Data Analytics on Graphs Part I: Graphs and Spectra on Graphs

Abstract

The area of Data Analytics on graphs promises a paradigm shift, as we approach information processing of new classes of data which are typically acquired on irregular but structured domains (such as social networks, various ad-hoc sensor networks). Yet, despite the long history of Graph Theory, current approaches tend to focus on aspects of optimisation of graphs themselves rather than on eliciting strategies relevant to the objective application of the graph paradigm, such as detection, estimation, statistical and probabilistic inference, clustering and separation from signals and data acquired on graphs. In order to bridge this gap, we first revisit graph topologies from a Data Analytics point of view, to establish a taxonomy of graph networks through a linear algebraic formalism of graph topology (vertices, connections, directivity). This serves as a basis for spectral Ljubiša Stanković, Danilo Mandic, Miloš Daković, Miloš Brajović, Bruno Scalzo, Shengxi Li and Anthony G. Constantinides (2020), “Data Analytics on Graphs Part I: Graphs and Spectra on Graphs”, Foundations and Trends © in Machine Learning: Vol. 13, No. 1, pp 1–157. DOI: 10.1561/2200000078-1.