Nonlinear Traffic Prediction as a Matrix Completion Problem with Ensemble Learning

This paper addresses the problem of short-term traffic prediction for signalized traffic operations management. Specifically, we focus on predicting sensor states in high-resolution (second-by-second). This contrasts with traditional traffic forecasting problems, which have focused on predicting aggregated traffic variables, typically over intervals that are no shorter than five minutes. Our contributions can be summarized as offering three insights: first, we show how the prediction problem can be modeled as a matrix completion problem. Second, we use a block-coordinate descent algorithm and demonstrate that the algorithm converges in sublinear time to a block coordinate-wise optimizer. This allows us to capitalize on the “bigness” of high-resolution data in a computationally feasible way. Third, we develop an ensemble learning (or adaptive boosting) approach to reduce the training error to within any arbitrary error threshold. The latter uses past days so that the boosting can be interpreted as capturing periodic patterns in the data. The performance of the proposed method is analyzed theoretically and tested empirically using both simulated data and a real-world high-resolution traffic data set from Abu Dhabi, United Arab Emirates. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms.

A Riemannian rank-adaptive method for low-rank matrix completion

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the optimization problem on the set of bounded-rank matrices. We propose a Riemannian rank-adaptive method, which consists of fixed-rank optimization, rank increase step and rank reduction step. We explore its performance applied to the low-rank matrix completion problem. Numerical experiments on synthetic and real-world datasets illustrate that the proposed rank-adaptive method compares favorably with state-of-the-art algorithms. In addition, it shows that one can incorporate each aspect of this rank-adaptive framework separately into existing algorithms for the purpose of improving performance.

Medical Image Denoising Via Matrix Norm Minimization Problems

This paper presents the matrix completion problem for image denoising. Three problems based on matrix norm are performing: Spectral norm minimization problem (SNP), Nuclear norm minimization problem (NNP), and Weighted nuclear norm minimization problem (WNNP). In general, images representing by a matrix this matrix contains the information of the image, some information is irrelevant or unfavorable, so to overcome this unwanted information in the image matrix, information completion is used to comperes the matrix and remove this unwanted information. The unwanted information is handled by defining {0,1}-operator under some threshold. Applying this operator on a given matrix keeps the important information in the image and removing the unwanted information by solving the matrix completion problem that is defined by P. The quadratic programming use to solve the given three norm-based minimization problems. To improve the optimal solution a weighted exponential is used to compute the weighted vector of spectral that use to improve the threshold of optimal low rank that getting from solving the nuclear norm and spectral norm problems. The result of applying the proposed method on different types of images is given by adopting some metrics. The results showed the ability of the given methods.

Robust Matrix Completion By Exploiting Dynamic Low-Dimensional Structures

This paper studies the robust matrix completion problem for time-varying models. Leveraging the low-rank property and the temporal information of the data, we develop novel methods to recover the original data from partially observed and corrupted measurements. We show that the reconstruction performance can be improved if one further leverages the information of the sparse corruptions in addition to the temporal correlations among a sequence of matrices. The dynamic robust matrix completion problem is formulated as a nonconvex optimization problem, and the recovery error is quantified analytically and proved to decay in the same order as that of the state-of-the-art method when there is no corruption. A fast iterative algorithm with convergence guarantee to the stationary point is proposed to solve the nonconvex problem. Experiments on synthetic data and real video dataset demonstrate the effectiveness of our method.

Speech Recognition: B

Online learning algorithms update their estimates as additional observations are made. Section 12.1 explains a simple example: online linear regression. The stochastic gradient projection algorithm is a general technique to update estimates based on additional observations; it is widely used in machine learning. Section 12.2 presents the theory behind that algorithm. When analyzing large amounts of data, one faces the problems of identifying the most relevant data and of how to use efficiently the available data. Section 12.3 explains three examples of how these questions are addressed: the LASSO algorithm, compressed sensing, and the matrix completion problem. Section 12.4 discusses deep neural networks for which the stochastic gradient projection algorithm is easy to implement.

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

This work formulates antiviral repositioning as a matrix completion problem where the antiviral drugs are along the rows and the viruses along the columns. The input matrix is partially filled, with ones in positions where the antiviral has been known to be effective against a virus. The curated metadata for antivirals (chemical structure and pathways) and viruses (genomic structure and symptoms) is encoded into our matrix completion framework as graph Laplacian regularization. We then frame the resulting multiple graph regularized matrix completion problem as deep matrix factorization. This is solved by using a novel optimization method called HyPALM (Hybrid Proximal Alternating Linearized Minimization). Results on our curated RNA drug virus association (DVA) dataset shows that the proposed approach excels over state-of-the-art graph regularized matrix completion 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 for trials for the same.<br>

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

This work formulates antiviral repositioning as a matrix completion problem where the antiviral drugs are along the rows and the viruses along the columns. The input matrix is partially filled, with ones in positions where the antiviral has been known to be effective against a virus. The curated metadata for antivirals (chemical structure and pathways) and viruses (genomic structure and symptoms) is encoded into our matrix completion framework as graph Laplacian regularization. We then frame the resulting multiple graph regularized matrix completion problem as deep matrix factorization. This is solved by using a novel optimization method called HyPALM (Hybrid Proximal Alternating Linearized Minimization). Results on our curated RNA drug virus association (DVA) dataset shows that the proposed approach excels over state-of-the-art graph regularized matrix completion 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 for trials for the same.<br>

The Q0-matrix completion problem

A matrix is a Q0-matrix if for every k∈{1,2,…,n}, the sum of all k×k principal minors is nonnegative. In this paper, we study some necessary and sufficient conditions for a digraph to have Q0-completion. Later on we discuss the relationship between Q and Q0-matrix completion problem. Finally, a classification of the digraphs of order up to four is done based on Q0-completion.