Related papers: Robust and Efficient Subspace Segmentation via Lea…

Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain…

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…

Deep neural networks have exhibited remarkable performance in image super-resolution (SR) tasks by learning a mapping from low-resolution (LR) images to high-resolution (HR) images. However, the SR problem is typically an ill-posed problem…

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…

The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. Focusing on data matrices that are simultaneously row-sparse and low-rank, we propose…

In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…

Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often…

In this work, we address the following matrix recovery problem: suppose we are given a set of data points containing two parts, one part consists of samples drawn from a union of multiple subspaces and the other part consists of outliers.…

We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…

Localizing more sources than sensors with a sparse linear array (SLA) has long relied on minimizing a distance between two covariance matrices and recent algorithms often utilize semidefinite programming (SDP). Although deep neural network…

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…

The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…

In this paper, we investigate the impact of compression on stochastic gradient algorithms for machine learning, a technique widely used in distributed and federated learning. We underline differences in terms of convergence rates between…

The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…

Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…