Related papers: Tensor Robust Principal Component Analysis with A …
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…
The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data…
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…
In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…
Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…
The nuclear norm and Schatten-$p$ quasi-norm are popular rank proxies in low-rank matrix recovery. However, computing the nuclear norm or Schatten-$p$ quasi-norm of a tensor is hard in both theory and practice, hindering their application…
Low-rank tensor recovery has attracted much attention among various tensor recovery approaches. A tensor rank has several definitions, unlike the matrix rank--e.g. the CP rank and the Tucker rank. Many low-rank tensor recovery methods are…
Recovering intrinsic low dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, there has been a lot of work that models subspace recovery as low rank minimization problems. We…
Principal Component Analysis (PCA) is well known for its capability of dimension reduction and data compression. However, when using PCA for compressing/reconstructing images, images need to be recast to vectors. The vectorization of images…
This work is concerned with the non-negative rank-1 robust principal component analysis (RPCA), where the goal is to recover the dominant non-negative principal components of a data matrix precisely, where a number of measurements could be…
Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…