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Matthieu Latapy

Publications and source records attributed to Matthieu Latapy.

At least 37 records · Page 2Linked to original sources

Computing Betweenness Centrality in Link Streams

Betweeness centrality is one of the most important concepts in graph analysis. It was recently extended to link streams, a graph generalization where links arrive over time. However, its computation raises non-trivial issues, due in particular to the fact that time is considered as continuous. We provide here the first algorithms to compute this generalized betweenness centrality, as well as several companion algorithms that have their own interest. They work in polynomial time and space, we illustrate them on typical examples, and we provide an implementation.

cs.DS↗

Partitions of an Integer into Powers

In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In particular, we show that the set of these partitions can be ordered in a natural way which gives the distributive lattice structure to this set. We also give a tree structure which allow efficient and simple enumeration of the partitions of an integer.

math.CO↗

Generalized Tilings with Height Functions

In this paper, we introduce a generalization of a class of tilings which appear in the literature: the tilings over which a height function can be defined (for example, the famous tilings of polyominoes with dominoes). We show that many properties of these tilings can be seen as the consequences of properties of the generalized tilings we introduce. In particular, we show that any tiling problem which can be modelized in our generalized framework has the following properties: the tilability of a region can be constructively decided in polynomial time, the number of connected components in the undirected flip-accessibility graph can be determined, and the directed flip-accessibility graph induces a distributive lattice structure. Finally, we give a few examples of known tiling problems which can be viewed as particular cases of the new notions we introduce.

math.CO↗

Post-Processing Hierarchical Community Structures: Quality Improvements and Multi-scale View

Dense sub-graphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Most existing community detection algorithms produce a hierarchical structure of community and seek a partition into communities that optimizes a given quality function. We propose new methods to improve the results of any of these algorithms. First we show how to optimize a general class of additive quality functions (containing the modularity, the performance, and a new similarity based quality function we propose) over a larger set of partitions than the classical methods. Moreover, we define new multi-scale quality functions which make it possible to detect the different scales at which meaningful community structures appear, while classical approaches find only one partition.

cs.DS↗

Degree-based Outlier Detection within IP Traffic Modelled as a Link Stream

This paper aims at precisely detecting and identifying anomalous events in IP traffic. To this end, we adopt the link stream formalism which properly captures temporal and structural features of the data. Within this framework, we focus on finding anomalous behaviours with respect to the degree of IP addresses over time. Due to diversity in IP profiles, this feature is typically distributed heterogeneously, preventing us to directly find anomalies. To deal with this challenge, we design a method to detect outliers as well as precisely identify their cause in a sequence of similar heterogeneous distributions. We apply it to several MAWI captures of IP traffic and we show that it succeeds in detecting relevant patterns in terms of anomalous network activity.

cs.SI↗

A general graph-based framework for top-N recommendation using content, temporal and trust information

Recommending appropriate items to users is crucial in many e-commerce platforms that contain implicit data as users' browsing, purchasing and streaming history. One common approach consists in selecting the N most relevant items to each user, for a given N, which is called top-N recommendation. To do so, recommender systems rely on various kinds of information, like item and user features, past interest of users for items, browsing history and trust between users. However, they often use only one or two such pieces of information, which limits their performance. In this paper, we design and implement GraFC2T2, a general graph-based framework to easily combine and compare various kinds of side information for top-N recommendation. It encodes content-based features, temporal and trust information into a complex graph, and uses personalized PageRank on this graph to perform recommendation. We conduct experiments on Epinions and Ciao datasets, and compare obtained performances using F1-score, Hit ratio and MAP evaluation metrics, to systems based on matrix factorization and deep learning. This shows that our framework is convenient for such explorations, and that combining different kinds of information indeed improves recommendation in general.

