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In this paper, we propose a novel graph kernel method for the wireless linkscheduling problem in device-to-device (D2D) networks on Riemannian manifold.The link scheduling problem can be considered as a binary classificationproblem since each D2D pair can only hold the state active or inactive. Ourgoal is to learn a novel metric that facilitates the design of an efficient butless computationally demanding machine learning (ML) solution for the binaryclassification task of link scheduling problem that requires no channel stateinformation (CSI) and a fewer number of training samples as opposed to otherbenchmark ML algorithms. To this aim, we first represent the wireless D2Dnetwork as a graph and model the features of each D2D pair, including itscommunication and interference links, as regularized (i.e., positively-shifted)Laplacian matrices which are symmetric positive definite (SPD) one. By doingso, we represent the feature information of each D2D pair as a point on the SPDmanifold, and we analyze the topology through Riemannian geometry. We computethe Riemannian metric, e.g., Log-Euclidean metric (LEM), which are suitabledistance measures between the regularized Laplacian matrices. The LEM is thenutilized to define a positive definite graph kernel for the binaryclassification of the link scheduling decisions. Simulation results demonstratethat the proposed graph Kernel-based method is computationally less demandingand achieves a sum rate of more than 95% of benchmark algorithm FPLinQ [1] for10 D2D pairs without using CSI and less than a hundred training networklayouts.

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