6G will exploit satellite, aerial and terrestrial platforms jointly to improve radio access capability and to unlock the support of on-demand edge cloud services in the three dimensional space (3D) by incorporating Mobile Edge Computing (MEC) functio
nalities on aerial platforms and low orbit satellites. This will extend the MEC support to devices and network elements in the sky and will forge a space borne MEC enabling intelligent personalized and distributed on demand services. 3D end users will experience the impression of being surrounded by a distributed computer fulfilling their requests in apparently zero latency. In this paper, we consider an architecture providing communication, computation, and caching (C3) services on demand, anytime and everywhere in 3D space, building on the integration of conventional ground (terrestrial) base stations and flying (non-terrestrial) nodes. Given the complexity of the overall network, the C3 resources and the management of the aerial devices need to be jointly orchestrated via AI-based algorithms, exploiting virtualized networks functions dynamically deployed in a distributed manner across terrestrial and non-terrestrial nodes.
Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse representation
of the graph signal leading to a modular graph whose Laplacian matrix admits the found dictionary as its eigenvectors. The role of sparsity here is to induce a band-limited representation or, equivalently, a modular structure of the graph. The proposed strategy is composed of two optimization steps: i) learning an orthonormal sparsifying transform from the data; ii) recovering the Laplacian, and then topology, from the transform. The first step is achieved through an iterative algorithm whose alternating intermediate solutions are expressed in closed form. The second step recovers the Laplacian matrix from the sparsifying transform through a convex optimization method. Numerical results corroborate the effectiveness of the proposed methods over both synthetic data and real brain data, used for inferring the brain functionality network through experiments conducted over patients affected by epilepsy.
