Related papers: Tensor Principal Component Analysis via Convex Opt…
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…
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…
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…
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
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…
Tensor robust principal component analysis (TRPCA) is a classical way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular value equally. However, for real-world visual data,…
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…
We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…
We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact}…
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…
Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…
The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such…
We study extensions of compressive sensing and low rank matrix recovery to the recovery of low rank tensors from incomplete linear information. While the reconstruction of low rank matrices via nuclear norm minimization is rather…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
Principal Component Analysis (PCA) is a widely used method for dimensionality reduction, but it often overlooks fairness, especially when working with data that includes demographic characteristics. This can lead to biased representations…