Matrix Completion Algorithm Research Articles

Two-Dimensional Direction Finding for L-Shaped Coprime Array via Minimization of the Ratio of the Nuclear Norm and the Frobenius Norm

More recently, the ability of the coprime array to yield large array apertures and high degrees of freedom in comparison with the uniform linear array (ULA) has drawn an enormous amount of attention. In light of this, we propose a low-rank matrix completion algorithm via minimization of the ratio of the nuclear norm and the Frobenius norm (N/F) to solve the two-dimensional (2D) direction finding problem for the L-shaped coprime array (LsCA). Specifically, we first interpolate the virtual co-array signal related to the cross-correlation matrix (CCM) and utilize the interpolated virtual signal for Toeplitz matrix reconstruction. Then, the N/F method is employed to perform low-rank matrix completion on the reconstructed matrix. Finally, exploiting the conjugate symmetry characteristics of the completed matrix, we further develop a direction-finding algorithm that enables 2D angle estimation. Remarkably, the 2D angles are able to be automatically paired by the proposed algorithm. Numerical simulation findings demonstrate that the proposed N/F algorithm generates excellent angular resolution and computational complexity. Furthermore, this algorithm yields better estimation accuracy compared to the competing algorithms.

Sex & marital differences in delayed pharyngeal cancer treatment before and after medicaid expansion

ObjectiveIn the United States, pharyngeal cancer has become the most common type of head and neck cancer, with 80 % of cases found in males. Although disparities in treatment delays have been observed in pharyngeal patients, less is known about how policies facilitate timely care. This study aimed to estimate the association between Medicaid expansion and delaying initiation of pharyngeal cancer treatment. MethodologyWe extracted Surveillance, Epidemiological, End Results (SEER) case data to analyze pharyngeal cancers diagnosed between 2000 and 2018. The outcome of interest was a binary variable indicating if the patient initiated treatment two or more months after diagnosis. We conducted subgroup analyses by sex, marital status, and type of treatment received (surgery, radiation, chemotherapy, post-operative radiation, systemic therapy). We implemented the Matrix Completion algorithm to account for staggered rollout of Medicaid expansion within our difference-in-differences design. ResultsOur sample included 79,433 patients diagnosed with pharynx cancer. Delayed treatment was lowest among married females receiving systemic therapy (5 %), and highest among married males and females not recommended to receive surgery (43 %). Generally, there was no association between Medicaid expansion and changes in delayed treatment. Subgroup analyses show that Medicaid expansion was associated with reduced treatment delays in unmarried females receiving systemic therapy (−4.5%-points), and married males receiving chemotherapy (Est. = −2.6%-points), radiotherapy (Est. = −3.1%-points), and married males not recommended to receive surgery (Est. = −4.6%-points). ConclusionsGiven the importance of timely pharyngeal cancer treatment, health systems must identify and address the drivers of treatment delays to advance cancer equity.

Robust low-rank matrix completion via sparsity-inducing regularizer

This paper proposes a sparsity-inducing regularizer associated with the Welsch function. We theoretically show that the regularizer is quasiconvex and the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Unlike conventional nonconvex regularizers like the ℓp-norm with 0<p<1 that generally needs iterations to obtain the corresponding proximity operator, the developed regularizer has a closed-form proximity operator. We utilize our regularizer to penalize the singular values as well as sparse outliers of the distorted data, and develop an efficient algorithm for robust matrix completion. Convergence of the suggested method is analyzed and we prove that any accumulation point is a stationary point. Finally, experimental results demonstrate that our algorithm is superior to the competing techniques in terms of restoration performance. MATALB codes are available at https://github.com/bestzywang/RMC-NNSR.

Multi-Channel Audio Completion Algorithm Based on Tensor Nuclear Norm

Multi-channel audio signals provide a better auditory sensation to the audience. However, missing data may occur in the collection, transmission, compression, or other processes of audio signals, resulting in audio quality degradation and affecting the auditory experience. As a result, the completeness of the audio signal has become a popular research topic in the field of signal processing. In this paper, the tensor nuclear norm is introduced into the audio signal completion algorithm, and the multi-channel audio signals with missing data are restored by using the completion algorithm based on the tensor nuclear norm. First of all, the multi-channel audio signals are preprocessed and are then transformed from the time domain to the frequency domain. Afterwards, the multi-channel audio with missing data is modeled to construct a third-order multi-channel audio tensor. In the next part, the tensor completion algorithm is used to complete the third-order tensor. The optimal solution of the convex optimization model of the tensor completion is obtained by using the convex relaxation technique and, ultimately, the data recovery of the multi-channel audio with data loss is accomplished. The experimental results of the tensor completion algorithm and the traditional matrix completion algorithm are compared using both objective and subjective indicators. The final result shows that the high-order tensor completion algorithm has a better completion ability and can restore the audio signal better.

Fast identification of coherent sound sources with the covariance matrix fitting method based on non-synchronous measurements

The Non-Synchronous Measurements is particularly effective at expanding the operating frequency range of a single microphone array. The completed cross-spectral matrix of the synthetic array, when combined with high-resolution imaging algorithms, can yield accurate sound source identification results. However, when matrix completion algorithms are applied to large synthetic arrays, their computational complexity increases significantly. Furthermore, existing integrations with high-resolution imaging algorithms often encounter difficulties in the presence of coherent sound sources. To address this problem, this paper introduces the accelerated gradient descent algorithm for the covariance matrix fitting by orthogonal least squares. The matrix completion model for non-synchronous measurements is initially simplified through matrix decomposition, thereby enabling the rapid completion of the cross-spectral matrix using the accelerated gradient descent algorithm. This is then followed by the application of the covariance matrix fitting by orthogonal least squares to achieve quick and precise identification of coherent sound sources employing the completed cross-spectral matrix. The performance of the algorithm is evaluated using numerical simulations and validated through loudspeaker experiments in an anechoic chamber. The results from these simulations and experiments reveal that the proposed algorithm not only improves matrix completion performance on large synthetic arrays but also accurately identifies the locations and correlation coefficients of coherent sound sources.

A Matrix Completion Method for Imputing Missing Values of Process Data

Real-time process data are the foundation for the successful implementation of intelligent manufacturing in the chemical industry. However, in the actual production process, process data may randomly be missing due to various reasons, thus affecting the practical application of intelligent manufacturing technology. Therefore, this paper proposes the application of appropriate matrix completion algorithms to impute the missing values of real-time process data. Considering the characteristics of online missing value imputation problems, this paper proposes an improved method for a matrix completion algorithm that is suitable for real-time missing data imputation. By utilizing real device data, this paper studies the impact of algorithm parameters on the effect of missing value imputing and compares it with several classical missing value imputing methods. The results show that the introduced method achieves higher accuracy in data imputation compared to the baseline method. Furthermore, the proposed enhancement significantly improves the speed performance of algorithms.

Gene Target Prediction of Environmental Chemicals Using Coupled Matrix-Matrix Completion.

Human exposure to toxic chemicals presents a huge health burden. Key to understanding chemical toxicity is knowledge of the molecular target(s) of the chemicals. Because a comprehensive safety assessment for all chemicals is infeasible due to limited resources, a robust computational method for discovering targets of environmental exposures is a promising direction for public health research. In this study, we implemented a novel matrix completion algorithm named coupled matrix-matrix completion (CMMC) for predicting direct and indirect exposome-target interactions, which exploits the vast amount of accumulated data regarding chemical exposures and their molecular targets. Our approach achieved an AUC of 0.89 on a benchmark data set generated using data from the Comparative Toxicogenomics Database. Our case studies with bisphenol A and its analogues, PFAS, dioxins, PCBs, and VOCs show that CMMC can be used to accurately predict molecular targets of novel chemicals without any prior bioactivity knowledge. Our results demonstrate the feasibility and promise of computationally predicting environmental chemical-target interactions to efficiently prioritize chemicals in hazard identification and risk assessment.

3D far-field Lidar sensing and computational modeling for human identification.

3D sensors offer depth sensing that may be used for task-specific data processing and computational modeling. Many existing methods for human identification using 3D depth sensors primarily focus on Kinect data, where the range is very limited. This work considers a 3D long-range Lidar sensor for far-field imaging of human subjects in 3D Lidar full motion video (FMV) of "walking" action. 3D Lidar FMV data for human subjects are used to develop computational modeling for automated human silhouette and skeleton extraction followed by subject identification. We propose a matrix completion algorithm to handle missing data in 3D FMV due to self-occlusion and occlusion from other subjects for 3D skeleton extraction. We further study the effect of noise in the 3D low resolution far-field Lidar data in human silhouette extraction performance of the model. Moreover, this work addresses challenges associated with far-field 3D Lidar including learning with a limited amount of data and low resolution. Moreover, we evaluate the proposed computational algorithm using a gallery of 10 subjects for human identification and show that our method is competitive with the state-of-the-art OpenPose and V2VPose skeleton extraction models using the same dataset for human identification.

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.

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.

Fast Robust Matrix Completion via Entry-Wise l0 -Norm Minimization.

