Josef Hoppe

vendredi 27 novembre 2023 à 11h en salle 24-25/405, LIP6, Sorbonne Université

Slides, codes, presentation at LoG

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such representations is to lift the graph structure to a simplicial complex: The eigenvectors of the associated Hodge-Laplacian, respectively the incidence matrices of the corresponding simplicial complex then induce a Hodge decomposition, which can be used to represent the observed data in terms of gradient, curl, and harmonic flows. In this paper, we generalize this approach to cellular complexes and introduce the flow representation learning problem, i.e., the problem of augmenting the observed graph by a set of cells, such that the eigenvectors of the associated Hodge Laplacian provide a sparse, interpretable representation of the observed edge flows on the graph. We show that this problem is NP-hard and introduce an efficient approximation algorithm for its solution. Experiments on real-world and synthetic data demonstrate that our algorithm outperforms state-of-the-art methods with respect to approximation error, while being computationally efficient.

Imane Taleb

vendredi 17 novembre 2023 à 14h en salle 26-00/124, LIP6, Sorbonne Université

Microservices are small, independent and scalable services used to build applications, offering flexibility and high-quality service. However, this model presents challenges in terms of network congestion, microservice placement, resource management and energy consumption. Based on an analysis revealing a lack of research on energy optimisation, this thesis focuses on assessing the energy efficiency of microservice placement, using graph partitioning techniques to optimise microservice placement across network architecture layers (Cloud, Fog, Edge).

Sebastiano Vigna

mercredi 24 mai 2023 à 11h en salle 24-25/405, LIP6, Sorbonne Université

Slides

Is it always beneficial to create a new relationship (have a new follower/friend) in a social network? This question can be formally stated as a property of the centrality measure that defines the importance of the actors of the network. Score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc improves the importance of the target of the arc relatively to the remaining nodes. It is known that most centralities are both score and rank monotone on directed, strongly connected graphs. In this paper, we study the problem of score and rank monotonicity for classical centrality measures in the case of undirected networks: in this case, we require that score, or relative importance, improve at both endpoints of the new edge. We show that, surprisingly, the situation in the undirected case is very different, and in particular that closeness, harmonic centrality, betweenness, eigenvector centrality, Seeley’s index, Katz’s index, and PageRank are not rank monotone; betweenness and PageRank are not even score monotone. In other words, while it is always a good thing to get a new follower, it is not always beneficial to get a new friend.

Vincent Labatut

vendredi 12 mai 2023 à 11h en salle 26-00/228 LIP6, Sorbonne Université

Slides

Straightness is a measure designed to characterize a pair of vertices in a spatial graph. In practice, it is often averaged over the whole graph, or a part of it. The standard approach consists in: 1) discretizing the graph edges, 2) processing the vertex-to-vertex Straightness considering the additional vertices resulting from this discretization, and 3) averaging the obtained values. However, this discrete approximation can be computationally expensive on large graphs, and its precision has not been clearly assessed. In this work, we adopt a continuous approach to average the Straightness over the edges of spatial graphs. This allows us to derive 5 distinct measures able to characterize precisely the accessibility of the whole graph, as well as individual vertices and edges. Our method is generic and could be applied to other measures designed for spatial graphs. We perform an experimental evaluation of our continuous average Straightness measures, and show how they behave differently from the traditional vertex-to-vertex ones. Moreover, we also study their discrete approximations, and show that our approach is globally less demanding in terms of both processing time and memory usage.

Lou Grimal

mardi 9 mai 2023 à 11h en salle 26-00/428 LIP6, Sorbonne Université

Une transition des systèmes socio-techniques semble être nécessaire afin de limiter le dépassement des limites planétaires. L’ingénierie, activité influencée par le contexte historique et épistémologique de son époque, peut être un levier pour cette transition. Ma thèse a permis de proposer un cadre théorique pour comprendre comment l’ingénierie peut exister dans des contextes de soutenabilité forte et explorer des outils informatiques qui peuvent être déployés dans ces contextes. Ce cadre est composé de 4 caractéristiques (éthique, objectif, démarche, expertise) et adresse le niveau de l’ingénierie et le niveau des interactions entre l’ingénieur et ses outils informatiques. La méthodologie Value Sensitive Design a été mise en œuvre pour explorer ce cadre théorique. Deux expérimentations ont été conduites pour tester une première médiatisation de la permaingénierie dans un outil informatique – outil mettant en œuvre une démarche d’analyse environnementale collaborative. Ces expérimentations ont permis de montrer un besoin de cadre conceptuel pour une ingénierie en contexte de soutenabilité forte et un manque de pratique des acteurs exprimant ce besoin. Trois contributions ont été identifiées : (1) la formalisation du cadre de permaingénierie, (2) l’approche par les interactions humains-machines pour adresser les questions de transitions culturelles et changement de valeurs, (3) l’impossibilité de transformer un outil d’ingénierie de soutenabilité faible en outil de soutenabilité forte.

Main author and presenter: Leo Cazenille
Other authors: Nicolas Lobato-Dauzier, Alessia Loi, Mika Ito, Olivier Marchal, Nathanael Aubert-Kato, Nicolas Bredeche, Anthony J. Genot

April 18th, 2023, 11am
Room: 24-25/405

Biological swarms have showcased their extraordinary capabilities in tackling geometric challenges by employing limited perception and mobility. They achieve this feat by internally diffusing information to bridge the gap between local and global scales, ultimately facilitating collective consensus and decision-making, even when individual agents only have access to local information. In this study, we strive to adapt this paradigm to robotic swarms, which consist of small robots with constrained sensing and computational abilities.

