Related papers: Vector-wise Joint Diagonalization of Almost Commut…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
In this article, we propose a quasi-Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The set-valued objective mapping under consideration is given by a…
In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
We design an additive approximation scheme for estimating the cost of the min-weight bipartite matching problem: given a bipartite graph with non-negative edge costs and $\varepsilon > 0$, our algorithm estimates the cost of matching all…
We present the design and analysis of a near linear-work parallel algorithm for solving symmetric diagonally dominant (SDD) linear systems. On input of a SDD $n$-by-$n$ matrix $A$ with $m$ non-zero entries and a vector $b$, our algorithm…
This paper deals with a hybrid joint diagonalization (JD) problem considering both Hermitian and transpose congruences. Such problem can be encountered in certain non-circular signal analysis applications including blind source separation.…
We develop a framework which allows us to prove the essential general quasi-orthogonality for the non-symmetric Johnson-Nedelec finite element/boundary element coupling. General quasi-orthogonality was first proposed in [Axioms of…
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…
We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…