Research

(under construction - probably forever)

Processing & Learning on Networks

My group focuses principally on the fundamental study of network-based data processing and learning techniques. The meta-level research question we try to answer is how to analyze and process network data to learn meaningful representations to better understand their behavior. For this, we use a mix of techniques from signal processing, machine learning, mathematical modeling, and network theory. The main research thrusts include:

Most of the research considers the temporal component in the data and/or topology as quite often we have that the data, their interpretation, and hidden pattern vary over time. Additionally, we try to integrate different forms of domain knowledge as inductive biases so as to have a more tractable world model to analyze. I find the latter particularly useful in data-driven solutions so as to develop more effective algorithms as well as to characterize the role the data topology has in their inner-working mechanisms. Below is more detail on the above research thrusts and respective publications.

Graph Neural Networks

Graph neural networks (GNNs) are machine learning techniques for graph-structured data that aim to learn hierarchical representation following the neural network principle. Due to the versatility of the graphs to represent multiple technological and natural complex systems, as well as the challenge of processing the information associated with them, GNNs provide a powerful data-driven solution to different tasks. They have for instance been used to detect fake news spreading on Twitter, provide recommendations on Pinterest and Linkedin, help discover new drugs from molecular graphs, as well as estimate time of arrival on Google Maps. Likewise, they have shown unprecedented performance in physical networks such as water, transportation, and power networks. In this research thrust, we focus on how: (i-Architecture Analysis) to develop and study GNN architectures; (ii- Uncertain Environment) to characterize GNNs' behavior when the underlying topology or data are uncertain due to estimation errors or adversarial attacks;(iii-Dynamic Graphs) to incorporate time-varying graphs into GNNs; (iv-Stability Analysis)   to understand the role of the different GNN components in uncertain environment.  More specifically:

Selected Publications

Architecture Analysis 

Uncertain Environment 

Dynamic Setting 

Stability Analysis

Graph Signal Processing

Graph signal processing (GSP) aims to develop techniques for processing data over networks by generalizing classical concepts commonly used for time series and images such as the Fourier transform, filtering, sampling, and interpolation, among others. For example, in a social network users represent the nodes of the graphs, their connections such as friendships or followers the edges, and the data signal may be user preferences for a particular topic. We then want to analyze how: (i-Fourier) this preference varies across the network; (ii-Filter) removes artifacts and noise in the data; (iii-Sampling and interpolation) collect the information from a few nodes (e.g., on which users to run a survey) and interpolate the missing values on the other nodes. While GSP covers a broad spectrum of fundamental research aspects, I have been mainly trying to answer the following research questions:

Selected Publications

Graph Filters

Graph-Time Signal Processing 

Dynamic Graphs 

Graph Learning

Higher-Order Networks

Higher-order networks (HONS) such as hypergraphs, simplicial, and cell complexes, can represent multiway relations in the data, which graphs fail to represent. They are particularly relevant to model flows on networks which can be seen as data associated with the edges (pairs of nodes). One particularity in this setting is that we may have present interdependent data on multiple levels such as data associated with nodes, edges, and triples of nodes. For example, in a water network, the pressure can be seen as node data and the flows as edge data, which intrinsically influence each other. Our main goal here is to understand this interdependency to develop data processing techniques that leverage HONS as an inductive bias. The two broader research thrusts are:

Selected Publications

HONS Signal Processing 

HONS Representation Learning

Applications

Networks and their higher-order generalization are quite versatile tools for modeling complex systems and irregular data structures. While in most cases they can be seen as one of the many tools to represent the data structure, with respective advantages and limitations, we find them particularly relevant in situations where the data generation process is intrinsically linked to the network structure. Examples of the latter are infrastructure networks such as water distribution networks, mobility networks, or power networks.  In another setting, we have evidence that graph-based abstraction of the data structure often carries specific meaning for the application at hand such as in flood modeling and recommender systems. The fundamental research we conduct is often inspired by challenges in these applications. In most cases, we provide a proof-of-concept in these domains by comparing them with baseline techniques but in other cases, we deeply investigate their impact with domain-specific collaborators. More specifically, we look at the following application domain challenges.


Selected Publications

Infrastructure Networks 

Proof of concept -- foundamental research inspired by application challenges and corroborated in a baseline setup

Flood Modeling 

Recommender Systems 

Proof of concept -- foundamental research inspired by application challenges and corroborated in a baseline setup

Sensor Networks

Proof of concept -- foundamental research inspired by application challenges and corroborated in a baseline setup