Related papers: A statistical interpretation of spectral embedding…
Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity…
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering…
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…
The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general…
Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility.…
Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
Latent space models play an important role in the modeling and analysis of network data. Under these models, each node has an associated latent point in some (typically low-dimensional) geometric space, and network formation is driven by…
Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…
Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors…
A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph…
Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this work, we propose a latent position model for these objects, called the dynamic multiplex random dot…
The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…
For graphs generated from stochastic blockmodels, adjacency spectral embedding is asymptotically consistent. Further, adjacency spectral embedding composed with universally consistent classifiers is universally consistent to achieve the…
Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various…
Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…