Related papers: Spectral graph clustering via the Expectation-Solu…
In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate…
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…
The Degree-Corrected Stochastic Block Model (DCSBM) is a popular model to generate random graphs with community structure given an expected degree sequence. The standard approach of community detection based on the DCSBM is to search for…
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…
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…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
We study here a Gaussian Mixture Model (GMM) with rare events data. In this case, the commonly used Expectation-Maximization (EM) algorithm exhibits extremely slow numerical convergence rate. To theoretically understand this phenomenon, we…
Finite mixtures of skew distributions provide a flexible tool for modelling heterogeneous data with asymmetric distributional features. However, parameter estimation via the Expectation-Maximization (EM) algorithm can become very…
Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…
In this work, we propose an original method for aggregating multiple clustering coming from different sources of information. Each partition is encoded by a co-membership matrix between observations. Our approach uses a mixture of…
We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth…
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…
The stochastic block model (SBM) is a random graph model in which the edges are generated according to the underlying cluster structure on the vertices. The (ferromagnetic) Ising model, on the other hand, assigns $\pm 1$ labels to vertices…
We systematically study various network Expectation-Maximization (EM) algorithms for the Gaussian mixture model within the framework of decentralized federated learning. Our theoretical investigation reveals that directly extending the…
This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass graph signals with…
Stochastic Block Models (SBMs) are a popular approach to modeling single real-world graphs. The key idea of SBMs is to partition the vertices of the graph into blocks with similar edge densities within, as well as between different blocks.…
This paper proposes a novel scalable community-based neural framework for graph learning. The framework learns the graph topology through the task of community detection and link prediction by optimizing with our proposed joint SBM loss…
We recently proposed a new ensemble clustering algorithm for graphs (ECG) based on the concept of consensus clustering. We validated our approach by replicating a study comparing graph clustering algorithms over benchmark graphs, showing…
Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of…
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…