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The network embedding task is to represent the node in the network as a low-dimensional vector while incorporating the topological and structural information. Most existing approaches solve this problem by factorizing a proximity matrix,…

Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large…

Anomaly detection is a fundamental problem in domains such as healthcare, manufacturing, and cybersecurity. This thesis proposes new unsupervised methods for anomaly detection in both structured and streaming data settings. In the first…

Modern networks are of huge sizes as well as high dynamics, which challenges the efficiency of community detection algorithms. In this paper, we study the problem of overlapping community detection on distributed and dynamic graphs. Given a…

Random-walk based network embedding algorithms like DeepWalk and node2vec are widely used to obtain Euclidean representation of the nodes in a network prior to performing downstream inference tasks. However, despite their impressive…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and…

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network's low-dimensional structure, and the…

We study model personalization under user-level differential privacy (DP) in the shared representation framework. In this problem, there are $n$ users whose data is statistically heterogeneous, and their optimal parameters share an unknown…

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…

Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and…

Deep graph embedding is an important approach for community discovery. Deep graph neural network with self-supervised mechanism can obtain the low-dimensional embedding vectors of nodes from unlabeled and unstructured graph data. The…

Heterogeneous graphs are ubiquitous in real-world applications because they can represent various relationships between different types of entities. Therefore, learning embeddings in such graphs is a critical problem in graph machine…

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…

We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community. Existing provably consistent algorithms often require…

Network embedding is an effective method to learn low-dimensional representations of nodes, which can be applied to various real-life applications such as visualization, node classification, and link prediction. Although significant…

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…

Since heterogeneity presents a fundamental challenge in graph federated learning, many existing methods are proposed to deal with node feature heterogeneity and structure heterogeneity. However, they overlook the critical homophily…

Several fundamental tasks in data science rely on computing an extremal eigenspace of size $r \ll n$, where $n$ is the underlying problem dimension. For example, spectral clustering and PCA both require the computation of the leading…

This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…