Efficient Node Proximity and Node Significance Computations in Graphs

abstract: Node proximity measures are commonly used for quantifying how nearby or otherwise related to two or more nodes in a graph are. Node significance measures are mainly used to find how much nodes are important in a graph. The measures of node proximity/significance have been highly effective in many predictions and applications. Despite their effectiveness, however, there are various shortcomings. One such shortcoming is a scalability problem due to their high computation costs on large size graphs and another problem on the measures is low accuracy when the significance of node and its degree in the graph are not related. The other problem is that their effectiveness is less when information for a graph is uncertain. For an uncertain graph, they require exponential computation costs to calculate ranking scores with considering all possible worlds. In this thesis, I first introduce Locality-sensitive, Re-use promoting, approximate Personalized PageRank (LR-PPR) which is an approximate personalized PageRank calculating node rankings for the locality information for seeds without calculating the entire graph and reusing the precomputed locality information for different locality combinations. For the identification of locality information, I present Impact Neighborhood Indexing (INI) to find impact neighborhoods with nodes' fingerprints propagation on the network. For the accuracy challenge, I introduce Degree Decoupled PageRank (D2PR) technique to improve the effectiveness of PageRank based knowledge discovery, especially considering the significance of neighbors and degree of a given node. To tackle the uncertain challenge, I introduce Uncertain Personalized PageRank (UPPR) to approximately compute personalized PageRank values on uncertainties of edge existence and Interval Personalized PageRank with Integration (IPPR-I) and Interval Personalized PageRank with Mean (IPPR-M) to compute ranking scores for the case when uncertainty exists on edge weights as interval values.Dissertation/ThesisDoctoral Dissertation Computer Science 201

A graph oriented approach for network forensic analysis

Network forensic analysis is a process that analyzes intrusion evidence captured from networked environment to identify suspicious entities and stepwise actions in an attack scenario. Unfortunately, the overwhelming amount and low quality of output from security sensors make it difficult for analysts to obtain a succinct high-level view of complex multi-stage intrusions. This dissertation presents a novel graph based network forensic analysis system. The evidence graph model provides an intuitive representation of collected evidence as well as the foundation for forensic analysis. Based on the evidence graph, we develop a set of analysis components in a hierarchical reasoning framework. Local reasoning utilizes fuzzy inference to infer the functional states of an host level entity from its local observations. Global reasoning performs graph structure analysis to identify the set of highly correlated hosts that belong to the coordinated attack scenario. In global reasoning, we apply spectral clustering and Pagerank methods for generic and targeted investigation respectively. An interactive hypothesis testing procedure is developed to identify hidden attackers from non-explicit-malicious evidence. Finally, we introduce the notion of target-oriented effective event sequence (TOEES) to semantically reconstruct stealthy attack scenarios with less dependency on ad-hoc expert knowledge. Well established computation methods used in our approach provide the scalability needed to perform post-incident analysis in large networks. We evaluate the techniques with a number of intrusion detection datasets and the experiment results show that our approach is effective in identifying complex multi-stage attacks

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

Graph Summarization

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is graph summarization. It denotes a series of application-specific algorithms designed to transform graphs into more compact representations while preserving structural patterns, query answers, or specific property distributions. As this problem is common to several areas studying graph topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily based on statistical and optimization methods. The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie

Web3Recommend: Decentralised recommendations with trust and relevance

Web3Recommend is a decentralized Social Recommender System implementation that enables Web3 Platforms on Android to generate recommendations that balance trust and relevance. Generating recommendations in decentralized networks is a non-trivial problem because these networks lack a global perspective due to the absence of a central authority. Further, decentralized networks are prone to Sybil Attacks in which a single malicious user can generate multiple fake or Sybil identities. Web3Recommend relies on a novel graph-based content recommendation design inspired by GraphJet, a recommendation system used in Twitter enhanced with MeritRank, a decentralized reputation scheme that provides Sybil-resistance to the system. By adding MeritRank's decay parameters to the vanilla Social Recommender Systems' personalized SALSA graph algorithm, we can provide theoretical guarantees against Sybil Attacks in the generated recommendations. Similar to GraphJet, we focus on generating real-time recommendations by only acting on recent interactions in the social network, allowing us to cater temporally contextual recommendations while keeping a tight bound on the memory usage in resource-constrained devices, allowing for a seamless user experience. As a proof-of-concept, we integrate our system with MusicDAO, an open-source Web3 music-sharing platform, to generate personalized, real-time recommendations. Thus, we provide the first Sybil-resistant Social Recommender System, allowing real-time recommendations beyond classic user-based collaborative filtering. The system is also rigorously tested with extensive unit and integration tests. Further, our experiments demonstrate the trust-relevance balance of recommendations against multiple adversarial strategies in a test network generated using data from real music platforms

Semi-supervised Eigenvectors for Large-scale Locally-biased Learning

In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that prespecified target region. For example, one might be interested in the clustering structure of a data graph near a prespecified "seed set" of nodes, or one might be interested in finding partitions in an image that are near a prespecified "ground truth" set of pixels. Locally-biased problems of this sort are particularly challenging for popular eigenvector-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities, thus limiting the applicability of eigenvector-based methods in situations where one is interested in very local properties of the data. In this paper, we address this issue by providing a methodology to construct semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these locally-biased eigenvectors can be used to perform locally-biased machine learning. These semi-supervised eigenvectors capture successively-orthogonalized directions of maximum variance, conditioned on being well-correlated with an input seed set of nodes that is assumed to be provided in a semi-supervised manner. We show that these semi-supervised eigenvectors can be computed quickly as the solution to a system of linear equations; and we also describe several variants of our basic method that have improved scaling properties. We provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning; and we discuss the relationship between our results and recent machine learning algorithms that use global eigenvectors of the graph Laplacian