Related papers: DeepVir -- Graphical Deep Matrix Factorization for…
In this work, we address the solution of both linear and nonlinear ill-posed inverse problems by developing a novel graph-based regularization framework, where the regularization term is formulated through an iteratively updated graph…
We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their…
We present EDIpack, an exact diagonalization package to solve generic quantum impurity problems. The algorithm includes a generalization of the look-up method introduced in [Lin, Gubernatis Comput. Phys., 7 (4) (1993), 400] and enables a…
The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion…
In cognitive neuroscience research, Representational Dissimilarity Matrices (RDMs) are often incomplete because pairwise similarity judgments cannot always be exhaustively collected as the number of pairs rapidly increases with the number…
Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…
The fast evolution of SARS-CoV-2 and other infectious viruses poses a grand challenge to the rapid response in terms of viral tracking, diagnostics, and design and manufacture of monoclonal antibodies (mAbs) and vaccines, which are both…
Efficiently solving sparse linear systems $Ax=b$, where $A$ is a large, sparse, symmetric positive semi-definite matrix, is a core challenge in scientific computing, machine learning, and optimization. A major bottleneck in Gaussian…
Recommender system is the most successful commercial technology in the past decade. Technical mammoth such as Temu, TikTok and Amazon utilize the technology to generate enormous revenues each year. Although there have been enough research…
We introduce a software package called HIFIR for preconditioning sparse, unsymmetric, ill-conditioned, and potentially singular systems. HIFIR computes a hybrid incomplete factorization, which combines multilevel incomplete LU factorization…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…
Medical image analysis using computer-based algorithms has attracted considerable attention from the research community and achieved tremendous progress in the last decade. With recent advances in computing resources and availability of…
We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…
Many processes, from gene interaction in biology to computer networks to social media, can be modeled more precisely as temporal hypergraphs than by regular graphs. This is because hypergraphs generalize graphs by extending edges to connect…
Partitioning sparse matrices and graphs is a common and important problem in many scientific and graph analytics applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as…
Currently, the number of patients with COVID-19 has significantly increased. Thus, there is an urgent need for developing treatments for COVID-19. Drug repurposing, which is the process of reusing already-approved drugs for new medical…
We introduce an algorithmic framework for performing QR factorization with column pivoting (QRCP) on general matrices. The framework enables the design of practical QRCP algorithms through user-controlled choices for the core subroutines.…
We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal), motivated by recent advances in near-term quantum computing hardware and the related embedding problems. We assemble a preprocessing…