Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space,
which has been shown to incur a large distortion when embedding real-world graphs with …

Abstract Representation learning has become an invaluable approach for learning from
symbolic data such as text and graphs. However, state-of-the-art embedding methods …

▶ Distortion of a pair of points a, b is| dV (f (a), f (b))− dU (a, b)|/dU (a, b). Average distortion
Davg is the average over all pairs of points.▶ mean Average Precision (mAP). Let G=(V, E) …

We introduce a novel approach to perform first-order optimization with orthogonal and
unitary constraints. This approach is based on a parametrization stemming from Lie group …

We consider the minimization of a cost function f on a manifold using Riemannian gradient
descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality …

Manifold optimization is ubiquitous in computational and applied mathematics, statistics,
engineering, machine learning, physics, chemistry, etc. One of the main challenges usually …

We introduce a framework to study the transformation of problems with manifold constraints
into unconstrained problems through parametrizations in terms of a Euclidean space. We …

We consider optimization problems over the Stiefel manifold whose objective function is the
summation of a smooth function and a nonsmooth function. Existing methods for solving this …

Conjugate gradient methods are important first-order optimization algorithms both in
Euclidean spaces and on Riemannian manifolds. However, while various types of conjugate …