Related papers: Advancing Matrix Completion by Modeling Extra Stru…
In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
The recently established RPCA method provides us a convenient way to restore low-rank matrices from grossly corrupted observations. While elegant in theory and powerful in reality, RPCA may be not an ultimate solution to the low-rank matrix…
We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…
Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random…
We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of…
There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient…
This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and…
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…
Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared…
This paper approaches high-rank matrix completion (HRMC) by filling missing entries in a data matrix where columns lie near a union of subspaces, clustering these columns, and identifying the underlying subspaces. Current methods often lack…
In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…
In this paper, we present a flexible low-rank matrix completion (LRMC) approach for topological interference management (TIM) in the partially connected K-user interference channel. No channel state information (CSI) is required at the…
The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization;…
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the…
In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…
The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators…