Related papers: Strongly Convex Programming for Principal Componen…

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…

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…

Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two…

We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both…

We consider the decomposition of a data matrix assumed to be a superposition of a low-rank matrix and a component which is sparse in a known dictionary, using a convex demixing method. We consider two sparsity structures for the sparse…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

Principal component pursuit (PCP) is a state-of-the-art approach for background estimation problems. Due to their higher computational cost, PCP algorithms, such as robust principal component analysis (RPCA) and its variants, are not…

We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…

In this paper, we revisit the problem of local optimization in RANSAC. Once a so-far-the-best model has been found, we refine it via Dual Principal Component Pursuit (DPCP), a robust subspace learning method with strong theoretical support…

We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…

We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank…