Geometric Machine Learning Over Riemannian Manifolds for Wireless Link Scheduling

In this paper, we propose two novel geometric machine learning (G-ML) methods for the wireless link scheduling problem in device-to-device (D2D) networks. In dynamic D2D networks (e.g., vehicular networks), obtaining a large number of training samples is time-consuming for real-time response, and acquiring accurate instantaneous channel state information (CSI) is challenging due to high mobility. Our goal is to efficiently represent D2D networks on Riemannian manifold and use G-ML with few training wireless network layouts and no CSI to approach the sum rate maximization performance as state-of-the-arts which is much needed in dynamic networks. To this aim, we first model the local graph around each D2D pair as a point through a set of regularized Laplacian matrices on the Riemannian manifold. We compute the Riemannian metric, e.g., Log-Euclidean metric (LEM), among D2D pairs, which are suitable measures of interference among these pairs. We use LEM in the geometric support vector machine (G-SVM) method to classify the link scheduling decisions in a supervised learning manner. Then we propose geometric
$k$
-means clustering for unsupervised scheduling method for the case when no labeled training is available in some dynamic networks. Simulation results demonstrate that the proposed methods achieve promising performance for sum rate maximization against the existing state-of-the-arts approaches with only around a hundred training wireless network layouts for training and without using CSI.