Related papers: Riemannian CUR Decompositions for Robust Principal…

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

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…

This work studies the recursive robust principal components' analysis(PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers. If the outlier is the signal-of-interest, this problem can be…

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…

Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods…

Principal component analysis (PCA) is widely used to analyze high-dimensional data, but it is very sensitive to outliers. Robust PCA methods seek fits that are unaffected by the outliers and can therefore be trusted to reveal them. FastHCS…

The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to…

Matrix completion is one of the crucial tools in modern data science research. Recently, a novel sampling model for matrix completion coined cross-concentrated sampling (CCS) has caught much attention. However, the robustness of the CCS…

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…

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…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or…

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) has been widely used for recovering low-rank matrices in many data mining and machine learning problems. It separates a data matrix into a low-rank part and a sparse part. The convex approach has…

This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge…