Stochastic Dykstra Algorithms for Metric Learning on Positive Semi-Definite Cone

TL;DR

This paper introduces a novel Dykstra algorithm-based metric learning method for covariance descriptors, demonstrating improved convergence and promising results in pattern recognition tasks.

Contribution

The paper proposes a new stochastic Dykstra algorithm for metric learning on positive semi-definite cones, with randomized half-space projections to accelerate convergence.

Findings

Randomized half-space order accelerates convergence

The method achieves promising pattern recognition results

Runs at O(n^3) computational complexity

Abstract

Recently, covariance descriptors have received much attention as powerful representations of set of points. In this research, we present a new metric learning algorithm for covariance descriptors based on the Dykstra algorithm, in which the current solution is projected onto a half-space at each iteration, and runs at O(n^3) time. We empirically demonstrate that randomizing the order of half-spaces in our Dykstra-based algorithm significantly accelerates the convergence to the optimal solution. Furthermore, we show that our approach yields promising experimental results on pattern recognition tasks.