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Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be…
The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…
The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem's feasible space. This paper presents an…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is…
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…
This paper presents a quantum-enhanced optimization approach for solving optimal power flow (OPF) by integrating the interior point method (IPM) with a coherent variational quantum linear solver (CVQLS). The objective is to explore the…
Graphical models have found widespread applications in many areas of modern statistics and machine learning. Iterative Proportional Fitting (IPF) and its variants have become the default method for undirected graphical model estimation, and…
Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…
The need to estimate a positive definite solution to an overdetermined linear system of equations with multiple right hand side vectors arises in several process control contexts. The coefficient and the right hand side matrices are…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is…
We propose a novel numerical approach to compute the Pareto front in multivariate polynomial multi-objective optimization problems. When the objective functions and (equality) constraints are multivariate polynomials, the Pareto front,…
This work explores non-negative low-rank matrix factorization based on regularized Poisson models (PF or "Poisson factorization" for short) for recommender systems with implicit-feedback data. The properties of Poisson likelihood allow a…
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset…
This paper proposes a learning-based approach to accelerate the interior-point method (IPM) for solving optimal power flow (OPF) problems by learning the structure of the IPM central path from its early stable iterations. Unlike traditional…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…
Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn…
Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different…