cs.IR↗

Link Stream Graph for Temporal Recommendations

Several researches on recommender systems are based on explicit rating data, but in many real world e-commerce platforms, ratings are not always available, and in those situations, recommender systems have to deal with implicit data such as users' purchase history, browsing history and streaming history. In this context, classical bipartite user-item graphs (BIP) are widely used to compute top-N recommendations. However, these graphs have some limitations, particularly in terms of taking temporal dynamic into account. This is not good because users' preference change over time. To overcome this limit, the Session-based Temporal Graph (STG) was proposed by Xiang et al. to combine long- and short-term preferences in a graph-based recommender system. But in the STG, time is divided into slices and therefore considered discontinuously. This approach loses details of the real temporal dynamics of user actions. To address this challenge, we propose the Link Stream Graph (LSG) which is an extension of link stream representation proposed by Latapy et al. and which allows to model interactions between users and items by considering time continuously. Experiments conducted on four real world implicit datasets for temporal recommendation, with 3 evaluation metrics, show that LSG is the best in 9 out of 12 cases compared to BIP and STG which are the most used state-of-the-art recommender graphs.

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Propagation of content similarity through a collaborative network for live show recommendation

We present a network-based recommender system for live shows (concerts, theater, circus, etc) that finds a set of people probably interested in a given, new show. We combine collaborative and content-based filtering to take benefit of past activity of users and of the features of the new show. Indeed, as this show is new we cannot rely on collaborative filtering only. To solve this cold-start problem, we perform network alignment and insert the new show in a way consistent with collaborative filtering. We refine the obtained similarities using spreading in the network. We illustrate the performances of our system on a large scale real-world dataset.

cs.SI↗

Predicting interactions between individuals with structural and dynamical information

Capturing both the structural and temporal aspects of interactions is crucial for many real world datasets like contact between individuals. Using the link stream formalism to capture the dynamic of the systems, we tackle the issue of activity prediction in link streams, that is to say predicting the number of links occurring during a given period of time and we present a protocol that takes advantage of the temporal and structural information contained in the link stream. Using a supervised learning method, we are able to model the dynamic of our system to improve the prediction. We investigate the behavior of our algorithm and crucial elements affecting the prediction. By introducing different categories of pair of nodes, we are able to improve the quality as well as increase the diversity of our prediction.

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Enumerating maximal cliques in link streams with durations

Link streams model interactions over time, and a clique in a link stream is defined as a set of nodes and a time interval such that all pairs of nodes in this set interact permanently during this time interval. This notion was introduced recently in the case where interactions are instantaneous. We generalize it to the case of interactions with durations and show that the instantaneous case actually is a particular case of the case with durations. We propose an algorithm to detect maximal cliques that improves our previous one for instantaneous link streams, and performs better than the state of the art algorithms in several cases of interest.

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Discovering Patterns of Interest in IP Traffic Using Cliques in Bipartite Link Streams

Studying IP traffic is crucial for many applications. We focus here on the detection of (structurally and temporally) dense sequences of interactions, that may indicate botnets or coordinated network scans. More precisely, we model a MAWI capture of IP traffic as a link streams, i.e. a sequence of interactions $(t_1 , t_2 , u, v)$ meaning that devices $u$ and $v$ exchanged packets from time $t_1$ to time $t_2$ . This traffic is captured on a single router and so has a bipartite structure: links occur only between nodes in two disjoint sets. We design a method for finding interesting bipartite cliques in such link streams, i.e. two sets of nodes and a time interval such that all nodes in the first set are linked to all nodes in the second set throughout the time interval. We then explore the bipartite cliques present in the considered trace. Comparison with the MAWILab classification of anomalous IP addresses shows that the found cliques succeed in detecting anomalous network activity.

cs.DS↗

Stream Graphs and Link Streams for the Modeling of Interactions over Time

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this paper, we generalize graph concepts in order to cope with both aspects in a consistent way. We start with elementary concepts like density, clusters, or paths, and derive from them more advanced concepts like cliques, degrees, clustering coefficients, or connected components. We obtain a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations. This formalism is self-consistent: usual relations between different concepts are preserved. It is also consistent with graph theory: graph concepts are special cases of the ones we introduce. This makes it easy to generalize higher-level objects such as quotient graphs, line graphs, k-cores, and centralities. This paper also considers discrete versus continuous time assumptions, instantaneous links, and extensions to more complex cases.

