Can I read A Riemannian Primal-dual Algorithm Based on Proximal Operator and its Application in Metric Learning on EtoBox?

A Riemannian Primal-dual Algorithm Based on Proximal Operator and its Application in Metric Learning by Wang, Shijun; Zhu, Baocheng; Ma, Lintao; Qi, Yuan is a scholarly article available to read on EtoBox.

What is A Riemannian Primal-dual Algorithm Based on Proximal Operator and its Application in Metric Learning about?

In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to optimize the primal and dual variables iteratively. In each optimization iteration, we employ a proximal operator to search optimal solution in the primal space. We prove convergence of the proposed algorithm and show its non-asymptotic convergence rate. By utilizing the proposed primal-dual optimization technique, we propose a novel metric learning algorithm which learns an optimal feature transformation matrix in the Riemannian space of positive definite matrices. Preliminary experimental results on an optimal fund selection problem in fund of funds (FOF) management for quantitative investment showed its efficacy.

Author

Wang, Shijun; Zhu, Baocheng; Ma, Lintao; Qi, Yuan

Published

2020

Language

EN