Related papers: A Consistently Oriented Basis for Eigenanalysis: I…
Repeated application of machine-learning, eigen-centric methods to an evolving dataset reveals that eigenvectors calculated by well-established computer implementations are not stable along an evolving sequence. This is because the sign of…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…
In this study, we propose a novel extended target tracking algorithm which is capable of representing the extent of dynamic objects as an ellipsoid with a time-varying orientation angle. A diagonal positive semi-definite matrix is defined…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polynomials. We give a backwards stability result which can be…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
Many problems in physics, chemistry and other fields are perturbative in nature, i.e. differ only slightly from related problems with known solutions. Prominent among these is the eigenvalue perturbation problem, wherein one seeks the…
We present a novel angular fingerprinting algorithm for detecting changes in the direction of rotation of a target with a monostatic, stationary sonar platform. Unlike other approaches, we assume that the target's centroid is stationary,…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
Estimating the head pose of a person is a crucial problem for numerous applications that is yet mainly addressed as a subtask of frontal pose prediction. We present a novel method for unconstrained end-to-end head pose estimation to tackle…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…