Work

A subspace method for large-scale trace ratio problems

Year: 2024

Type: article

Abstract: A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is addressed in the search subspace. Additionally, the algorithm is endowed with a restarting strategy, that ensures the monotonicity of the trace ratio value throughout the iterations. The behavior of the approximate solution is investigated from a theoretical viewpoint, extending existing results on Ritz values and vectors, as the angle between the search subspace and the exact solution approaches zero. Numerical experiments in multigroup classification show that this new subspace method tends to be more efficient than iterative approaches relying on (partial) eigenvalue decompositions at each step.

Source: Computational Statistics & Data Analysis

DOI: 10.1016/j.csda.2024.108108

Authors: Giulia Ferrandi, Michiel E. Hochstenbach, M. Rosário Oliveira

Institution: Eindhoven University of Technology

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,440

Funder: Fundação para a Ciência e a Tecnologia