Jérôme Kunegis

The slashdot zoo: mining a social network with negative edges

We analyse the corpus of user relationships of the Slashdot technology news site. The data was collected from the Slashdot Zoo feature where users of the website can tag other users as friends and foes, providing positive and negative endorsements. We adapt social network analysis techniques to the problem of negative edge weights. In particular, we consider signed variants of global network characteristics such as the clustering coefficient, node-level characteristics such as centrality and popularity measures, and link-level characteristics such as distances and similarity measures. We evaluate these measures on the task of identifying unpopular users, as well as on the task of predicting the sign of links and show that the network exhibits multiplicative transitivity which allows algebraic methods based on matrix multiplication to be used. We compare our methods to traditional methods which are only suitable for positively weighted edges.

KONECT: the Koblenz network collection

We present the Koblenz Network Collection (KONECT), a project to collect network datasets in the areas of web science, network science and related areas, as well as provide tools for their analysis. In the cited areas, a surprisingly large number of very heterogeneous data can be modeled as networks and consequently, a unified representation of networks can be used to gain insight into many kinds of problems. Due to the emergence of the World Wide Web in the last decades many such datasets are now openly available. The KONECT project thus has the goal of collecting many diverse network datasets from the Web, and providing a way for their systematic study. The main parts of KONECT are (1) a collection of over 160 network datasets, consisting of directed, undirected, unipartite, bipartite, weighted, unweighted, signed and temporal networks collected from the Web, (2) a Matlab toolbox for network analysis and (3) a website giving a compact overview the various computed statistics and plots. In this paper, we describe KONECTs taxonomy of networks datasets, give an overview of the datasets included, review the supported statistics and plots, and briefly discuss KONECTs role in the area of web science and network science.

Bad news travel fast: a content-based analysis of interestingness on Twitter

On the microblogging site Twitter, users can forward any message they receive to all of their followers. This is called a retweet and is usually done when users find a message particularly interesting and worth sharing with others. Thus, retweets reflect what the Twitter community considers interesting on a global scale, and can be used as a function of interestingness to generate a model to describe the content-based characteristics of retweets. In this paper, we analyze a set of high- and low-level content-based features on several large collections of Twitter messages. We train a prediction model to forecast for a given tweet its likelihood of being retweeted based on its contents. From the parameters learned by the model we deduce what are the influential content features that contribute to the likelihood of a retweet. As a result we obtain insights into what makes a message on Twitter worth retweeting and, thus, interesting.

Learning spectral graph transformations for link prediction

We present a unified framework for learning link prediction and edge weight prediction functions in large networks, based on the transformation of a graphs algebraic spectrum. Our approach generalizes several graph kernels and dimensionality reduction methods and provides a method to estimate their parameters efficiently. We show how the parameters of these prediction functions can be learned by reducing the problem to a one-dimensional regression problem whose runtime only depends on the methods reduced rank and that can be inspected visually. We derive variants that apply to undirected, weighted, unweighted, unipartite and bipartite graphs. We evaluate our method experimentally using examples from social networks, collaborative filtering, trust networks, citation networks, authorship graphs and hyperlink networks.

The link prediction problem in bipartite networks

We define and study the link prediction problem in bipartite networks, specializing general link prediction algorithms to the bipartite case. In a graph, a link prediction function of two vertices denotes the similarity or proximity of the vertices. Common link prediction functions for general graphs are defined using paths of length two between two nodes. Since in a bipartite graph adjacency vertices can only be connected by paths of odd lengths, these functions do not apply to bipartite graphs. Instead, a certain class of graph kernels (spectral transformation kernels) can be generalized to bipartite graphs when the positive-semidefinite kernel constraint is relaxed. This generalization is realized by the odd component of the underlying spectral transformation. This construction leads to several new link prediction pseudokernels such as the matrix hyperbolic sine, which we examine for rating graphs, authorship graphs, folksonomies, document-feature networks and other types of bipartite networks.

Preferential attachment in online networks: measurement and explanations

We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network considered. The classical preferential attachment model for networks by Barabási and Albert (1999) assumes a linear relationship between the number of neighbors of a node in a network and the probability of attachment. Although this assumption is widely made in Web Science and related fields, the underlying linearity is rarely measured. To fill this gap, this paper performs an empirical longitudinal (time-based) study on forty-seven diverse Web network datasets from seven network categories and including directed, undirected and bipartite networks. We show that contrary to the usual assumption, preferential attachment is nonlinear in the networks under consideration. Furthermore, we observe that the deviation from linearity is dependent on the type of network, giving sublinear attachment in certain types of networks, and superlinear attachment in others. Thus, we introduce the preferential attachment exponent β as a novel numerical network measure that can be used to discriminate different types of networks. We propose explanations for the behavior of that network measure, based on the mechanisms that underly the growth of the network in question.

Network growth and the spectral evolution model

We introduce and study the spectral evolution model, which characterizes the growth of large networks in terms of the eigenvalue decomposition of their adjacency matrices: In large networks, changes over time result in a change of a graphs spectrum, leaving the eigenvectors unchanged. We validate this hypothesis for several large social, collaboration, authorship, rating, citation, communication and tagging networks, covering unipartite, bipartite, signed and unsigned graphs. Following these observations, we introduce a link prediction algorithm based on the extrapolation of a networks spectral evolution. This new link prediction method generalizes several common graph kernels that can be expressed as spectral transformations. In contrast to these graph kernels, the spectral extrapolation algorithm does not make assumptions about specific growth patterns beyond the spectral evolution model. We thus show that it performs particularly well for networks with irregular, but spectral, growth patterns.

Hydra: a hybrid recommender system [cross-linked rating and content information]

This paper discusses the combination of collaborative and content-based filtering in the context of web-based recommender systems. In particular, we link the well-known MovieLens rating data with supplementary IMDB content information. The resulting network of user-item relations and associated content features is converted into a unified mathematical model, which is applicable to our underlying neighbor-based prediction algorithm. By means of various experiments, we demonstrate the influence of supplementary user as well as item features on the prediction accuracy of Hydra, our proposed hybrid recommender. In order to decrease system runtime and to reveal latent user and item relations, we factorize our hybrid model via singular value decomposition (SVD).

Detecting non-gaussian geographical topics in tagged photo collections

Nowadays, large collections of photos are tagged with GPS coordinates. The modelling of such large geo-tagged corpora is an important problem in data mining and information retrieval, and involves the use of geographical information to detect topics with a spatial component. In this paper, we propose a novel geographical topic model which captures dependencies between geographical regions to support the detection of topics with complex, non-Gaussian distributed spatial structures. The model is based on a multi-Dirichlet process (MDP), a novel generalisation of the hierarchical Dirichlet process extended to support multiple base distributions. Our method thus is called the MDP-based geographical topic model (MGTM). We show how to use a MDP to dynamically smooth topic distributions between groups of spatially adjacent documents. In systematic quantitative and qualitative evaluations using independent datasets from prior related work, we show that such a model can exploit the adjacency of regions and leads to a significant improvement in the quality of topics compared to the state of the art in geographical topic modelling.

Link prediction on evolving data using tensor factorization

Within the last few years a lot of research has been done on large social and information networks. One of the principal challenges concerning complex networks is link prediction. Most link prediction algorithms are based on the underlying network structure in terms of traditional graph theory. In order to design efficient algorithms for large scale networks, researchers increasingly adapt methods from advanced matrix and tensor computations. This paper proposes a novel approach of link prediction for complex networks by means of multi-way tensors. In addition to structural data we furthermore consider temporal evolution of a network. Our approach applies the canonical Parafac decomposition to reduce tensor dimensionality and to retrieve latent trends. For the development and evaluation of our proposed link prediction algorithm we employed various popular datasets of online social networks like Facebook and Wikipedia. Our results show significant improvements for evolutionary networks in terms of prediction accuracy measured through mean average precision.