Related papers: Informed Non-convex Robust Principal Component Ana…

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…

In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…

In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex…

We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an…

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…

This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based…

Particle Image Velocimetry (PIV) data processing procedures are adversely affected by light reflections and backgrounds as well as defects in the models and sticky particles that occlude the inner walls of the boundaries. In this paper, a…

We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm,…

This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of matrices $\mathbf{D}=\mathbf{L}+\mathbf{S}$ where…

Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…

We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA. While previous works…

Robust principal component analysis (RPCA) is a powerful method for learning low-rank feature representation of various visual data. However, for certain types as well as significant amount of error corruption, it fails to yield…

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…

Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems that have composite objectives---this already includes the extensively studied convex, composite objective problems as a…

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…