Regularized Matrix Completion Research Articles

Approximate estimation of cell-type resolution transcriptome in bulk tissue through matrix completion.

Single-cell RNA sequencing (scRNA-seq) has emerged as a powerful tool for uncovering cellular heterogeneity. However, the high costs associated with this technique have rendered it impractical for studying large patient cohorts. We introduce ENIGMA (Deconvolution based on Regularized Matrix Completion), a method that addresses this limitation through accurately deconvoluting bulk tissue RNA-seq data into a readout with cell-type resolution by leveraging information from scRNA-seq data. By employing a matrix completion strategy, ENIGMA minimizes the distance between the mixture transcriptome obtained with bulk sequencing and a weighted combination of cell-type-specific expression. This allows the quantification of cell-type proportions and reconstruction of cell-type-specific transcriptomes. To validate its performance, ENIGMA was tested on both simulated and real datasets, including disease-related tissues, demonstrating its ability in uncovering novel biological insights.

DeepVir: Graphical Deep Matrix Factorization for In Silico Antiviral Repositioning-Application to COVID-19.

This study formulates antiviral repositioning as a matrix completion problem wherein the antiviral drugs are along the rows and the viruses are along the columns. The input matrix is partially filled, with ones in positions where the antiviral drug has been known to be effective against a virus. The curated metadata for antivirals (chemical structure and pathways) and viruses (genomic structure and symptoms) are encoded into our matrix completion framework as graph Laplacian regularization. We then frame the resulting multiple graph regularized matrix completion (GRMC) problem as deep matrix factorization. This is solved by using a novel optimization method called HyPALM (Hybrid Proximal Alternating Linearized Minimization). Results of our curated RNA drug-virus association data set show that the proposed approach excels over state-of-the-art GRMC techniques. When applied to in silico prediction of antivirals for COVID-19, our approach returns antivirals that are either used for treating patients or are under trials for the same.

Regularized matrix completion with partial side information

Side information has been shown useful for improving the performance of matrix completion applications. However, in most cases, only partial side information of either the column or row space is available. In this work, we propose a novel regularization based model to incorporate partial side information in matrix completion. We provide theoretical guarantees to ensure the success of the proposed model. It is proved that the proposed model achieves the state-of-the-art sample complexity when the given partial side information is exact, and an error bound for inexact partial side information is also provided. Moreover, we provide a deterministic rule for the selection of regularization parameter. We conduct extensive experiments on both synthetic and real-world data-sets. Experimental results show that our model succeeds to incorporate partial side information, and outperforms the state-of-the-art models on most data-sets.

L 2, 1‐Norm Regularized Matrix Completion for Attack Detection in Collaborative Filtering Recommender Systems

Collaborative filtering recommender systems (CFRSs) are known to be highly vulnerable to profile injection attacks, in which malicious users insert fake profiles into the rating database in order to bias the systems' output, since their openness, and attack detection is still a challenging problem in CFRSs. In order to provide more accurate recommendations, many schemas have been proposed to detect such shilling attacks. However, almost all of them are proposed to detect one or several specific attack types, and few of them can handle hybrid attack types, which usually happen in practice. With this problem in mind, we propose a novel L2, 1-norm regularized matrix completion incorporating prior information (LRMCPI) model to detect shilling attacks by combining matrix completion and L2, 1-norm. The proposed LRMCPI formalizes the attack detection problem as a missing value estimation problem, and it is appropriate because the user-item rating matrix is approximately low-rank and attack profiles could be considered as structural noise. The proposed LRMCPI model not only can better recover the rating matrix using correct rating value but also can detect the positions where the attackers are injected. We evaluate our model on three well-known data sets with different density and the experimental results show that our model outperforms baseline algorithms in both single and hybrid attack types.

