Related papers: Factor Fitting, Rank Allocation, and Partitioning …
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…
The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…
This paper is concerned with factor left prime factorization problems for multivariate polynomial matrices without full row rank. We propose a necessary and sufficient condition for the existence of factor left prime factorizations of a…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
Machine learning techniques for Recommendation System (RS) and Classification has become a prime focus of research to tackle the problem of information overload. RS are software tools that aim at making informed decisions about the services…
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…
The components underpinning PLMs -- large weight matrices -- were shown to bear considerable redundancy. Matrix factorization, a well-established technique from matrix theory, has been utilized to reduce the number of parameters in PLM.…
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented. The key idea is to establish a relationship between a matrix and its full…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
We examine a special case of the multilevel factor model, with covariance given by multilevel low rank (MLR) matrix~\cite{parshakova2023factor}. We develop a novel, fast implementation of the expectation-maximization algorithm, tailored for…
A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…
Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational…
In this work, we present randomized compression algorithms for flat rank-structured matrices with shared bases, termed uniform Block Low-Rank (BLR) matrices. Our main contribution is a technique called tagging, which improves upon the…