Related papers: Generalized Low-Rank Matrix Completion Model with …
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…
Given a matrix $M\in \mathbb{R}^{m\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\top$ for $U\in \mathbb{R}^{m\times k}$ and $V\in \mathbb{R}^{n\times k}$ by only observing a few…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
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 singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from…
Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Missing values challenge data analysis because many supervised and unsupervised learning methods cannot be applied directly to incomplete data. Matrix completion based on low-rank assumptions are very powerful solution for dealing with…
Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…
Matrix completion is fundamental for predicting missing data with a wide range of applications in personalized healthcare, e-commerce, recommendation systems, and social network analysis. Traditional matrix completion approaches typically…
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…
Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method…
Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under…
We study a matrix completion problem where both the ground truth $R$ matrix and the unknown sampling distribution $P$ over observed entries are low-rank matrices, and \textit{share a common subspace}. We assume that a large amount $M$ of…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
We propose orthogonal inductive matrix completion (OMIC), an interpretable approach to matrix completion based on a sum of multiple orthonormal side information terms, together with nuclear-norm regularization. The approach allows us to…
Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods…
Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…