Matrix completion (MC) aims at recovering missing entries, given an incomplete matrix. Existing algorithms for MC are mainly designed for noiseless or Gaussian noise scenarios and, thus, they are not robust to impulsive noise. For outlier resistance, entry-wise lp -norm with and M-estimation are two popular approaches. Yet the optimum selection of p for the entrywise lp -norm-based methods is still an open problem. Besides, M-estimation is limited by a breakdown point, that is, the largest proportion of outliers. In this article, we adopt entrywise l0 -norm, namely, the number of nonzero entries in a matrix, to separate anomalies from the observed matrix. Prior to separation, the Laplacian kernel is exploited for outlier detection, which provides a strategy to automatically update the entrywise l0 -norm penalty parameter. The resultant multivariable optimization problem is addressed by block coordinate descent (BCD), yielding l0 -BCD and l0 -BCD-F. The former detects and separates outliers, as well as its convergence is guaranteed. In contrast, the latter attempts to treat outlier-contaminated elements as missing entries, which leads to higher computational efficiency. Making use of majorization-minimization (MM), we further propose l0 -BCD-MM and l0 -BCD-MM-F for robust non-negative MC where the nonnegativity constraint is handled by a closed-form update. Experimental results of image inpainting and hyperspectral image recovery demonstrate that the suggested algorithms outperform several state-of-the-art methods in terms of recovery accuracy and computational efficiency.

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.

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.

Adaptive thresholding for iterative matrix completion with heterogeneous missing probability: H-AdaptiveImpute

Several low-rank matrix completion algorithms have been developed, which often employ thresholded singular value decomposition (SVD) iteratively. Their performance depends on the choice of thresholding tuning parameters and initial input matrix. In particular, the initialization of the non-convex optimization algorithms plays a pivotal role. However, they often use a zero matrix or a consistent low-rank matrix estimator under the simple homogeneous observation probability assumption as the initial input matrix. This paper proposes a non-convex low-rank matrix completion algorithm with an intelligent initial matrix under the heterogeneous observation probability structure. Specifically, the proposed algorithm iterates the thresholded SVD starting from a tailored initialization based on the estimator of the singular values and vectors of the underlying matrix. We show that the proposed initial estimator is consistent, and the adaptive thresholding tuning parameters are estimated using theoretically justified and data-driven procedures. The results of the numerical experiments show that the proposed algorithm performs well compared to the existing method.

Radio map construction based on BERT for fingerprint-based indoor positioning system

Due to the heavy workload of RSS collection, the instability of WLAN signal strength and the disappearance of signals caused by complex indoor environments, the construction of radio map for wireless local area network (WLAN) fingerprint-based indoor positioning system is time-consuming and laborious. In order to rapidly deploy indoor WLAN positioning system, the bidirectional encoder representation from transformers (BERT) model is used to fill the missing signal in radio map and quickly build radio map. The radio map is imported into the BERT model in the form of natural language text, and the missing signal is filled by the BERT model. Since the number of input data in BERT model cannot exceed 512 words, the structure of BERT model is not suitable for WLAN signals with large data volume. Therefore, we redefine the model structure based on the original BERT model and fill in the missing signals in the radio map in parallel. In addition, the loss function is redefined. Except that each segment has a loss function, the weighted average value of all segment loss functions is defined as the total loss function. The experimental results show that the BERT model is better than the traditional linear interpolation method, compressed sensing algorithm and matrix completion algorithm in filling the missing signals in the fingerprint database, and the probability of error within 2 m reaches about 94%.

Robust rank-one matrix completion with rank estimation

Matrix completion aims at estimating the missing entries of a low-rank and incomplete data matrix. It frequently arises in many applications such as computer vision, pattern recognition, recommendation system, and data mining. Most of the existing methods face two problems. Firstly, the data matrix in real world is often disturbed by noise. Noise may change the date structure of the incomplete matrix, thereby degrade the performance of matrix completion algorithms. Secondly, some existing methods need to preset a reasonable rank as input, and the value of rank will affect the performance of the algorithms. Therefore, we proposed a robust rank-one matrix completion method with rank estimation in this paper. To mitigate the influence of noise, we divide the incomplete and noisy data matrix into two parts iteratively: low-rank and sparse parts. Besides, we use a weighted rank-one matrix pursuit algorithm to approximate the low-rank part of the data matrix, and the rank of the matrix can be estimated with the adaptive weight vector. The performance of the proposed method is demonstrated by experiments on both synthetic datasets and image datasets. The experimental results demonstrate the performance of the proposed method with incompleted matrices distrubed by sparse noise.

Image inpainting using non-convex low rank decomposition and multidirectional search

Low-rank (LR) and nonlocal self-similarity (NSS) are two important priors for image inpainting as a typical inverse problem. Nuclear norm minimization (NNM) is a widely used convex relaxation for relevant rank minimization problems. However, NNM regularizes each singular value equally and ignores the significance of bigger singular values. In this paper, we propose a non-convex low-rank decomposition (NC-LRD) model that is based on robust principal component analysis (RPCA) with a weighted L1 norm. Utilizing NSS prior for image inpainting we search similar patches by using a newly designed multidirectional search (MS) method, and apply the NC-LRD model to complete each corrupted patch matrix (low-rank decomposition with multidirectional search, MS-LRD). We focus on the spatial distribution of similar patches by restricting matched N patches to locate at N different directions relative to a target patch, while previous state-of-the-art methods do not consider the spatial distribution in similarity criterion. The MS method solves the problem that many patch-based inpainting algorithms fail to complete missing lines. Experimental results on line missing demonstrate that the proposed NC-LRD method has lower reconstruction error in matrix completion, and it converges faster than several state-of-the-art matrix completion algorithms. At the same time, the effectiveness and superiority of MS-LRD over other competitive inpainting algorithms are also verified.

GSMAC: GAN-Based Signal map Construction With Active Crowdsourcing

With the dawn of 5G network, a new set of requirements for site spectrum monitoring, cellular planning are emerging, all of which are relying on fine-grained signal map. Although with significant importance, the traditional signal map construction could be time-consuming and labor-intensive. The state-of-the arts usually employ crowdsourcing scheme and matrix completion algorithm to solve the dilemma. However, the crowdsourcing scheme usually suffers from uneven distributed and inadequate participants. To this end, in this paper, we study how to effectively reconstruct and update the signal map in the case of partially measured signal maps with smaller cost and propose a GAN-based active signal map reconstruction method (GSMAC). Our method is mainly innovative in two parts: GSMC, GAN-based signal map construction, and ACS, an active crowdsourcing scheme. Specifically, GSMC can effectively update the signal map with only a small number of observations while updating the signal map online. ACS consists of a reinforce learning-based active query mechanism which quantitatively evaluates the most valuable measurement site for reconstruction. The simulation results and real implemented data-driven experiments demonstrate the advantages and effectiveness of our approach in both accuracy and cost.

A novel hybrid model for missing deformation data imputation in shield tunneling monitoring data

Complete and high-quality deformation monitoring data are critical for shield tunnel construction safety and quality. In engineering practices, data missing frequently occurs during instrumentation, adversely impacting further analysis and decision making. Existing imputation methods either ignore the crucial interactions between different parameters during shield tunneling or focus on the global characteristics of deformation data while neglect their local difference. This paper proposes a novel hybrid model, MCCB, combining multi-view matrix completion algorithms, convolutional neural network (CNN), and bidirectional long short-term memory (BiLSTM) algorithms to impute missing deformation values in shield tunnel monitoring data. The performance of the proposed method is verified using bridge deformation data from a practical project in Beijing. Different missing patterns of the bridge deformation data are filled. The experiment results show that the proposed model can effectively learn the various characteristics of the deformation data and outperforms the four selected models and its two sub-models, and can be used to improve the accuracy of the deformation prediction through data imputation. The novelty of this study includes two aspects. First is that the complicated interaction between different parameters and local difference of the data are considered simultaneously. They have not been addressed before by existing studies. Second is that the innovative combination of matrix completion and deep learning algorithm for application in missing deformation values imputation. To our best knowledge, no research on engineering construction has implemented this technique before.

Accelerated matrix completion algorithm using continuation strategy and randomized SVD

The matrix completion (MC) problem aims to recover the complete matrix from the observed matrix with missing entries. The unknown matrix is generally assumed to have a low-rank structure. It is well known that the low-rank minimization problem is NP-hard, so the rank function of the matrix is approximated by a surrogate function. In this paper, we firs t apply the optimization transfer technique to formulate the minimization problem into a bi-variate minimization problem by adding an auxiliary variable. We apply the alternating minimization method to find the minimizer of the bi-variate minimization problem. For the auxiliary variable, the minimum can be formulated as a linear combination of the observation data and the original variable. For the original variable, the minimum is a generalized singular thresholding (GSVT) operator of the auxiliary variable. However, most existing iteration methods for matrix completion problem use fixed thresholding value and also suffer from full singular value decomposition (SVD), which need more computation time for iteration. Thus, they become inefficient for large-scale problems. In order to handle these limitations, we apply the continuation strategy and the randomized singular value decomposition (RSVD) to reduce the computational costs. The threshold value of the continuous strategy is reduced in each iteration until a given minimum thresholding value is reached, while the RSVD only needs to decompose small-scale matrices. Hence, using both strategies simultaneously can effectively reduce the computation time for iteration. Numerical experiments demonstrate that the proposed algorithm can effectively recover the missing entries both in synthetic and real data.