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Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques,…
Non-negative matrix factorization (NMF) has become a popular method for representing meaningful data by extracting a non-negative basis feature from an observed non-negative data matrix. Some of the unique features of this method in…
Matrix Factorization is a widely adopted technique in the field of recommender system. Matrix Factorization techniques range from SVD, LDA, pLSA, SVD++, MatRec, Zipf Matrix Factorization and Item2Vec. In recent years, distributed word…
Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
We introduce a new fundamental algorithm called Matrix-POAFD to solve the matrix least square problem. The method is based on the matching pursuit principle. The method directly extracts, among the given features as column vectors of the…
This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column sparsity of…
Matrix factorization is a fundamental method in statistics and machine learning for inferring and summarizing structure in multivariate data. Modern data sets often come with "side information" of various forms (images, text, graphs) that…
The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the…
In this work, we propose a novel discrete-time distributed algorithm for finding least-squares solutions of linear algebraic equations with a scheduling protocol to further enhance its scalability. Each agent in the network is assumed to…
We propose a novel methodology for forecasting spatio-temporal data using supervised semi-nonnegative matrix factorization (SSNMF) with frequency regularization. Matrix factorization is employed to decompose spatio-temporal data into…