Graph Neural Networks: a learning journey since 2008 -- Diffusion Convolutional Neural Networks

What is the real power of the adjacency matrix in a graph? In this series, we are following and studying the evolution of machine learning algorithms to deal with graphs [1,2]. Graphs can store an impressive amount of information in a very concise way [3–6], they can be employed to assess clusters of people [7–9] based on their social relationship or exploiting latent features which cannot be detected with simple linear analyses [10]. On the other side graphs are complicated mathematical structures [11,12], their input signal cannot be described on a grid and it is hard to define dominant local statistics unless we perform an average around nodes' neighbours. For these reasons, the application of powerful ML algorithms such as Convolutional Neural Network [13–15] is sometimes complicated and requires a look at the mathematical basis of what graphs are.