Related papers: Exact Recovery of Tensor Robust Principal Componen…
We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
Robust Principal Component Analysis (PCA) has received massive attention in recent years. It aims to recover a low-rank matrix and a sparse matrix from their sum. This paper proposes a novel nonconvex Robust PCA algorithm, coined Riemannian…
We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value…
The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
Various problems in data analysis and statistical genetics call for recovery of a column-sparse, low-rank matrix from noisy observations. We propose ReFACTor, a simple variation of the classical Truncated Singular Value Decomposition (TSVD)…
The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics…
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,…
To do dimensionality reduction on the datasets with outliers, the $\ell_1$-norm principal component analysis (L1-PCA) as a typical robust alternative of the conventional PCA has enjoyed great popularity over the past years. In this work, we…
Tensor sparse modeling as a promising approach, in the whole of science and engineering has been a huge success. As is known to all, various data in practical application are often generated by multiple factors, so the use of tensors to…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low…
Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…
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…