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We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to…

The contextual stochastic block model (cSBM) was proposed for unsupervised community detection on attributed graphs where both the graph and the high-dimensional node information correlate with node labels. In the context of machine…

We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems,…

The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer security and bioinformatics. This…

We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…

The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that the rows of an SBM's adjacency spectral embedding (ASE) and Laplacian spectral embedding (LSE)…

We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the…

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing…

Graph embeddings have emerged as a powerful tool for understanding the structure of graphs. Unlike classical spectral methods, recent methods such as DeepWalk, Node2Vec, etc. are based on solving nonlinear optimization problems on the…

The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study…

Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network…

We consider the problem of partially recovering hidden binary variables from the observation of (few) censored edge weights, a problem with applications in community detection, correlation clustering and synchronization. We describe two…

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…

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of…

In network inference applications, it is often desirable to detect community structure, namely to cluster vertices into groups, or blocks, according to some measure of similarity. Beyond mere adjacency matrices, many real networks also…

The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works…

Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…

In this paper we prove the strong consistency of several methods based on the spectral clustering techniques that are widely used to study the community detection problem in stochastic block models (SBMs). We show that under some weak…

The stochastic block model (SBM) and degree-corrected block model (DCBM) are network models often selected as the fundamental setting in which to analyze the theoretical properties of community detection methods. We consider the problem of…

We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…