相关论文: A Comparative Study for the Nuclear Norms Minimiza…

We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…

The acquisition of MRI images offers a trade-off in terms of acquisition time, spatial/temporal resolution and signal-to-noise ratio (SNR). Thus, for instance, increasing the time efficiency of MRI often comes at the expense of reduced SNR.…

Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in…

Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…

The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…

Group sparse representation (GSR) based method has led to great successes in various image recovery tasks, which can be converted into a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm…

Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…

This paper considers the problem of minimizing the sum of a smooth function and the Schatten-$p$ norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the…

This paper describes a new algorithm for computing Nonnegative Low Rank Matrix (NLRM) approximation for nonnegative matrices. Our approach is completely different from classical nonnegative matrix factorization (NMF) which has been studied…

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…

Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of…

Weighted nuclear norm minimization has been recently recognized as a technique for reconstruction of a low-rank matrix from compressively sampled measurements when some prior information about the column and row subspaces of the matrix is…

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…

Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore,…

It is an efficient and effective strategy to utilize the nuclear norm approximation to learn low-rank matrices, which arise frequently in machine learning and computer vision. So the exploration of nuclear norm minimization problems is…

Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…

This study evaluates thresholds for removing singular values from singular value decomposition-based low-rank approximations of deep neural network weight matrices. Each weight matrix is modeled as the sum of signal and noise matrices. The…

Group-prior based regularization method has led to great successes in various image processing tasks, which can usually be considered as a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear…

The rank minimization problem is to find the lowest-rank matrix in a given set. Nuclear norm minimization has been proposed as an convex relaxation of rank minimization. Recht, Fazel, and Parrilo have shown that nuclear norm minimization…

We present a novel family of language model (LM) estimation techniques named Sparse Non-negative Matrix (SNM) estimation. A first set of experiments empirically evaluating it on the One Billion Word Benchmark shows that SNM $n$-gram LMs…