Dual Laplacian regularized matrix completion for microRNA-disease associations prediction

ABSTRACT Since lots of miRNA-disease associations have been verified, it is meaningful to discover more miRNA-disease associations for serving disease diagnosis and prevention of human complex diseases. However, it is not practical to identify potential associations using traditional biological experimental methods since the process is expensive and time consuming. Therefore, it is necessary to develop efficient computational methods to accomplish this task. In this work, we introduced a matrix completion model with dual Laplacian regularization (DLRMC) to infer unknown miRNA-disease associations in heterogeneous omics data. Specifically, DLRMC transformed the task of miRNA-disease association prediction into a matrix completion problem, in which the potential missing entries of the miRNA-disease association matrix were calculated, the missing association can be obtained based on the prediction scores after the completion procedure. Meanwhile, the miRNA functional similarity and the disease semantic similarity were fully exploited to serve the miRNA-disease association matrix completion by using a dual Laplacian regularization term. In the experiments, we conducted global and local Leave-One-Out Cross Validation (LOOCV) and case studies to evaluate the efficacy of DLRMC on the Human miRNA-disease associations dataset obtained from the HMDDv2.0 database. As a result, the AUCs of DLRMC is 0.9174 and 0.8289 in global LOOCV and local LOOCV, respectively, which significantly outperform a variety of previous methods. In addition, in the case studies on four significant diseases related to human health including Colon Neoplasms, Kidney neoplasms, Lymphoma and Prostate neoplasms, 90%, 92%, 92% and 94% out of the top 50 predicted miRNAs has been confirmed, respectively.

Drug-Target Interaction Prediction via Dual Laplacian Graph Regularized Matrix Completion.

Drug-target interactions play an important role for biomedical drug discovery and development. However, it is expensive and time-consuming to accomplish this task by experimental determination. Therefore, developing computational techniques for drug-target interaction prediction is urgent and has practical significance. In this work, we propose an effective computational model of dual Laplacian graph regularized matrix completion, referred to as DLGRMC briefly, to infer the unknown drug-target interactions. Specifically, DLGRMC transforms the task of drug-target interaction prediction into a matrix completion problem, in which the potential interactions between drugs and targets can be obtained based on the prediction scores after the matrix completion procedure. In DLGRMC, the drug pairwise chemical structure similarities and the target pairwise genomic sequence similarities are fully exploited to serve the matrix completion by using a dual Laplacian graph regularization term; i.e., drugs with similar chemical structure are more likely to have interactions with similar targets and targets with similar genomic sequence similarity are more likely to have interactions with similar drugs. In addition, during the matrix completion process, an indicator matrix with binary values which indicates the indices of the observed drug-target interactions is deployed to preserve the experimental confirmed interactions. Furthermore, we develop an alternative iterative strategy to solve the constrained matrix completion problem based on Augmented Lagrange Multiplier algorithm. We evaluate DLGRMC on five benchmark datasets and the results show that DLGRMC outperforms several state-of-the-art approaches in terms of 10-fold cross validation based AUPR values and PR curves. In addition, case studies also demonstrate that DLGRMC can successfully predict most of the experimental validated drug-target interactions.

Wireless Sensor Network Localization via Matrix Completion Based on Bregman Divergence

One of the main challenges faced by wireless sensor network (WSN) localization is the positioning accuracy of the WSN node. The existing algorithms are arduous to use for dealing with the pulse noise that is universal and ineluctable in practical considerations, resulting in lower positioning accuracy. Aimed at this problem and introducing Bregman divergence, we propose in this paper a novel WSN localization algorithm via matrix completion (LBDMC). Based on the natural low-rank character of the Euclidean Distance Matrix (EDM), the problem of EDM recovery is formulated as an issue of matrix completion in a noisy environment. A regularized matrix completion model is established, smoothing the pulse noise by leveraging -norm and the multivariate function Bregman divergence is defined to solve the model to obtain the EDM estimator. Furthermore, node localization is available based on the multi-dimensional scaling (MDS) method. Multi-faceted comparison experiments with existing algorithms, under a variety of noise conditions, demonstrate the superiority of LBDMC to other algorithms regarding positioning accuracy and robustness, while ensuring high efficiency. Notably, the mean localization error of LBDMC is about ten times smaller than that of other algorithms when the sampling rate reaches a certain level, such as >30%.

