相关论文: An Accelerated Alternating Partial Bregman Algorit…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

This paper presents a nonlinear model reduction method for systems of equations using a structured neural network. The neural network takes the form of a "three-layer" network with the first layer constrained to lie on the Grassmann…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth…

We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the…

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs…

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used…

Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product of two much smaller matrices. In this paper, we study the…

Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers…

Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear…

Activation functions play a key role in providing remarkable performance in deep neural networks, and the rectified linear unit (ReLU) is one of the most widely used activation functions. Various new activation functions and improvements on…

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 this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…

Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced…

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the…

We develop an accelerated algorithm for computing an approximate eigenvalue decomposition of bistochastic normalized kernel matrices. Our approach constructs a low rank approximation of the original kernel matrix by the pivoted partial…