相关论文: An Inverse-free Truncated Rayleigh-Ritz Method for…

We present a novel technique for sparse principal component analysis. This method, named Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…

Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…

There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…

Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…

In this paper we develop efficient first-order algorithms for the generalized trust-region subproblem (GTRS), which has applications in signal processing, compressed sensing, and engineering. Although the GTRS, as stated, is nonlinear and…

We examine a method for solving an infinite-dimensional tensor eigenvalue problem $H x = \lambda x$, where the infinite-dimensional symmetric matrix $H$ exhibits a translational invariant structure. We provide a formulation of this type of…

The central importance of large scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine…

A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…

EEG-based Emotion recognition holds significant promise for applications in human-computer interaction, medicine, and neuroscience. While deep learning has shown potential in this field, current approaches usually rely on large-scale…

Sparse representation-based classification (SRC) has attracted much attention by casting the recognition problem as simple linear regression problem. SRC methods, however, still is limited to enough labeled samples per category,…

We consider regularized least-squares problems of the form $\min_{x} \frac{1}{2}\Vert Ax - b\Vert_2^2 + \mathcal{R}(Lx)$. Recently, Zheng et al., 2019, proposed an algorithm called Sparse Relaxed Regularized Regression (SR3) that employs a…

The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…

The residual cutting (RC) method has been proposed as an outer-inner loop iteration for efficiently solving large and sparse linear systems of equations arising in solving numerically problems of elliptic partial differential equations.…

Phase retrieval (PR) is an ill-conditioned inverse problem which can be found in various science and engineering applications. Assuming sparse priority over the signal of interest, recent algorithms have been developed to solve the phase…

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced…

This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method.…

Given a graph $G$, one may ask: "What sets of eigenvalues are possible over all weighted adjacency matrices of $G$?" (The weight of an edge is positive or negative, while the diagonal entries can be any real numbers.) This is known as the…

This paper addresses the Kidnapped Robot Problem (KRP), a core localization challenge of relocalizing a robot in a known map without prior pose estimate upon localization loss or at SLAM initialization. For this purpose, a passive 2-D…