Millimeter-Wave InSAR Image Reconstruction Approach by Total Variation Regularized Matrix Completion

Millimeter-wave interferometric synthetic aperture radiometer (InSAR) can provide high-resolution observations for many applications by using small antennas to achieve very large synthetic aperture. However, reconstruction of a millimeter-wave InSAR image has been proven to be an ill-posed inverse problem that degrades the performance of InSAR imaging. In this paper, a novel millimeter-wave InSAR image reconstruction approach, referred to as InSAR-TVMC, by total variation (TV) regularized matrix completion (MC) in two-dimensional data space, is proposed. Based on the a priori knowledge that natural millimeter-wave images statistically hold the low-rank property, the proposed approach represents the object images as low-rank matrices and formulates the data acquisition of InSAR in two-dimensional data space directly to undersample visibility function samples. Subsequently, using the undersampled visibility function samples, the optimal solution of the InSAR image reconstruction problem is obtained by simultaneously adopting MC techniques and TV regularization. Experimental results on simulated and real millimeter-wave InSAR image data demonstrate the effectiveness and the significant improvement of the reconstruction performance of the proposed InSAR-TVMC approach over conventional and one-dimensional sparse InSAR image reconstruction approaches.

Noise-Tolerant Wireless Sensor Networks Localization via Multinorms Regularized Matrix Completion

Accurate and sufficient location information is the prerequisite for most wireless sensor networks (WSNs) applications. Existing range-based localization approaches often suffer from incomplete and corrupted range measurements. Recently, some matrix completion-based localization approaches have been proposed, which only take into account Gaussian noise and outlier noise when modeling the range measurements. However, in some real-world applications, the inevitable structural noise usually degrades the localization accuracy and prevents the outlier recognition drastically. To address these challenges, we propose a noise-tolerant localization via multi-norms regularized matrix completion (LMRMC) approach in this paper. Leveraging the intrinsic low-rank property of euclidean distance matrix (EDM), the reconstruction problem of true underlying EDM is formulated as a multi-norms regularized matrix completion model, where the outlier noise and structural noise are explicitly sifted by $L_1$ -norm and $L_{1,2}$ -norm, respectively, while the Gaussian noise is implicitly smoothed by employing the well-known alternating direction method of multiplier optimization method. To the best of our knowledge, this is the first scheme being able to efficiently recover the unknown range measurements under the coexistence of Gaussian noise, outlier noise, and structural noise. Extensive experiments validate the superiority of our proposed LMRMC approach, outperforming the state-of-the-art localization approaches with regard to the localization accuracy. Besides, LMRMC can also achieve an accurate detection of both outlier noise and structural noise, making it promising for further nodes fault diagnosis and topology control in WSNs.

Manifold regularized matrix completion for multi-label learning with ADMM

Multi-label learning is a common machine learning problem arising from numerous real-world applications in diverse fields, e.g, natural language processing, bioinformatics, information retrieval and so on. Among various multi-label learning methods, the matrix completion approach has been regarded as a promising approach to transductive multi-label learning. By constructing a joint matrix comprising the feature matrix and the label matrix, the missing labels of test samples are regarded as missing values of the joint matrix. With the low-rank assumption of the constructed joint matrix, the missing labels can be recovered by minimizing its rank. Despite its success, most matrix completion based approaches ignore the smoothness assumption of unlabeled data, i.e., neighboring instances should also share a similar set of labels. Thus they may under exploit the intrinsic structures of data. In addition, the matrix completion problem can be less efficient. To this end, we propose to efficiently solve the multi-label learning problem as an enhanced matrix completion model with manifold regularization, where the graph Laplacian is used to ensure the label smoothness over it. To speed up the convergence of our model, we develop an efficient iterative algorithm, which solves the resulted nuclear norm minimization problem with the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real-world data have shown the promising results of the proposed approach.

