Analysis of On-Line Social Networks Represented as Graphs -Extraction of an Approximation of Community Structure Using Sampling

Abstract. In this paper we benchmark two distinct algorithms for extracting community structure from social networks represented as graphs, considering how we can representatively sample an OSN graph while maintaining its community structure. We also evaluate the extraction algorithms' optimum value (modularity) for the number of communities using five well-known benchmarking datasets, two of which represent real online OSN data. Also we consider the assignment of the filtering and sampling criteria for each dataset. We find that the extraction algorithms work well for finding the major communities in the original and the sampled datasets. The quality of the results is measured using an NMI (Normalized Mutual Information) type metric to identify the grade of correspondence between the communities generated from the original data and those generated from the sampled data. We find that a representative sampling is possible which preserves the key community structures of an OSN graph, significantly reducing computational cost and also making the resulting graph structure easier to visualize. Finally, comparing the communities generated by each algorithm, we identify the grade of correspondence

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Bayesian nonparametric sparse VAR models

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR models that can improve estimation efficiency and prediction accuracy. Our hierarchical prior overcomes overparametrization and overfitting issues by clustering the VAR coefficients into groups and by shrinking the coefficients of each group toward a common location. Clustering and shrinking effects induced by the BNP-Lasso prior are well suited for the extraction of causal networks from time series, since they account for some stylized facts in real-world networks, which are sparsity, communities structures and heterogeneity in the edges intensity. In order to fully capture the richness of the data and to achieve a better understanding of financial and macroeconomic risk, it is therefore crucial that the model used to extract network accounts for these stylized facts.Comment: Forthcoming in "Journal of Econometrics" ---- Revised Version of the paper "Bayesian nonparametric Seemingly Unrelated Regression Models" ---- Supplementary Material available on reques

Strategies for online inference of model-based clustering in large and growing networks

In this paper we adapt online estimation strategies to perform model-based clustering on large networks. Our work focuses on two algorithms, the first based on the SAEM algorithm, and the second on variational methods. These two strategies are compared with existing approaches on simulated and real data. We use the method to decipher the connexion structure of the political websphere during the US political campaign in 2008. We show that our online EM-based algorithms offer a good trade-off between precision and speed, when estimating parameters for mixture distributions in the context of random graphs.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS359 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org