Related papers: Dimensionality Reduction on Grassmannian via Riema…

This work puts forth low-complexity Riemannian subspace descent algorithms for the minimization of functions over the symmetric positive definite (SPD) manifold. Different from the existing Riemannian gradient descent variants, the proposed…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.

Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannian and sub-Riemannian geometries in a comprehensive framework…

Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

In this paper, we revamp the forgotten classical Semi-Supervised Distance Metric Learning (SSDML) problem from a Riemannian geometric lens, to leverage stochastic optimization within a end-to-end deep framework. The motivation comes from…

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

Manifold learning techniques for nonlinear dimension reduction assume that high-dimensional feature vectors lie on a low-dimensional manifold, then attempt to exploit manifold structure to obtain useful low-dimensional Euclidean…

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

This paper presents a Riemannian metric-based model to solve the optimal path planning problem on two-dimensional smooth submanifolds in high-dimensional space. Our model is based on constructing a new Riemannian metric on a two-dimensional…

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…

We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of $L$-smooth and geodesically convex (g-convex) or $\mu$-strongly g-convex…

Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after…

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change…

We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient…

Gradient descent with momentum has been widely applied in various signal processing and machine learning tasks, demonstrating a notable empirical advantage over standard gradient descent. However, momentum-based distributed Riemannian…