A Randomized Nonmonotone Block Proximal Gradient Method for a Class of Structured Nonlinear Programming

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves typically several associated proximal subproblems that usually have a closed-form solution, until a certain progress on objective value is achieved. In contrast to the usual randomized block coordinate descent method [P. Richtárik and M. Takáč, Math. Program., 144 (2014), pp. 1--38; A. Patrascu and I. Necoara, J. Global Optim., 61 (2015), pp. 19--46], our method has a nonmonotone flavor and uses variable stepsizes that can partially utilize the local curvature information of the smooth component of objective function. We show that any accumulation point of the solution sequence of the method is a stationary point of the problem almost surely and the method is capable of finding an approximate stationary point with high probability. We also establish a sublinear rate of convergence for the method in terms of the minimal expected squared norm of certain proximal gradients over the iterations. When the problem under consideration is convex, we show that the expected objective values generated by RNBPG converge to the optimal value of the problem. Under some assumptions, we further establish a sublinear and linear rate of convergence on the expected objective values generated by a monotone version of RNBPG. Finally, we conduct some preliminary experiments to test the performance of RNBPG on the $\ell_1$-regularized least-squares problem, a dual support vector machine problem in machine learning, the $\ell_0$-regularized least-squares problem, and a regularized matrix completion model. The computational results demonstrate that our method substantially outperforms the randomized block coordinate descent method with fixed or variable stepsizes.

Manifold regularized matrix completion for multilabel classification

Multilabel learning is an important research problem arising in a number of practical applications from diverse fields. Recent studies on multilabel learning have suggested the approach of matrix completion as a novel and promising approach to transductive multilabel learning. Here the missing labels of test data are regarded as missing values from the construction matrix composed of feature-by-item and label-by-item matrices. With the assumption of the low rank of the construction matrix, by minimizing its rank under the constraints of observed data and labels, we can recover all the missing labels. Despite its success, however, naive matrix completion methods ignore the smoothness assumption of the large amount of unlabel data, i.e., similar data should share similar labels, which may under exploit the intrinsic structure of data. To this end, we propose to solve the multi-label learning problem as an enhanced matrix completion problem with manifold regularization, where the graph Laplacian is used to ensuring the label smoothness over the label space. The resulting nuclear norm minimization problem is solved with a modified fixed-point continuation method that is guaranteed to find the global optimum. Experiments on both synthetic and real-world data have shown the promising results of the proposed approach.

Localization Algorithm for Wireless Sensor Networks via Norm Regularized Matrix Completion

Localization Algorithm for Wireless Sensor Networks via Norm Regularized Matrix Completion

A DCT Regularized Matrix Completion Algorithm for Energy Efficient Data Gathering in Wireless Sensor Networks

This paper presents a novel matrix completion algorithm to enable energy efficient data gathering in wireless sensor networks. The algorithm takes full advantage of both the low-rankness and the DCT compactness features in the sensory data to improve the recovery accuracy. The time complexity of the algorithm is analyzed, which indicates it has a low computational cost. Moreover, the recovery error is carefully analyzed and a theoretical upper bound is derived. The error bound is then validated by experimental results. Extensive experiments are conducted on three datasets collected from two testbeds. Experimental results show that the proposed algorithm outperforms state-of-the-art methods for low sampling rate and achieves a good recovery accuracy even if the sampling rate is very low.

Expert Finding for Question Answering via Graph Regularized Matrix Completion

Expert finding for question answering is a challenging problem in community-based question answering (CQA) systems, arising in many real applications such as question routing and identification of best answers. In order to provide high-quality experts, many existing approaches learn the user model from their past question-answering activities in CQA systems. However, the past activities of users in most CQA systems are rather few, and thus the user model may not be well inferred in practice. In this paper, we consider the problem of expert finding from the viewpoint of missing value estimation. We then employ users' social networks for inferring user model, and thus improve the performance of expert finding in CQA systems. In addition, we develop a novel graph-regularized matrix completion algorithm for inferring the user model. We further develop two efficient iterative procedures, GRMC-EGM and GRMC-AGM, to solve the optimization problem. GRMC-EGM utilizes the Extended Gradient Method (EGM), while GRMC-AGM applies the Accelerated proximal Gradient search Method (AGM), for the optimization. We evaluate our methods on the well-known question answering system Quora, and the popular social network Twitter. Our empirical study shows the effectiveness of the proposed algorithms in comparison to the state-of-the-art expert finding algorithms.