4 citations · 13 across the 11 of their papers we have counts for
12 papers
The Exponential of Skew-Symmetric Matrices: A Nearby Inverse and Efficient Computation of Derivatives
Zhifeng Deng, P. -A. Absil, Kyle A. Gallivan +1
The matrix exponential restricted to skew-symmetric matrices has numerous applications, notably in view of its interpretation as the Lie group exponential and Riemannian exponentia…
First-order optimization on stratified sets
Guillaume Olikier, Kyle A. Gallivan, P. -A. Absil
We consider the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on a stratified set and present a first-order algorithm designed to find…
Scalable Clustering: Large Scale Unsupervised Learning of Gaussian Mixture Models with Outliers
Yijia Zhou, Kyle A. Gallivan, Adrian Barbu
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theo…
A Riemannian Optimization Approach to Clustering Problems
Wen Huang, Meng Wei, Kyle A. Gallivan +1
This paper considers the optimization problem in the form of where is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X…
On the analysis of optimization with fixed-rank matrices: a quotient geometric view
Shuyu Dong, Bin Gao, Wen Huang +1
We study a type of Riemannian gradient descent (RGD) algorithm, designed through Riemannian preconditioning, for optimization on -- the set of $m\times…
Comparison of an Apocalypse-Free and an Apocalypse-Prone First-Order Low-Rank Optimization Algorithm
Guillaume Olikier, Kyle A. Gallivan, P. -A. Absil
We compare two first-order low-rank optimization algorithms, namely (Schneider and Uschmajew, 2015), which has been proven to be apocalypse-prone (Levin et al…