This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of recovering a large matrix from a small subset of its entries (the famous Netflix problem). Off-the-sh...

An unknown m by n matrix X0 is to be estimated from noisy measurements Y = X0 + Z, where the noise matrix Z has i.i.d Gaussian entries. A popular matrix denoising scheme solves the nuclear norm penalization problem minX‖Y − X‖F /2 + λ‖X‖∗, where ‖X‖∗ denotes the nuclear norm (sum of singular values). This is the analog, for matrices, of `1 penalization in the vector case. It has been empiricall...

This paper describes a new algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex optimization formulation with a cost function consisting of the sum of a likelihood function and a regularization function which the nuclear norm of the matrix...

This paper presents a fast model-agnosticmethod for recovering noisy Phasor Measurement Unit (PMU) data streams with missing entries. The measurements are first transformed into Page matrix, and the original signals reconstructed using low-rank matrix estimation based on optimal singular value thresholding. Two variations of recovery algorithm shown- a) an offline block-processing method imputi...

This paper proposes a proximal iteratively reweighted algorithm to recover a low-rank matrix based on the weighted fixed point method. The weighted singular value thresholding problem gains a closed form solution because of the special properties of nonconvex surrogate functions. Besides, this study also has shown that the proximal iteratively reweighted algorithm lessens the objective function...

In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate—holding in a Gaussian model—for any spectral estimator obeying some mild regularity assumptions. In particular, we give an unbiased risk estimate formula for singular value thresholding (SVT), a popular estimation stra...

Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of feature selection in which only a subset of the predictors Xt are dependent on the multidimensional variate Y , and the remainder of the predictors constitute a “noise set” Xu independent of Y . Using Monte Carlo simulations, we investigated the relative perfor...

Singular value decomposition is a widely used tool for dimension reduction in multivariate analysis. However, when used for statistical estimation in high-dimensional low rank matrix models, singular vectors of the noise-corrupted matrix are inconsistent for their counterparts of the true mean matrix. In this talk, we suppose the true singular vectors have sparse representations in a certain ba...