Geometric Optimization in Machine Learning

N/ACitations
Citations of this article
24Readers
Mendeley users who have this article in their library.
Get full text

Abstract

Machine learning models often rely on sparsity, low-rank, orthogonality, correlation, or graphical structure. The structure of interest in this chapter is geometric, specifically the manifold of positive definite (PD) matrices. Though these matrices recur throughout the applied sciences, our focus is on more recent developments in machine learning and optimization. In particular, we study (i) models that might be nonconvex in the Euclidean sense but are convex along the PD manifold; and (ii) ones that are neither Euclidean nor geodesic convex but are nevertheless amenable to global optimization. We cover basic theory for (i) and (ii); subsequently, we present a scalable Riemannian limited-memory BFGS algorithm (that also applies to other manifolds). We highlight some applications from statistics and machine learning that benefit from the geometric structure studies.

Cite

CITATION STYLE

APA

Sra, S., & Hosseini, R. (2016). Geometric Optimization in Machine Learning. In Advances in Computer Vision and Pattern Recognition (pp. 73–91). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-319-45026-1_3

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free