5 research outputs found
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Analyzing, Mining, and Predicting Networked Behaviors
Network structure exists in various types of data in the real world, such as online and offline social networks, traffic networks, computer networks, brain networks, and countless other cases where there are relationships between different entities in the data. What are the roles of network structures in these data? First, the network captures inherent characteristics of the data themselves. This is clear from the definition of the network, which represents the relationship between entities: e.g., the social links among people in a social network describe how they interact with each other; a road network summarizes how the roads are laid out geographically; a brain network obtained from fMRI images represents pairs of brain regions that are active at the same time; a computer network constrains the paths via which internet packages and thus information or viruses can spread. Second, the network structures affect the evolution of the data over time. For example, new friendship links in an online social network are frequently created between friends of friends. Similarly, the current road network structure is without a doubt taken into consideration when roads are added or temporarily closed. As we grow, our brains also grow, including the additions of useful links or the clean up of unnecessary links between brain regions. Third, the network structures act as guidance for many different processes happening in the data. For instance, the links between users on social network dictate how gossips can spread; the roads influence how traffic flows in a city; the links between brain regions affects the way we think and how effectively we do things; the connections between computers route the transfer of any information on the internet.In this thesis, I studied the network effect in various networked behaviors, including analyzing such effect, finding its patterns, and predicting future networked behaviors. First, I gained insights into the data by analyzing the accompanied network structures as well as its evolution. Second, I proposed algorithms for mining different network patterns that help summarize the effect of the network structures on different networked behaviors. Finally, I proposed models to predict the evolution of networked behaviors over time. Toward these tasks, I explored a wide variety of network data, including protein-protein interaction networks, online social networks, collaboration networks, chemical compounds, and traffic networks. Overall, I tackled these network data in different aspects and developed a number of methods for effectively mining and forecasting networked behaviors in data
Modeling and Analysis of Affiliation Networks with Subsumption
An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network.
We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number of affiliations is sampled uniformly at random and then nodes are selected from these affiliations with a fixed probability. This results in an implicit preferential attachment growth and a power-law in the degree distribution (where degree is defined as the number of affiliations a node belongs to).
We develop a theoretical model of this network generation procedure, prove that the degree distribution in the hypergraph case is governed by the Yule-Simon distribution, then find the exponent of its power-law tail. Similarly, we show that in the simplicial complex case, the degree distribution also has a power-law tail, and we develop a numerical technique for computing its exponent.
We show that the affiliation size distributions can be concisely described via their generating functions. We develop two numerical techniques for solving the resulting functional equations, find the generating functions and compute their PMFs. Furthermore, we show that at the limit the affiliation size distribution can be approximated by a shifted Poisson or related distribution.
We study the process of a giant component formation in the network, develop a theoretical estimate of the critical threshold for one of the model parameters and compare it with experiments.
For a qualitative analysis of our network generation procedure, we study the average pairwise distance in the network, its assortativity, and clustering coefficient, and use Q-analysis methods to compare our networks with other synthetic networks and real-world networks