Related papers: A consistent adjacency spectral embedding for stoc…

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…

A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links.…

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and…

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We…

Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…

Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. To gain some insight into the performance of various estimators for this task, we perform a theoretical study in a context…

This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random…

We revisit the problem of spectral clustering in multimodal settings, where each data modality is encoded as a graph Laplacian. While classical approaches--including joint diagonalization, spectral co-regularization, and multiview…

Joint spectral embeddings facilitate analysis of multiple network data by simultaneously mapping vertices in each network to points in Euclidean space where statistical inference is then performed. In this work, we consider one such joint…

We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on…

Spectral clustering is a key research topic in the field of machine learning and data mining. Most of the existing spectral clustering algorithms are built upon Gaussian Laplacian matrices, which are sensitive to parameters. We propose a…

Representation learning has recently been successfully used to create vector representations of entities in language learning, recommender systems and in similarity learning. Graph embeddings exploit the locality structure of a graph and…

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…

We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the…

This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to…

Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a…

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…

Modeling relations between individuals is a classical question in social sciences and clustering individuals according to the observed patterns of interactions allows to uncover a latent structure in the data. Stochastic block model (SBM)…

Network embedding aims to represent each node in a network as a low-dimensional feature vector that summarizes the given node's (extended) network neighborhood. The nodes' feature vectors can then be used in various downstream machine…

Significant progress has been made recently on theoretical analysis of estimators for the stochastic block model (SBM). In this paper, we consider the multi-graph SBM, which serves as a foundation for many application settings including…