Search Results for author: Andi Han

Found 6 papers, 2 papers with code

Generalized Bures-Wasserstein Geometry for Positive Definite Matrices

1 code implementation20 Oct 2021 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

This paper proposes a generalized Bures-Wasserstein (BW) Riemannian geometry for the manifold of symmetric positive definite matrices.

A Discussion On the Validity of Manifold Learning

no code implementations3 Jun 2021 Dai Shi, Andi Han, Yi Guo, Junbin Gao

In this work, we investigate the validity of learning results of some widely used DR and ManL methods through the chart mapping function of a manifold.

Dimensionality Reduction Speech Recognition

On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry

1 code implementation NeurIPS 2021 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill-conditioned SPD matrices.

Riemannian optimization

Escape saddle points faster on manifolds via perturbed Riemannian stochastic recursive gradient

no code implementations23 Oct 2020 Andi Han, Junbin Gao

In this paper, we propose a variant of Riemannian stochastic recursive gradient method that can achieve second-order convergence guarantee and escape saddle points using simple perturbation.

Riemannian stochastic recursive momentum method for non-convex optimization

no code implementations11 Aug 2020 Andi Han, Junbin Gao

We propose a stochastic recursive momentum method for Riemannian non-convex optimization that achieves a near-optimal complexity of $\tilde{\mathcal{O}}(\epsilon^{-3})$ to find $\epsilon$-approximate solution with one sample.

Variance reduction for Riemannian non-convex optimization with batch size adaptation

no code implementations3 Jul 2020 Andi Han, Junbin Gao

Variance reduction techniques are popular in accelerating gradient descent and stochastic gradient descent for optimization problems defined on both Euclidean space and Riemannian manifold.

Riemannian optimization

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