Sequences of matrices with increasing size naturally arise in several contexts and especially
in the discretization of continuous problems, such as integral and differential equations. The …

We revisit the task of learning a Euclidean metric from data. We approach this problem from
first principles and formulate it as a surprisingly simple optimization problem. Indeed, our …

Abstract The Barzilai–Borwein (BB) method, an effective gradient descent method with
clever choice of the step length, is adapted from nonlinear optimization to Riemannian …

The symmetric eigenvalue decomposition and the singular value decomposition (SVD) are
fundamental matrix decompositions with many applications. Conventional algorithms for …

Signed networks allow to model positive and negative relationships. We analyze existing
extensions of spectral clustering to signed networks. It turns out that existing approaches do …

Multi-dimensional classification (MDC) refers to learning an association between individual
inputs and their multiple dimensional output discrete variables, and is thus more general …

As an effective method for XOR problems, generalized eigenvalue proximal support vector
machine (GEPSVM) recently has gained widespread attention accompanied with many …

We develop a new kind of nonnegativity certificate for univariate polynomials on an interval.
In many applications, nonnegative Bernstein coefficients are often used as a simple way of …

This paper is triggered by the preprint"\emph {Computing Matrix Squareroot via Non Convex
Local Search}" by Jain et al.(\textit {\textcolor {blue}{arXiv: 1507.05854}}), which analyzes …

We investigate different approaches for computing the action of the weighted geometric
mean of two large-scale positive definite matrices on a vector. We derive and analyze …