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The classical Heisenberg model has been solved in spatial d dimensins, exactly in d=1 and by the Migdal-Kadanoff approximation in d>1, by using a Fourier-Legendre expansion. The phase transition temperatures, the energy densities, and the…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model generalizes the random geometric…
Community detection for large networks poses challenges due to the high computational cost as well as heterogeneous community structures. In this paper, we consider widely existing real-world networks with ``grouped communities'' (or ``the…
The K-subspaces (KSS) method is a generalization of the K-means method for subspace clustering. In this work, we present local convergence analysis and a recovery guarantee for KSS, assuming data are generated by the semi-random union of…
This paper produces an efficient Semidefinite Programming (SDP) solution for community detection that incorporates non-graph data, which in this context is known as side information. SDP is an efficient solution for standard community…
A relevant, sometimes overlooked, quality criterion for communities in graphs is that they should be well-connected in addition to being edge-dense. Prior work has shown that leading community detection methods can produce poorly-connected…
Community detection in directed networks is a central task in network analysis. Unlike undirected networks, directed networks encode inherently asymmetric relationships, giving rise to sender and receiver roles that may each follow distinct…
Deep learning has aroused extensive attention due to its great empirical success. The efficiency of the block coordinate descent (BCD) methods has been recently demonstrated in deep neural network (DNN) training. However, theoretical…
Community detection and orthogonal group synchronization are both fundamental problems with a variety of important applications in science and engineering. In this work, we consider the joint problem of community detection and orthogonal…
This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex…
We investigate privacy-preserving spectral clustering for community detection within stochastic block models (SBMs). Specifically, we focus on edge differential privacy (DP) and propose private algorithms for community recovery. Our work…
We introduce the Markov Stochastic Block Model (MSBM): a growth model for community based networks where node attributes are assigned through a Markovian dynamic. We rely on HMMs' literature to design prediction methods that are robust to…
Community identification in a network is an important problem in fields such as social science, neuroscience, and genetics. Over the past decade, stochastic block models (SBMs) have emerged as a popular statistical framework for this…
This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not…
We study the fundamental limits for reconstruction in weighted graph (or matrix) database alignment. We consider a model of two graphs where $\pi^*$ is a planted uniform permutation and all pairs of edge weights $(A_{i,j},…
The geometric block model is a recently proposed generative model for random graphs that is able to capture the inherent geometric properties of many community detection problems, providing more accurate characterizations of practical…
We consider the sparse stochastic block model in the case where the degrees are uninformative. The case where the two communities have approximately the same size has been extensively studied and we concentrate here on the community…
The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to…
A $k$-deck of a (coloured) graph is a multiset of its induced $k$-vertex subgraphs. Given a graph $G$, when is it possible to reconstruct with high probability a uniformly random colouring of its vertices in $r$ colours from its $k$-deck?…
We propose a model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co-authorship datasets. Our model…