相关论文: Two-way Spectrum Pursuit for CUR Decomposition and…

We consider the problem of learning a linear subspace from data corrupted by outliers. Classical approaches are typically designed for the case in which the subspace dimension is small relative to the ambient dimension. Our approach works…

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces…

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…

CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…

We extend the theoretical analysis of a recently proposed single subspace learning algorithm, called Dual Principal Component Pursuit (DPCP), to the case where the data are drawn from of a union of hyperplanes. To gain insight into the…

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…

This paper develops column partition based distributed schemes for a class of large-scale convex sparse optimization problems, e.g., basis pursuit (BP), LASSO, basis pursuit denosing (BPDN), and their extensions, e.g., fused LASSO. We are…

In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…

This paper studies the subspace clustering problem in which data points collected from high-dimensional ambient space lie in a union of linear subspaces. Subspace clustering becomes challenging when the dimension of intersection between…

A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset…

The energy efficiency of future networks is becoming a significant and urgent issue, calling for greener network designs. At the same time, rapid development of wireless networks shows a trend of increasing complexity in network structure…

The inclusion of spatial information into spectral classifiers for fine-resolution hyperspectral imagery has led to significant improvements in terms of classification performance. The task of spectral-spatial hyperspectral image…

Based on the Scale-Splitting (SCSP) iteration method presented by Hezari et al. in (A new iterative method for solving a class of complex symmetric system linear of equations, Numerical Algorithms 73 (2016) 927-955), we present a new…

The widespread adoption of mobile communication technology has led to a severe shortage of spectrum resources, driving the development of cognitive radio technologies aimed at improving spectrum utilization, with spectrum sensing being the…

Spectrum sensing is an essential enabling functionality for cognitive radio networks to detect spectrum holes and opportunistically use the under-utilized frequency bands without causing harmful interference to legacy networks. This paper…

A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…

Recent methods for learning a linear subspace from data corrupted by outliers are based on convex $\ell_1$ and nuclear norm optimization and require the dimension of the subspace and the number of outliers to be sufficiently small. In sharp…

The Minimum Set Cover Problem (MSCP) is a classical NP-hard combinatorial optimization problem with numerous applications in science and engineering. Although a wide range of exact, approximate, and metaheuristic approaches have been…

Sparse matrix coloring and bicoloring are fundamental building blocks of sparse automatic differentiation. Bicoloring is particularly advantageous for rectangular Jacobian matrices with at least one dense row and column. Indeed, in such…

The problem of finding the sparsest solution to a linear underdetermined system of equations, often appearing, e.g., in data analysis, optimal control, system identification, or sensor selection problems, is considered. This non-convex…