SAKE: Estimating Katz Centrality Based on Sampling for Large-Scale Social Networks

Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz–Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE, a Sampling-based Algorithm for fast Katz centrality Estimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks

Scalable Methods and Algorithms for Very Large Graphs Based on Sampling

Analyzing real-life networks is a computationally intensive task due to the sheer size of networks. Direct analysis is even impossible when the network data is not entirely accessible. For instance, user networks in Twitter and Facebook are not available for third parties to explore their properties directly. Thus, sampling-based algorithms are indispensable. This dissertation addresses the confidence interval (CI) and bias problems in real-world network analysis. It uses estimations of the number of triangles (hereafter ∆) and clustering coefficient (hereafter C) as a case study. Metric ∆ in a graph is an important measurement for understanding the graph. It is also directly related to C in a graph, which is one of the most important indicators for social networks. The methods proposed in this dissertation can be utilized in other sampling problems. First, we proposed two new methods to estimate ∆ based on random edge sampling in both streaming and non-streaming models. These methods outperformed the state-of-the-art methods consistently and could be better by orders of magnitude when the graph is very large. More importantly, we proved the improvement ratio analytically and verified our result extensively in real-world networks. The analytical results were achieved by simplifying the variances of the estimators based on the assumption that the graph is very large. We believe that such big data assumption can lead to interesting results not only in triangle estimation but also in other sampling problems. Next, we studied the estimation of C in both streaming and non-streaming sampling models. Despite numerous algorithms proposed in this area, the bias and variance of the estimators remain an open problem. We quantified the bias using Taylor expansion and found that the bias can be determined by the structure of the sampled data. Based on the understanding of the bias, we gave new estimators that correct the bias. The results were derived analytically and verified in 56 real networks ranging in different sizes and structures. The experiments reveal that the bias ranges widely from data to data. The relative bias can be as high as 4% in non-streaming model and 2% in streaming model, or it can be negative. We also derived the variances of the estimators, and the estimators for the variances. Our simplified estimators can be used in practice to control the accuracy level of estimations

Learning Embeddings for Academic Papers

Academic papers contain both text and citation links. Representing such data is crucial for many downstream tasks, such as classification, disambiguation, duplicates detection, recommendation and influence prediction. The success of Skip-gram with Negative Sampling model (hereafter SGNS) has inspired many algorithms to learn embeddings for words, documents, and networks. However, there is limited research on learning the representation of linked documents such as academic papers. This dissertation first studies the norm convergence issue in SGNS and propose to use an L2 regularization to fix the problem. Our experiments show that our method improves SGNS and its variants on different types of data. We observe improvements upto 17.47% for word embeddings, 1.85% for document embeddings, and 46.41% for network embeddings. To learn the embeddings for academic papers, we propose several neural network based algorithms that can learn high-quality embeddings from different types of data. The algorithms we proposed are N2V (network2vector) for networks, D2V (document2vector) for documents, and P2V (paper2vector) for academic papers. Experiments show that our models outperform traditional algorithms and the state-of-the-art neural network methods on various datasets under different machine learning tasks. With the high quality embeddings, we design and present four applications on real-world datasets, i.e., academic paper and author search engines, author name disambiguation, and paper influence prediction