Related papers: Robust Matrix Completion via Maximum Correntropy C…

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…

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observation with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the…

Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…

Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a…

We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which…

Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this…

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

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…

The common task in matrix completion (MC) and robust principle component analysis (RPCA) is to recover a low-rank matrix from a given data matrix. These problems gained great attention from various areas in applied sciences recently,…

Nonnegative matrix factorization (NMF) has been successfully applied to many areas for classification and clustering. Commonly-used NMF algorithms mainly target on minimizing the $l_2$ distance or Kullback-Leibler (KL) divergence, which may…

In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…

Sparse adaptive channel estimation problem is one of the most important topics in broadband wireless communications systems due to its simplicity and robustness. So far many sparsity-aware channel estimation algorithms have been developed…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error…

The maximum correntropy criterion (MCC) has been employed to design outlier-robust adaptive filtering algorithms, among which the recursive MCC (RMCC) algorithm is a typical one. Motivated by the success of our recently proposed…

Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and…

In this paper we study how the choice of loss functions of non-convex optimization problems affects their robustness and optimization landscape, through the study of noisy matrix sensing. In traditional regression tasks, mean squared error…