cs.SI↗

Identifying roles in an IP network with temporal and structural density

Captures of IP traffic contain much information on very different kinds of activities like file transfers, users interacting with remote systems, automatic backups, or distributed computations. Identifying such activities is crucial for an appropriate analysis, modeling and monitoring of the traffic. We propose here a notion of density that captures both temporal and structural features of interactions, and generalizes the classical notion of clustering coefficient. We use it to point out important differences between distinct parts of the traffic, and to identify interesting nodes and groups of nodes in terms of roles in the network.

cs.NI↗

Computing maximal cliques in link streams

A link stream is a collection of triplets $(t, u, v)$ indicating that an interaction occurred between u and v at time t. We generalize the classical notion of cliques in graphs to such link streams: for a given $Δ$, a $Δ$-clique is a set of nodes and a time interval such that all pairs of nodes in this set interact at least once during each sub-interval of duration $Δ$. We propose an algorithm to enumerate all maximal (in terms of nodes or time interval) cliques of a link stream, and illustrate its practical relevance on a real-world contact trace.

cs.DS↗

Analysis of the temporal and structural features of threads in a mailing-list

A link stream is a collection of triplets $(t,u,v)$ indicating that an interaction occurred between $u$ and $v$ at time $t$. Link streams model many real-world situations like email exchanges between individuals, connections between devices, and others. Much work is currently devoted to the generalization of classical graph and network concepts to link streams. In this paper, we generalize the existing notions of intra-community density and inter-community density. We focus on emails exchanges in the Debian mailing-list, and show that threads of emails, like communities in graphs, are dense subsets loosely connected from a link stream perspective.

cs.SI↗

Comparing paedophile activity in different P2P systems

Peer-to-peer (P2P) systems are widely used to exchange content over the Internet. Knowledge on paedophile activity in such networks remains limited while it has important social consequences. Moreover, though there are different P2P systems in use, previous academic works on this topic focused on one system at a time and their results are not directly comparable. We design a methodology for comparing \kad and \edonkey, two P2P systems among the most prominent ones and with different anonymity levels. We monitor two \edonkey servers and the \kad network during several days and record hundreds of thousands of keyword-based queries. We detect paedophile-related queries with a previously validated tool and we propose, for the first time, a large-scale comparison of paedophile activity in two different P2P systems. We conclude that there are significantly fewer paedophile queries in \kad than in \edonkey (approximately 0.09% \vs 0.25%).

cs.CY↗

Quantifying Paedophile Activity in a Large P2P System

Increasing knowledge of paedophile activity in P2P systems is a crucial societal concern, with important consequences on child protection, policy making, and internet regulation. Because of a lack of traces of P2P exchanges and rigorous analysis methodology, however, current knowledge of this activity remains very limited. We consider here a widely used P2P system, eDonkey, and focus on two key statistics: the fraction of paedophile queries entered in the system and the fraction of users who entered such queries. We collect hundreds of millions of keyword-based queries; we design a paedophile query detection tool for which we establish false positive and false negative rates using assessment by experts; with this tool and these rates, we then estimate the fraction of paedophile queries in our data; finally, we design and apply methods for quantifying users who entered such queries. We conclude that approximately 0.25% of queries are paedophile, and that more than 0.2% of users enter such queries. These statistics are by far the most precise and reliable ever obtained in this domain.

cs.CY↗

Internal links and pairs as a new tool for the analysis of bipartite complex networks

Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such graphs as most existing measures and methods are suited to classical graphs. A usual but limited approach consists in deriving 1-mode graphs (called projections) from the underlying bipartite structure, though it causes important loss of information and data storage issues. We introduce here internal links and pairs as a new notion useful for such analysis: it gives insights on the information lost by projecting the bipartite graph. We illustrate the relevance of theses concepts on several real-world instances illustrating how it enables to discriminate behaviors among various cases when we compare them to a benchmark of random networks. Then, we show that we can draw benefit from this concept for both modeling complex networks and storing them in a compact format.

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