Carlos Gómez Tapia

Non-Euclidean data refers to a set of points that cannot be represented on a two-dimensional space since they violate at least one of the axioms of Euclidean geometry. Graphs are a non-Euclidean data structure composed of nodes (objects) and edges (relations) since they violate the triangle inequality principle. By mapping real-world data onto a graph, it is possible to model complex systems such as physics systems and social networks from which rich relational information can be extracted. Graph analysis is a process aimed at extracting information from graphs and some of the objectives include node classification, link prediction and clustering. Examples of techniques employed in graph analysis include those for finding the minimum spanning tree or producing adjacency matrices. These techniques have been used for applications in aviation, such as for aircraft scheduling as well as in multiprocessor systems for task allocation. Recently Deep Learning (DL) based methods such as Convolutional (CNNs) or Recurrent Neural Networks (RNNs) have been employed for graph analysis. However, here the structure of a graph must be explicit to fully exploit the relations between the objects. These methods function with Euclidean data in one- or two-dimensional spaces thus not suitable for processing graph inputs efficiently. To overcome this issue, a recent research field Geometric Deep Learning (GDL) is devoted to build models that can be trained efficiently with non-Euclidean data. One of techniques for such a type of learning is Graph Neural Network (GNN) and one of its peculiarities is its invariance for changes in the order in which non-Euclidean inputs are presented to the learning mechanism. Here, the edges among nodes are treated as dependencies rather than features, in contrast to traditional Euclidean-based learning approaches. This project will be devoted to better understanding the functioning and application of Graph Neural Networks as well as formally comparing them against traditional approaches for deep learning.