A Fast Graph Kernel Based Classification Method for Wireless Link Scheduling on Riemannian Manifold

In this paper, we propose a novel graph kernel method for the wireless link scheduling problem in device-to-device (D2D) networks on Riemannian manifold. The link scheduling problem can be considered as a binary classification problem since each D2D pair can only hold the state active or inactive. Our goal is to learn a novel metric that facilitates the design of an efficient but less computationally demanding machine learning (ML) solution for the binary classification task of link scheduling problem that requires no channel state information (CSI) and a fewer number of training samples as opposed to other benchmark ML algorithms. To this aim, we first represent the wireless D2D network as a graph and model the features of each D2D pair, including its communication and interference links, as regularized (i.e., positively-shifted) Laplacian matrices which are symmetric positive definite (SPD) one. By doing so, we represent the feature information of each D2D pair as a point on the SPD manifold, and we analyze the topology through Riemannian geometry. We compute the Riemannian metric, e.g., Log-Euclidean metric (LEM), which are suitable distance measures between the regularized Laplacian matrices. The LEM is then utilized to define a positive definite graph kernel for the binary classification of the link scheduling decisions. Simulation results demonstrate that the proposed graph Kernel-based method is computationally less demanding and achieves a sum rate of more than 95% of benchmark algorithm FPLinQ [1] for 10 D2D pairs without using CSI and less than a hundred training network layouts.