Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation

TL;DR

This paper introduces a novel domain adaptation method leveraging parallel transport on the cone manifold of SPD matrices, supported by theoretical analysis and validated through experiments on simulated and real data.

Contribution

It presents a new approach using Riemannian geometry for domain adaptation with SPD matrices, offering theoretical insights and practical validation.

Findings

The method improves domain adaptation performance.

Theoretical guarantees are established using Riemannian geometry.

Experimental results demonstrate effectiveness on real and simulated data.

Abstract

In this paper, we consider the problem of domain adaptation. We propose to view the data through the lens of covariance matrices and present a method for domain adaptation using parallel transport on the cone manifold of symmetric positive-definite matrices. We provide rigorous analysis using Riemanninan geometry, illuminating the theoretical guarantees and benefits of the presented method. In addition, we demonstrate these benefits using experimental results on simulations and real-measured data.