industry, such as aviation manufacturing. This paper presents a real-time full-field displacement perception method for the combination of online multipoint displacement monitoring and matrix completion theory. Firstly, a conceptual full-field displacement perception model based on the observed information of the multi-points is established. To obtain the full-field displacements of a core component, the component is divided into plentiful discrete points, including observed and unobserved points, based on which the relationship between the observed points and the full-field displacements is established. Then, the solution method of the full-field displacement perception model is proposed. Based on the matrix completion principle and the big data of the simulation, the optimization problem is employed to work out the model and, meanwhile, the pseudo-code is put forward. Finally, the full-field displacement perception experiments are performed. Repeated experiments show that the max error of the displacements calculated by the proposed method can be less than 0.094 mm and the median error can be less than 0.054 mm, while the average time frame can be less than 0.48 s, which is promising considering the high precision and efficiency requirements of the assembly of large aircraft.

Matrix completion by deep matrix factorization

A strong restricted isometry property, with an application to phaseless compressed sensing

The matrix sensing problem is an important low-rank optimization problem that has found a wide range of applications, such as matrix completion, phase synchornization/retrieval, robust principal component analysis (PCA), and power system state estimation. In this work, we focus on the general matrix sensing problem with linear measurements that are corrupted by random noise. We investigate the scenario where the search rank r is equal to the true rank [Formula: see text] of the unknown ground truth (the exact parametrized case), as well as the scenario where r is greater than [Formula: see text] (the overparametrized case). We quantify the role of the restricted isometry property (RIP) in shaping the landscape of the nonconvex factorized formulation and assisting with the success of local search algorithms. First, we develop a global guarantee on the maximum distance between an arbitrary local minimizer of the nonconvex problem and the ground truth under the assumption that the RIP constant is smaller than [Formula: see text]. We then present a local guarantee for problems with an arbitrary RIP constant, which states that any local minimizer is either considerably close to the ground truth or far away from it. More importantly, we prove that this noisy, overparametrized problem exhibits the strict saddle property, which leads to the global convergence of perturbed gradient descent algorithm in polynomial time. The results of this work provide a comprehensive understanding of the geometric landscape of the matrix sensing problem in the noisy and overparametrized regime. Funding: This work was supported by grants from the National Science Foundation, Office of Naval Research, Air Force Office of Scientific Research, and Army Research Office.

One-bit matrix completion is an important class of positive-unlabeled (PU) learning problems where the observations consist of only positive examples, e.g., in top-N recommender systems. For the first time, we show that 1-bit matrix completion can be formulated as the problem of recovering clean graph signals from noise-corrupted signals in hypergraphs. This makes it possible to enjoy recent advances in graph signal learning. Then, we propose the spectral graph matrix completion (SGMC) method, which can recover the underlying matrix in distributed systems by filtering the noisy data in the graph frequency domain. Meanwhile, it can provide micro- and macro-level explanations by following vertex-frequency analysis. To tackle the computational and memory issue of performing graph signal operations on large graphs, we construct a scalable Nystrom algorithm which can efficiently compute orthonormal eigenvectors. Furthermore, we also develop polynomial and sparse frequency filters to remedy the accuracy loss caused by the approximations. We demonstrate the effectiveness of our algorithms on top-N recommendation tasks, and the results on three large-scale real-world datasets show that SGMC can outperform state-of-the-art top-N recommendation algorithms in accuracy while only requiring a small fraction of training time compared to the baselines.

Determining drug indications is a critical part of the drug development process. However, traditional drug discovery is expensive and time-consuming. Drug repositioning aims to find potential indications for existing drugs, which is considered as an important alternative to the traditional drug discovery. In this article, we propose a multi-view learning with matrix completion (MLMC) method to predict the potential associations between drugs and diseases. Specifically, MLMC first learns the comprehensive similarity matrices from five drug similarity matrices and two disease similarity matrices based on the multi-view learning (ML) with Laplacian graph regularization, and updates the drug-disease association matrix simultaneously. Then, we introduce matrix completion (MC) to add some positive entries in original association matrix based on low-rank structure, and re-execute the multi-view learning algorithm for association prediction. At last, the prediction results of the above two operations are integrated as the final output. Evaluated by 10-fold cross-validation and de novo tests, MLMC achieves higher prediction accuracy than the current state-of-the-art methods. Moreover, case studies confirm the ability of our method in novel drug-disease association discovery. The codes of MLMC are available at https://github.com/BioinformaticsCSU/MLMC. Contact: jxwang@mail.csu.edu.cn.

The experimental determination of drug-target interaction is time-consuming and expensive. Therefore, a continuous demand for more effective prediction of drug-target interaction using computing technology. Many algorithms have been designed to infer potential interactions. Most of these algorithms rely on drug similarity and target similarity as auxiliary information in modeling, but they ignore the problem that there are a lot of missing auxiliary data of existing drugs or targets, which affects the prediction performance of the model and fails to achieve the expected effect. Here, we propose a calculation model named MCLO, which is based on the matrix completion and linear optimization technology to predict novel drug-target interactions. First, the proposed method calculate the side effect similarity of drugs and protein-protein interaction similarity of targets. Then we utilize the idea of linear neighbor representation learning to predict the potential drug-target interaction. It is worth mentioning that our method uses the idea of matrix completion technology to complete the imperfect similarity before drug-target interactions prediction. To evaluate the performance of MCLO, we carry out experiments on four gold standard datasets. The experimental results show that MCLO can be effectively applied to identify drug-target interactions.

Time delay estimation is of great significance in multipath propagation to recover overlapped signals and identify the channel characteristics. However, achieving a high accuracy in this purpose may pose many problems in ultra-wideband (UWB) applications. In UWB systems, capturing a signal with high sampling rates cannot readily be done; hence classical methods for time delay estimation substantially lose their precision. To overcome this challenge, the authors incorporate a robust estimation approach and supplementary sampling process in a unified algorithm to retrieve time delays from signals with low sampling rates. Toward that pursuit, a model based least squares estimator is proposed as the main approach to calculate time delays and a modified method based on multiple signal classification (MUSIC) is also presented for comparison aim. Then, the authors have developed the algorithm by embedding two additional pre-processing steps of under sampling and interpolation to achieve a higher sampling rate and a better resolution. To show the high accuracy of work, root mean square error is computed in different values of time delay. Simulation and experiment results show the considerably higher precision of the proposed algorithm in comparison with presented MUSIC type method and also previously proposed methods in literature.

Given an undirected graph G=(V,E) with node set V=[1,n], a subset $S\subseteq V$, and a rational vector $a\in {\rm\bf Q}^{S\cup E}$, the positive semidefinite matrix completion problem consists of determining whether there exists a real symmetric n × n positive semidefinite matrix X=(xij) satisfying xii=ai ($i\in S$) and xij=aij ($ij\in E$). Similarly, the Euclidean distance matrix completion problem asks for the existence of a Euclidean distance matrix completing a partially defined given matrix. It is not known whether these problems belong to NP. We show here that they can be solved in polynomial time when restricted to the graphs having a fixed minimum fill-in, the minimum fill-in of graph G being the minimum number of edges needed to be added to G in order to obtain a chordal graph. A simple combinatorial algorithm permits us to construct a completion in polynomial time in the chordal case. We also show that the completion problem is polynomially solvable for a class of graphs including wheels of fixed length (assuming all diagonal entries are specified). The running time of our algorithms is polynomially bounded in terms of n and the bitlength of the input a. We also observe that the matrix completion problem can be solved in polynomial time in the real number model for the class of graphs containing no homeomorph K4.

In cognitive radio networks, wideband spectrum sensing (WSS) has been advocated as an effective approach to increase the spectrum access opportunity of the secondary users. On the other hand, because of the increase of sampling rate and sensing time duration cost by the analog-to-digital converter (ADC), energy saving has been a significant problem for WSS. In this paper, taking advantage of the frequency-domain sparsity of the wideband spectrum, a WSS scheme combining compressed sensing and multi-band joint detection technique is proposed to reduce the energy consumption. Based on extensive analysis and simulation, we identify the sparsity order of the wideband spectrum, the received signal-to-noise ratio (SNR) of the primary signal, and the compression rate employed in sampling as three key factors that affect the sensing performance. In particular, we derive a closed-form analytical model of the scheme. Based on these observations, the energy efficiency, defined as the ratio of the spectrum access opportunity to the energy consumption, is maximized through the optimization process of the compression rate under the sensing performance constraints. We also indicate the uniqueness of the optimal compression rate for maximizing the energy efficiency. Numerical and simulation results show that our proposed scheme is more energy efficient if the wideband spectrum is sparser in the frequency domain.

Positive semidefinite matrix completion, universal rigidity and the Strong Arnold Property

Achieving both high resolution and high sample rates is a major difficulty in the field of high-speed analog-to-digital conversion for 5G communications. In order to improve speed and resolution, this work presents a novel method that combines an 8-bit Sigma-Delta (ΣΔ) ADC with a 3-bit Flash analog-to-digital converter (ADC). The proposed High-Speed and Sample Hold-Digital-Analog Converter (SHDAC) may operate at sampling frequencies ranging from 1 giga-samples per second (Gsps) to 14 Gsps and across a variety of voltage sampling ranges from 2 to 32 scales. The SHDAC successfully strikes a balance between speed and accuracy by utilizing the high-speed conversion capability of the 3-bit Flash ADC and the oversampling and noise reduction advantages of the 8-bit Sigma-Delta ADC. This makes it ideal for 5G digital communication and signal processing applications. The use of a digital scaling mechanism that dynamically modifies the SHDAC's bit resolution to 4, 8, 16, or 32 bits depending on system requirements is a significant breakthrough in this architecture. Because of its versatility, the SHDAC can be used for a variety of 5G applications, such as high-precision signal processing with lower sample rates and ultra-fast data gathering with lesser resolution. High precision, scalability, and adaptability are ensured by the front-end Verilog model used to implement the suggested SHDAC architecture. The efficiency of the SHDAC is validated by Vivado simulations, which show sampling rates ranging from 1 to 14 Gsps and an ultra-low dynamic power usage of 0.0007w, Sampling rate is 4.286GSpS and SNDR value is 68.98dB, These findings demonstrate how the SHDAC with parasitic capacitance using Counter design with linear correction process for high-speed design can facilitate fast, and to energy-efficient data conversion for upcoming 5G communication systems.

The development of matrix completion theory provides new approaches for data gathering in Wireless Sensor Networks (WSN). The existing matrix completion algorithms for WSN mainly consider how to reduce the sampling number without considering the real-time performance when recovering the data matrix. In order to guarantee the recovery accuracy and reduce the recovery time consumed simultaneously, we propose a new Augmented Lagrange Multiplier (ALM) algorithm to recover the weather monitoring data. A large amount of experiments have been carried out to investigate the performance of the proposed ALM algorithm by using different parameter settings, different sampling rates and sampling models. In addition, we compare the proposed ALM algorithm with some existing algorithms in the literature. Experimental results show that the ALM algorithm can obtain better overall recovery accuracy with less computing time, which demonstrate that the ALM algorithm is an effective and efficient approach for recovering the real world weather monitoring data in WSN.