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For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

Optimization and Control · Mathematics 2015-06-23 Weimin Miao , Shaohua Pan , Defeng Sun

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

Machine Learning · Computer Science 2009-11-04 Raghunandan H. Keshavan , Andrea Montanari , Sewoong Oh

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Machine Learning · Statistics 2022-05-17 Hsin-Hsiung Huang , Feng Yu , Xing Fan , Teng Zhang

We study the problem of symmetric positive semi-definite low-rank matrix completion (MC) with deterministic entry-dependent sampling. In particular, we consider rectified linear unit (ReLU) sampling, where only positive entries are…

Machine Learning · Computer Science 2024-06-11 Huikang Liu , Peng Wang , Longxiu Huang , Qing Qu , Laura Balzano

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…

Optimization and Control · Mathematics 2013-04-26 B. Mishra , G. Meyer , R. Sepulchre

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

Optimization and Control · Mathematics 2025-07-16 Lei Wang , Le Bao , Xin Liu

Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…

Machine Learning · Statistics 2020-01-28 Kaiyi Ji , Jian Tan , Jinfeng Xu , Yuejie Chi

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Optimization and Control · Mathematics 2024-04-08 Zhichun Yang , Fu-quan Xia , Kai Tu , Man-Chung Yue

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…

Machine Learning · Statistics 2022-12-12 Florentin Goyens , Coralia Cartis , Armin Eftekhari

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

Machine Learning · Statistics 2020-06-18 Lijun Ding , Yudong Chen

Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…

Machine Learning · Computer Science 2018-09-17 Zaiyi Chen

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…

Information Theory · Computer Science 2012-03-01 Arvind Ganesh , Kerui Min , John Wright , Yi Ma

We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…

Machine Learning · Computer Science 2026-04-14 Antonina Krajewska , Ewa Niewiadomska-Szynkiewicz

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…

Computer Vision and Pattern Recognition · Computer Science 2016-04-14 Ankit Parekh , Ivan W. Selesnick

We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and…

Information Theory · Computer Science 2016-09-20 Xinyang Yi , Dohyung Park , Yudong Chen , Constantine Caramanis

Matrix completion is one of the crucial tools in modern data science research. Recently, a novel sampling model for matrix completion coined cross-concentrated sampling (CCS) has caught much attention. However, the robustness of the CCS…

Machine Learning · Statistics 2025-04-17 HanQin Cai , Longxiu Huang , Chandra Kundu , Bowen Su

The low-rank matrix completion (LRMC) technology has achieved remarkable results in low-level visual tasks. There is an underlying assumption that the real-world matrix data is low-rank in LRMC. However, the real matrix data does not…

Computer Vision and Pattern Recognition · Computer Science 2024-07-23 Wenjing Lu , Zhuang Fang , Liang Wu , Liming Tang , Hanxin Liu , Chuanjiang He

The robust tensor completion (RTC) problem, which aims to reconstruct a low-rank tensor from partially observed tensor contaminated by a sparse tensor, has received increasing attention. In this paper, by leveraging the superior expression…

Computer Vision and Pattern Recognition · Computer Science 2021-10-19 Yun-Yang Liu , Xi-Le Zhao , Guang-Jing Song , Yu-Bang Zheng , Ting-Zhu Huang

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…

Machine Learning · Computer Science 2017-10-06 Paris V. Giampouras , Athanasios A. Rontogiannis , Konstantinos D. Koutroumbas

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

Statistics Theory · Mathematics 2015-09-11 Yudong Chen , Martin J. Wainwright