首页|Probabilistic Generative Models for Learning with Hypergraphs

Probabilistic Generative Models for Learning with Hypergraphs

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Hypergraphs extend conventional graphs by allowing hyperedges to connect any number of nodes. Despite increasing interest in hypergraphs and numerous attempts to exploit their higher-order connections, existing hypergraph analytics solutions have been limited in their effectiveness, primarily due to the complexity arising from the exponential hyperedge space. This dissertation first examines the efficacy of previous hypergraph analytics methods by developing two network anomaly detection approaches: one based on regular graphs and the other leveraging existing hypergraph analytics techniques. While experimental results demonstrate the effectiveness of the former approach, the latter proves to be less successful, indicating a demand for more advanced hypergraph-based frameworks.To address this demand, this dissertation introduces Hypergraph Simultaneous Generators (HySGen), a versatile probabilistic hypergraph model that formulates its generative process by conditioning the distribution of hyperedges on the nodes' community affiliations. Distinguishing itself from previous models, HySGen does not alter the nature of the hyperedges or constrain their size, and provides a novel method for detecting overlapping communities by effectively utilizing the higher-order connection information in hypergraphs.To tackle the intractable complexity associated with representing the entire state space of the hyperedges, this dissertation introduces a complexity reduction method that reduces the super-exponential inference time to linear without sacrificing any significant precision. Additionally, an algorithmic solution is presented for a runtime issue arising in situations requiring extremely high precision. To objectively assess detected overlapping communities, this dissertation introduces a novel performance measure that addresses the limitations of existing metrics. Experimental results demonstrate the effectiveness, scalability, and superiority of the introduced models and methods compared to current state-of-the-art techniques. The implementations of these models and methods have been incorporated into a popular open-source network analysis and graph mining library. This dissertation lays the foundation for a new line of future research and establishes a framework for developing innovative and effective hypergraph analytics algorithms, addressing the challenges and complexities associated with this field.

Approximate inferenceCommunity detectionGraphical modelsHypergraph learningNetwork analysisSimilarity measureHypergraph Simultaneous Generators

Pedrood, Bahman.

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博士

Computer science.;Computer engineering.

Domeniconi, Carlotta、Laskey, Kathryn B.

2023

George Mason University.

英文

TP