Related papers: A consistent adjacency spectral embedding for stoc…
In community detection on graphs, the semi-supervised learning problem entails inferring the ground-truth membership of each node in a graph, given the connectivity structure and a limited number of revealed node labels. Different subsets…
Modeling relations between individuals is a classical question in social sciences, ecology, etc. In order to uncover a latent structure in the data, a popular approach consists in clustering individuals according to the observed patterns of…
We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…
We prove a central limit theorem for the components of the eigenvectors corresponding to the $d$ largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for…
Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be…
Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative model for graphs with "communities" for which, because of…
There has been an intense recent activity in embedding of very high dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part we cover…
We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
This paper discusses how to generate general graph node embeddings from knowledge graph representations. The embedded space is composed of a number of sub-features to mimic both local affinity and remote structural relevance. These…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis…
Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…
We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio statistic. To this end, we introduce a method that combines spectral clustering with binary segmentation. This…
We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature…
We propose a simple yet effective method for detecting anomalous instances on an attribute graph with label information of a small number of instances. Although with standard anomaly detection methods it is usually assumed that instances…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number $K$ of blocks, the subgraph densities of a…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…