Related papers: Robust Principal Component Analysis?
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning,…
Robust principal component analysis seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimizing the sum of entrywise absolute residuals, leading to a…
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…
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…
In this paper, we consider 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 based on the recently proposed tensor-tensor product…
Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called REAPER, aims to find the principal components by solving a convex…
Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…
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…
Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
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…
The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…
Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known…
This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…
In computer vision most iterative optimization algorithms, both sparse and dense, rely on a coarse and reliable dense initialization to bootstrap their optimization procedure. For example, dense optical flow algorithms profit massively in…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…