Privacy and spectral analysis of social network randomization

Social networks are of significant importance in various application domains. Un- derstanding the general properties of real social networks has gained much attention due to the proliferation of networked data. Many applications of networks such as anonymous web browsing and data publishing require relationship anonymity due to the sensitive, stigmatizing, or confidential nature of the relationship. One general ap- proach for this problem is to randomize the edges in true networks, and only release the randomized networks for data analysis. Our research focuses on the development of randomization techniques such that the released networks can preserve data utility while preserving data privacy. Data privacy refers to the sensitive information in the network data. The released network data after a simple randomization could incur various disclosures including identity disclosure, link disclosure and attribute disclosure. Data utility refers to the information, features, and patterns contained in the network data. Many important features may not be preserved in the released network data after a simple randomiza- tion. In this dissertation, we develop advanced randomization techniques to better preserve data utility of the network data while still preserving data privacy. Specifi- cally we develop two advanced randomization strategies that can preserve the spectral properties of the network or can preserve the real features (e.g., modularity) of the network. We quantify to what extent various randomization techniques can protect data privacy when attackers use different attacks or have different background knowl- edge. To measure the data utility, we also develop a consistent spectral framework to measure the non-randomness (importance) of the edges, nodes, and the overall graph. Exploiting the spectral space of network topology, we further develop fraud detection techniques for various collaborative attacks in social networks. Extensive theoretical analysis and empirical evaluations are conducted to demonstrate the efficacy of our developed techniques

A combinatorial approach to role discovery

We provide a new formulation for the problem of role discovery in graphs. Our definition is structural and recursive: two vertices should be assigned to the same role if the roles of their neighbors, when viewed as multi-sets, are similar enough. An attractive characteristic of our approach is that it is based on optimizing a well-defined objective function, and thus, contrary to previous approaches, the role-discovery task can be studied with the tools of combinatorial optimization. We demonstrate that, when fixing the number of roles to be used, the proposed role-discovery problem is NP-hard, while another (seemingly easier) version of the problem is NP-hard to approximate. On the positive side, despite the recursive nature of our objective function, we can show that finding a perfect (zero-cost) role assignment with the minimum number of roles can be solved in polynomial time. We do this by connecting the zero-cost role assignment with the notion of equitable partition. For the more practical version of the problem with fixed number of roles we present two natural heuristic methods, and discuss how to make them scalable in large graphs

Efficient Network Domination for Life Science Applications

With the ever-increasing size of data available to researchers, traditional methods of analysis often cannot scale to match problems being studied. Often only a subset of variables may be utilized or studied further, motivating the need of techniques that can prioritize variable selection. This dissertation describes the development and application of graph theoretic techniques, particularly the notion of domination, for this purpose. In the first part of this dissertation, algorithms for vertex prioritization in the field of network controllability are studied. Here, the number of solutions to which a vertex belongs is used to classify said vertex and determine its suitability in controlling a network. Novel efficient scalable algorithms are developed and analyzed. Empirical tests demonstrate the improvement of these algorithms over those already established in the literature. The second part of this dissertation concerns the prioritization of genes for loss-of-function allele studies in mice. The International Mouse Phenotyping Consortium leads the initiative to develop a loss-of-function allele for each protein coding gene in the mouse genome. Only a small proportion of untested genes can be selected for further study. To address the need to prioritize genes, a generalizable data science strategy is developed. This strategy models genes as a gene-similarity graph, and from it selects subset that will be further characterized. Empirical tests demonstrate the method’s utility over that of pseudorandom selection and less computationally demanding methods. Finally, part three addresses the important task of preprocessing in the context of noisy public health data. Many public health databases have been developed to collect, curate, and store a variety of environmental measurements. Idiosyncrasies in these measurements, however, introduce noise to data found in these databases in several ways including missing, incorrect, outlying, and incompatible data. Beyond noisy data, multiple measurements of similar variables can introduce problems of multicollinearity. Domination is again employed in a novel graph method to handle autocorrelation. Empirical results using the Public Health Exposome dataset are reported. Together these three parts demonstrate the utility of subset selection via domination when applied to a multitude of data sources from a variety of disciplines in the life sciences

A Network Science perspective of Graph Convolutional Networks: A survey

The mining and exploitation of graph structural information have been the focal points in the study of complex networks. Traditional structural measures in Network Science focus on the analysis and modelling of complex networks from the perspective of network structure, such as the centrality measures, the clustering coefficient, and motifs and graphlets, and they have become basic tools for studying and understanding graphs. In comparison, graph neural networks, especially graph convolutional networks (GCNs), are particularly effective at integrating node features into graph structures via neighbourhood aggregation and message passing, and have been shown to significantly improve the performances in a variety of learning tasks. These two classes of methods are, however, typically treated separately with limited references to each other. In this work, aiming to establish relationships between them, we provide a network science perspective of GCNs. Our novel taxonomy classifies GCNs from three structural information angles, i.e., the layer-wise message aggregation scope, the message content, and the overall learning scope. Moreover, as a prerequisite for reviewing GCNs via a network science perspective, we also summarise traditional structural measures and propose a new taxonomy for them. Finally and most importantly, we draw connections between traditional structural approaches and graph convolutional networks, and discuss potential directions for future research