Related papers: A Novel M-Estimator for Robust PCA

The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties…

Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate…

Analyzing principal components for multivariate data from its spatial sign covariance matrix (SCM) has been proposed as a computationally simple and robust alternative to normal PCA, but it suffers from poor efficiency properties and is…

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…

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

In this paper, we propose a cone projected power iteration algorithm to recover the first principal eigenvector from a noisy positive semidefinite matrix. When the true principal eigenvector is assumed to belong to a convex cone, the…

This work analyzes the subspace-constrained Tyler's estimator (STE), a method designed to recover a low-dimensional subspace from a dataset that may be heavily corrupted by outliers. The STE has previously been shown to be competitive for…

In this paper, we explore the theoretical properties of subspace recovery using Winsorized Principal Component Analysis (WPCA), utilizing a common data transformation technique that caps extreme values to mitigate the impact of outliers.…

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…

We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…

This work studies the robust subspace tracking (ST) problem. Robust ST can be simply understood as a (slow) time-varying subspace extension of robust PCA. It assumes that the true data lies in a low-dimensional subspace that is either fixed…

Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…

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…

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…

The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

In this paper we initiate the study of whether or not sparse estimation tasks can be performed efficiently in high dimensions, in the robust setting where an $\eps$-fraction of samples are corrupted adversarially. We study the natural…

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…