Narrow Results

In heterogeneous wireless sensor networks, the data collection method based on compressed sensing technology is susceptible to packet loss and noise, which leads to a decrease in data reconstruction accuracy in unreliable links. Combining compressed sensing and matrix completion, we propose a clustering optimization algorithm based on structured noise matrix completion, in which the cluster head transmits the compressed sampling data and compression strategy to the base station. The algorithm we proposed can reduce the energy consumption of the node in the process of data collection, redundant data and transmission delay. The rank-1 matrix completion algorithm constructs an extremely sparse observation matrix, which is adopted by the sink node to complete the reconstruction of the whole network data. Simulation experiments show that the proposed algorithm reduces network transmission data, balances node energy consumption, improves data transmission efficiency and reconstruction accuracy, and extends the network life cycle.

Low-rank matrix completion, which aims to recover a matrix with many missing values, has attracted much attention in many fields of computer science. A low-rank matrix fitting (LMaFit) method has been proposed for fast matrix completion recently. However, this method cannot converge accurately on matrices of real-world images. For improving the accuracy of LMaFit method, an improved low-rank matrix fitting (ILMF) method based on the weighted $L_{1,p}$ norm minimization is proposed in this paper, where the $L_{1,p}$ norm is the summation of the $p$-power $(0<p<2)$ of $L_1$ norms of rows in a matrix. In the proposed method, i.e. the ILMF method, the incomplete matrix that may be corrupted by noises is decomposed into the summation of a low-rank matrix and a noise matrix at first. Then, a weighted $L_{1,p}$ norm minimization problem is solved by using an alternating direction method for improving the accuracy of matrix completion. Experimental results on real-world images show that the ILMF method has much better performances in terms of both the convergence accuracy and convergence speed than the compared methods.

The low rank matrix completion problem which aims to recover a matrix from that having missing entries has received much attention in many fields such as image processing and machine learning. The rank of a matrix may be measured by the ${\ell }_0$ norm of the vector of its singular values. Due to the nonconvexity and discontinuity of the ${\ell }_0$ norm, solving the low rank matrix completion problem which is clearly NP hard suffers from computational challenges. In this paper, we propose a constrained matrix completion model in which a novel nonconvex continuous rank surrogate is used to approximate the rank function of a matrix, promote low rank of the recovered matrix and address the computational challenges. The proposed rank surrogate differs from the convex nuclear norm and other existing state-of-the-art nonconvex surrogates in a way that it alleviates the discontinuity and nonconvexity of the rank function through a local ${\ell }_2$-relaxation of the ${\ell }_0$ norm so that it possesses several desirable properties. These properties ensure that it accurately approximates the rank function by choosing an appropriate relaxation parameter. We moreover develop an efficient iterative algorithm to solve the resulting model. We also propose strategies of automatically updating the relaxation parameter to practically ensure the global convergence and speed up the algorithm. We establish theoretical convergence results for the proposed algorithm. Experimental results are presented to demonstrate significant performance improvements of the proposed model and the associated algorithm as compared to state-of-the-art methods in both recoverability and computational efficiency.

Matrix completion is critical in a wide range of scientific and engineering applications, such as image restoration and recommendation systems. This topic is commonly expressed as a low-rank matrix optimization framework. In this paper, a universal and effective rank approximation method for matrix completion (RAMC) is provided. Fundamental to this strategy is developing a general function that meets specific conditions in order to directly approach the rank function and subsequently utilizing it to build a RAMC model. The major goal is to investigate a more accurate estimate of the rank function, allowing for more effective acquisition of the low-rank structure of incomplete data. Further, the RAMC model is easily implemented by a viable iterative method that may be successfully used to matrix completion tasks. Extensive experiments using the synthetic data and natural images reveal the excellent applicability of RAMC over the existing methods.

Identification of potential drug–target interactions (DTIs) plays a pivotal role in the development of drug and target discovery in the public healthcare sector. However, biological experiments for predicting interactions between drugs and targets are still expensive, complicated, and time-consuming. Thus, computational methods are widely applied for aiding drug–target interaction prediction. In this paper, we propose a novel model, named GCMCDTI, for DTIs prediction which adopts a graph convolutional network based on matrix completion. We regard the association prediction between drugs and targets as link prediction and treat the process as matrix completion, and then a graph convolutional auto-encoder framework is employed to construct the drug and target embeddings. Then, a bilinear decoder is applied to reconstruct the DTI matrix. We conduct our experiments on four benchmark datasets consisting of enzymes, G protein-coupled receptors (GPCRs), ion channels, and nuclear receptors. The five-fold cross-validation results achieve the high average AUC values of 95.78%, 95.31%, 93.90%, and 91.77%, respectively. To further evaluate our method, we compare our proposed method with other state-of-the-art approaches. The comparison results illustrate that our proposed method obtains improvement in performance on DTI prediction. The proposed method will be a good choice in the field of DTI prediction.

A real $n\times n$ matrix is a $Q$-matrix if for $k=1,\dots ,n$ the sum of all $k\times k$ principal minors is positive. A digraph $D$ is said to have positive $Q$-completion if every partial positive $Q$-matrix specifying $D$ can be completed to a positive $Q$-matrix. In this paper, necessary conditions for a digraph to have positive $Q$-completion are obtained and sufficient conditions for a digraph to have positive $Q$-completion are provided. The digraphs of order at most 4 that include all loops and have positive $Q$-completion are characterized. Tournaments whose complements have positive $Q$-completion are singled out. Further, some comparisons between the $Q$-matrix and positive $Q$-matrix completion problems have been made.

In this work, the difference convex function based on capped nuclear norm minimization (CNNM-DC) method, a cross-spectral matrix (CSM) completion iterative algorithm with excellent noise immunity, is proposed to realize acoustic imaging of non-synchronous measurements (NSM) under the condition of low signal-to-noise ratio (SNR). Compared with the CSM completion algorithm based on the nuclear norm minimization (NNM) model, the truncated nuclear norm regularization (TNNR) model, and the weighted nuclear norm minimization (WNNM) model, the proposed method can obtain the acoustic image with narrow main lobes and no sidelobe under the condition of low SNR. The simulation results show that, under conditions of low SNR, the proposed method effectively reduces the width of the main lobe, suppresses the side lobes, and achieves more accurate imaging results than the previous method. Finally, experiments were conducted to verify the feasibility of CNNM-DC. The experimental results show that the proposed method is an accurate acoustic imaging algorithm for NSM under low SNR, which lays a foundation for acoustic imaging in industrial occasions with strong background noise interference.

Due to the rapid development of Internet of Things (IoT), numerous IoT-based applications have been designed and implemented in a wide range of fields. In IoT-based agricultural applications, the sensors are deployed outdoors and subject to conditions of harsh environment and limited energy source, hence the frequent failure of sensors and the resultant missing data severely affect the effectiveness of IoT applications. This paper proposes an agricultural sensor data recovery method based on the matrix completion theory to tackle this problem. This method treats the different types of sensor data collected in a time series as a sensor data matrix and the missing sensor data is estimated by the matrix completion method. The results demonstrate that this method can effectively recover the missing sensor data.