Year: 2010
Type: conference-paper
Abstract: In this paper, we adopt a geometric viewpoint to tackle the problem of estimating a linear model whose parameter is a fixed-rank positive semidefinite matrix.We consider two gradient descent flows associated to two distinct Riemannian quotient geometries that underlie this set of matrices.The resulting algorithms are non-linear and can be viewed as a generalization of Least Mean Squares that instrically constrain the parameter within the manifold search space.Such algorithms designed for low-rank matrices find applications in high-dimensional distance learning problems for classification or clustering.This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office.The scientific responsibility rests with its authors.G.M.
Source: ORBi (University of Liège)
Authors: Silvère Bonnabel, Gilles Meyer, Rodolphe Sepulchre
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2235320717