Machado, Luís (Univ. of Trás-os-Montes e Alto Douro), Silva Leite, Fatima (Univ. of Coimbra), hueper, knut (National ICT Australia Ltd)

An Extension of the Classical Least Squares Method to Non-Euclidean Spaces

Scheduled for presentation during the Mini-Symposium "Geometric Optimisation in Systems and Control II" (ThA07), Thursday, July 27, 2006, 10:25−10:50, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

We present an alternative approach to the classical Euclidean least squares method that can be naturally adapted to non-Euclidean spaces. This approach is based on the formulation of an optimization problem on a Riemannian manifold, depending on a smoothing parameter, which gives rise to what we call smoothing geometric splines. The crucial fact here is that as long as the smoothing parameter goes to infinity, the smoothing geometric spline approximates a polynomial curve that best fits the given data. As particular cases, we can get the Riemannian mean of the given points and a geodesic that best fits the data.