Project Description

Project PID2019-110977GA-I00 funded by MCIN/ AEI /10.13039/501100011033

Graphs are an ubiquitous data structure, employed extensively within computer science and related fields, including pattern recognition, social networks, transportation networks, and biological systems, to name but a few. Recently, Graph Neural Networks (GNN) have emerged as a deep learning framework able to operate on graph domains to perform inference tasks in an end-to-end fashion. When the graph is explicit, GNN haven proven to be an extremely powerful modeling paradigm. However, in a variety of data domains, including point clouds, text corpora and untrimmed video, the graph structure underlying the data is unknown, and must be assumed or inferred.

Generally speaking, inferring graph topologies from observations is an ill-posed problem, and there are many ways of associating a topology with the observed data samples. Modern approaches for graph topology inference adopt a Graph Signal Processing (GSP) perspective, which explicitly models certain properties of the graph signals (e.g., smoothness, sparsity). While this emphasizes the relation between graph topology and the associated graph signals, the approach is tied to strong a priori assumptions on the signals.

The goal of the current project is the theoretical and computational investigation of models, methods and algorithms for defining a novel framework that enables to learn graph topology jointly with an inference task on a graph in a data-driven, end-to-end formulation, hence combining the strengths of GNN and GSP.

The proposed methodological developments will be put to test on real-world data in the challenging computer vision tasks of temporal event/action segmentation and event/action localization. This is motivated by recent neuroscientific findings showing that neural event representations in humans arise form temporal community structures akin to graphs. The proposed solutions are however not limited to this context and may contribute to many other areas of application that share similar challenges, e.g., anomaly detection, change detection, or image and motion segmentation.
The work plan of the project is structured around the following specific objectives:
1. Exploring the use of different techniques for graph learning regularization, with special emphasis on nonlocal methods to reveal complex
long-range data inter-dependencies.
2. Modeling the joint learning of graph topology and graph embedding in an unsupervised fashion.
3. Modeling end-to-end graph topology learning and clustering by absorbing application-driven priors in the learning problem.
4. Modeling end-to-end graph topology learning and weakly supervised node classification, leveraging on dynamic GNN formulations.

The research pursued by this project will constitute a significant theoretical advance in the understanding of graph neural networks in unstructured contexts, so far a totally unexplored field. It will provide novel set of advanced methodological and operational tools for
hierarchical representation, segmentation, clustering and classification that will open the door to a new generation of high social impact
applications in various fields.