Our bio-inspired approach leverages spectral shape analysis, enabling the robotic swarms to identify the shape of a given arena. By estimating the second eigenvalue of the Laplacian collectively through information exchange, the robots can effectively obtain a fingerprint of the arena’s geometry. This metric, known as algebraic connectivity, proves invaluable in the context of swarm-based problem-solving and coordination.

To evaluate the performance of our proposed method, we conducted experiments involving 25 real robots as well as simulations using Kilombo, a state-of-the-art simulator for kilobots. Our objective was to assess the efficacy of our approach by attempting to classify a set of 8 shapes with varying geometric properties. The results of these experiments and simulations indicate that the diffusion-based spectral analysis can indeed empower robotic swarms to accurately sense and classify the geometry of their environment.

In conclusion, our innovative approach offers a promising avenue for advancing swarm-based problem-solving and coordination by drawing inspiration from the remarkable capabilities of biological swarms in addressing geometric challenges with limited perception and mobility.

(Presentation in French with slides in English).

Laurent Viennot

mercredi 25 janvier 2023, 26-00/332 LIP6, Sorbonne Université

Slides

A 2-hop labeling (a.k.a. hub labeling) consists in assigning to each node of a graph a small subset of nodes called hubs so that any pair of nodes have a common hub lying on a shortest path joining them. Such labelings appeared to provide a very efficient representation of distances in practical road network where surprisingly small hub sets can be computed. A graph parameter called skeleton dimension allows to explain this behaviour. Connecting any two nodes through a common hub can be seen as a 2-hop shortest path in a super-graph of the original graph. A natural extension is to consider more hops and is related to the notion of hopsets introduced in parallel computation of shortest paths. Surprisingly, a 3-hop construction leads to a data-structure for representing distances which is asymptotically both smaller and faster than 2-hop labeling in graphs of bounded skeleton dimension. Another natural question is to ask whether 2-hop labelings can be efficient more generally in sparse graphs. Unfortunately, this is not the case as there exists bounded degree graphs that require quasi-linear average hub set size. The construction of such difficult graphs is related to the construction of dense graphs with n nodes that can be decomposed into n induced matchings as introduced by Ruzsa and Szemerédi in the seventies.

Maroua Bahri

June 27th, 2022, 11am

Room : 24-25/405

Slides

Data streams pose several challenges for learning algorithms, including mainly, but not limited to, restricted resources (in terms of memory and processing time), high-dimensionality, and concept drift constraints. To process these evolving data, we need efficient and accurate techniques and strategies, such as window models, summarization techniques, and other manners to restrict the storage to a part of — and/or synopsis information from — the stream instead of maintaining it in its entirety. This talk will present how such challenges can be addressed and how we can reduce machine learning algorithms’ resource costs while maintaining good accuracy.

Stephany Rajeh

April 4th, 2022, 11am
Room : 24-25/405

While there is a great deal of work on designing centrality measures, the mainstream does not exploit the network’s community structure. Nevertheless, communities are pervasive in many real-world networks. A community is generally apprehended as a group of nodes densely connected between each other and sparsely connected with other nodes. As communities play a significant role in understanding how nodes behave in networks, a research area concerned with the relation between community structure and the importance of nodes has recently emerged in network science. These works have shown that incorporating community structure information allows designing more effective centrality measures. We refer to them as “community-aware” centrality measures. In this talk, we shed light on how classical (i.e., community-agnostic) centrality measures relate to community-aware centrality measures given a network’s macroscopic and mesoscopic topology. Then, we show the subtility of using these measures in different dynamic models, namely the Susceptible-Infected-Recovered (SIR) model and the Linear Threshold (LT) model. Additionally, as there are plenty of works to detect overlapping communities, few scientists make use of the overlapping community structure to identify critical nodes. Indeed, nodes may belong to several communities in many situations, indicating an overlapping community structure. We propose a framework to target influential nodes in networks with an overlapping community structure inspired by the concept of vitality. Finally, ascribable to the significance of communities in real-world networks, we present a backbone extraction method that maintains the network’s modularity while essentially reducing its  original size.

Christian Lyngby Vestergaard, PhD

March 25th, 2022, 11am
Room : 26-00/332

Video: https://nuage.lip6.fr/s/db5bsrFMssEAoQD

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies and dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged as a general and versatile toolbox for studying such systems. Defined as random networks with given features constrained to match those of an input (empirical) network, they may for example be used to identify important features of empirical networks and their effects on dynamical processes unfolding in the network. RRMs are typically implemented as procedures that reshuffle an empirical network, making them very generally applicable. However, the effects of most shuffling procedures on network features remain poorly understood, rendering their use non-trivial and susceptible to misinterpretation. I will describe a unified framework for the important class of RRMs generated by uniform shuffling procedures, which we by analogy to statistical physics will name microcanonical RRMs (MRRMs). MRRMs constrain chosen features to take exactly the same value as in the empirical network but are otherwise maximally random. Our framework lets us build a taxonomy of MRRMs that orders them and deduces their effects on important network features. It additionally tells us how we may generate new MRRMs by composition of existing ones. I will show examples of how the framework can be applied to unravel the influence of different features of an empirical network of mobile-phone calls on the spread of information and to characterize structural circuit motifs in the brain wiring diagrams (connectomes) of small animals. If time permits, I will finally discuss how we may use graph compression techniques to alleviate the statistical problems associated to classical null hypothesis testing for network motif discovery.
Reference: hal.archives-ouvertes.fr/hal-01817633v4