The edge cloud: A holistic view of communication, computation and caching

The evolution of communication networks shows a clear shift of focus from just improving the communications aspects to enabling new important services, from Industry 4.0 to automated driving, virtual/augmented reality, Internet of Things (IoT), and so on. This trend is evident in the roadmap planned for the deployment of the fifth generation (5G) communication networks. This ambitious goal requires a paradigm shift towards a vision that looks at communication, computation and caching (3C) resources as three components of a single holistic system. The further step is to bring these 3C resources closer to the mobile user, at the edge of the network, to enable very low latency and high reliability services. The scope of this chapter is to show that signal processing techniques can play a key role in this new vision. In particular, we motivate the joint optimization of 3C resources. Then we show how graph-based representations can play a key role in building effective learning methods and devising innovative resource allocation techniques.Comment: to appear in the book "Cooperative and Graph Signal Pocessing: Principles and Applications", P. Djuric and C. Richard Eds., Academic Press, Elsevier, 201

Forecasting Time Series with VARMA Recursions on Graphs

Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task. This work provides contributions in this direction by considering the forecasting of a process evolving over a graph. We make use of the (approximate) time-vertex stationarity assumption, i.e., timevarying graph signals whose first and second order statistical moments are invariant over time and correlated to a known graph topology. The latter is combined with VAR and VARMA models to tackle the dimensionality issues present in predicting the temporal evolution of multivariate time series. We find out that by projecting the data to the graph spectral domain: (i) the multivariate model estimation reduces to that of fitting a number of uncorrelated univariate ARMA models and (ii) an optimal low-rank data representation can be exploited so as to further reduce the estimation costs. In the case that the multivariate process can be observed at a subset of nodes, the proposed models extend naturally to Kalman filtering on graphs allowing for optimal tracking. Numerical experiments with both synthetic and real data validate the proposed approach and highlight its benefits over state-of-the-art alternatives.Comment: submitted to the IEEE Transactions on Signal Processin

Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.Comment: In review for IEEE Signal Processing Magazin