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Motivated by recent progress in quantum technologies and in particular quantum software, research and industrial communities have been trying to discover new applications of quantum algorithms such as quantum optimization and machine…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
Boolean matrix factorization (BMF) is a fundamental tool for analyzing binary data and discovering latent information hidden in the data. Formal Concept Analysis (FCA) provides us with an essential insight into BMF and the design of…
In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain…
Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens of dual-graph regularization, which has significantly improved the performance of multidisciplinary machine learning tasks…
Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
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…
Recommender system recommends interesting items to users based on users' past information history. Researchers have been paying attention to improvement of algorithmic performance such as MAE and precision@K. Major techniques such as matrix…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…
Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared…
Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…