Related papers: A subspace method for large-scale trace ratio prob…
We propose an adaptive tracking algorithm where the object is modelled as a continuously updated bag of affine subspaces, with each subspace constructed from the object's appearance over several consecutive frames. In contrast to linear…
We present a method based on Dickson's lemma to compute the "approximate radical" of a zero dimensional ideal I in C[x1, . . ., xm] which has zero clusters: the approximate radical ideal has exactly one root in each cluster for sufficiently…
The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the…
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…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…
We introduce an innovative method for incremental nonparametric probabilistic inference in high-dimensional state spaces. Our approach leverages \slices from high-dimensional surfaces to efficiently approximate posterior distributions of…
The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…
This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…
We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves iteratively a sequence of auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from…
There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to…
The symplectic eigenvalue problem for symmetric positive-definite (spd) matrices plays a crucial role in various scientific fields, including quantum mechanics and control theory. This paper introduces a trace-penalty minimization method,…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…
Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…
The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an…
This paper studies the problem of completing a low-rank matrix from a few of its random entries with the aid of prior information. We suggest a strategy to incorporate prior information into the standard matrix completion procedure by…