Tanya Y. Berger-Wolf

A framework for analysis of dynamic social networks

Finding patterns of social interaction within a population has wide-ranging applications including: disease modeling, cultural and information transmission, and behavioral ecology. Social interactions are often modeled with networks. A key characteristic of social interactions is their continual change. However, most past analyses of social networks are essentially static in that all information about the time that social interactions take place is discarded. In this paper, we propose a new mathematical and computational framework that enables analysis of dynamic social networks and that explicitly makes use of information about when social interactions occur.

Sampling community structure

We propose a novel method, based on concepts from expander graphs, to sample communities in networks. We show that our sampling method, unlike previous techniques, produces subgraphs representative of community structure in the original network. These generated subgraphs may be viewed as stratified samples in that they consist of members from most or all communities in the network. Using samples produced by our method, we show that the problem of community detection may be recast into a case of statistical relational learning. We empirically evaluate our approach against several real-world datasets and demonstrate that our sampling method can effectively be used to infer and approximate community affiliation in the larger network.

Mining Periodic Behavior in Dynamic Social Networks

Social interactions that occur regularly typically correspond to significant yet often infrequent and hard to detect interaction patterns. To identify such regular behavior, we propose a new mining problem of finding periodic or near periodic subgraphs in dynamic social networks. We analyze the computational complexity of the problem, showing that, unlike any of the related subgraph mining problems, it is polynomial. We propose a practical, efficient and scalable algorithm to find such subgraphs that takes imperfect periodicity into account. We demonstrate the applicability of our approach on several real-world networks and extract meaningful and interesting periodic interaction patterns.

Finding spread blockers in dynamic networks

Social interactions are conduits for various processes spreading through a population, from rumors and opinions to behaviors and diseases. In the context of the spread of a disease or undesirable behavior, it is important to identify blockers: individuals that are most effective in stopping or slowing down the spread of a process through the population. This problem has so far resisted systematic algorithmic solutions. In an effort to formulate practical solutions, in this paper we ask: Are there structural network measures that are indicative of the best blockers in dynamic social networks? Our contribution is two-fold. First, we extend standard structural network measures to dynamic networks. Second, we compare the blocking ability of individuals in the order of ranking by the new dynamic measures. We found that overall, simple ranking according to a nodes static degree, or the dynamic version of a nodes degree, performed consistently well. Surprisingly the dynamic clustering coefficient seems to be a good indicator, while its static version performs worse than the random ranking. This provides simple practical and locally computable algorithms for identifying key blockers in a network.

Discrete sensor placement problems in distribution networks

We consider the problem of placing sensors in a network to detect and identify thesource of any contamination. We consider two variants of this problem:0(1)sensor-constrained: we are allowed a fixed number of sensors and want to minimize contaminationdetection time; and (2)time-constrained: we must detect contamination within a given time limit and want to minimize the number of sensors required. Our main results are as follows. First, we give a necessary and sufficient condition for source identification.Second, we show that the sensor and time constrained versions of the problem are polynomially equivalent. Finally, we show that the sensor-constrained version of the problem is polynomially equivalent to the asymmetric k-center problem and that the time-constrained version of the problem is polynomially equivalent to the dominating set problem.

Index assignment for multichannel communication under failure

We consider the problem of constructing multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We model this as a combinatorial optimization problem of number arrangements in a matrix. This approach gives a general technique for deriving lower bounds on the distortion at given channel rates. This technique is constructive, thus allowing an algorithm that gives an upper bound. For the case of two communication channels with equal rates, the bounds coincide, thus giving the precise lowest achievable distortion at fixed rates. The bounds are within a small constant for a higher number of channels. To the best of our knowledge, this is the first result involving systems with more than two communication channels.

Structure Prediction in Temporal Networks using Frequent Subgraphs

There are several types of processes which can be modeled explicitly by recording the interactions between a set of actors over time. In such applications, a common objective is, given a series of observations, to predict exactly when certain interactions will occur in the future. We propose a representation for this type of temporal data and a generic, streaming, adaptive algorithm to predict the pattern of interactions at any arbitrary point in the future. We test our algorithm on predicting patterns in e-mail logs, correlations between stock closing prices, and social grouping in herds of Plains zebras. Our algorithm averages over 85% accuracy in predicting a set of interactions at any unseen timestep. To the best of our knowledge, this is the first algorithm that predicts interactions at the finest possible time grain

Visualizing the evolution of community structures in dynamic social networks

Social network analysis is the study of patterns of interaction between social entities. The field is attracting increasing attention from diverse disciplines including sociology, epidemiology, and behavioral ecology. An important sociological phenomenon that draws the attention of analysts is the emergence of communities, which tend to form, evolve, and dissolve gradually over a period of time. Understanding this evolution is crucial to sociologists and domain scientists, and often leads to a better appreciation of the social system under study. Therefore, it is imperative that social network visualization tools support this task. While graph‐based representations are well suited for investigating structural properties of networks at a single point in time, they appear to be significantly less useful when used to analyze gradual structural changes over a period of time. In this paper, we present an interactive visualization methodology for dynamic social networks. Our technique focuses on revealing the community structure implied by the evolving interaction patterns between individuals. We apply our visualization to analyze the community structure in the US House of Representatives. We also report on a user study conducted with the participation of behavioral ecologists working with social network datasets that depict interactions between wild animals. Findings from the user study confirm that the visualization was helpful in providing answers to sociological questions as well as eliciting new observations on the social organization of the population under study.

Biometric animal databases from field photographs: identification of individual zebra in the wild

We describe an algorithmic and experimental approach to a fundamental problem in field ecology: computer-assisted individual animal identification. We use a database of noisy photographs taken in the wild to build a biometric database of individual animals differentiated by their coat markings. A new image of an unknown animal can then be queried by its coat markings against the database to determine if the animal has been observed and identified before. Our algorithm, called StripeCodes, efficiently extracts simple image features and uses a dynamic programming algorithm to compare images. We test its accuracy against two different classes of methods: Eigenface, which is based on algebraic techniques, and matching multi-scale histograms of differential image features, an approach from signal processing. StripeCodes performs better than all competing methods for our dataset, and scales well with database size.

Meaningful selection of temporal resolution for dynamic networks

The understanding of dynamics of data streams is greatly affected by the choice of temporal resolution at which the data are discretized, aggregated, and analyzed. Our paper focuses explicitly on data streams represented as dynamic networks. We propose a framework for identifying meaningful resolution levels that best reveal critical changes in the network structure, by balancing the reduction of noise with the loss of information. We demonstrate the applicability of our approach by analyzing various network statistics of both synthetic and real dynamic networks and using those to detect important events and changes in dynamic network structure.