Related papers: Local Differential Privacy-Preserving Spectral Clu…
In a graph bisection problem, we are given a graph $G$ with two equally-sized unlabeled communities, and the goal is to recover the vertices in these communities. A popular heuristic, known as spectral clustering, is to output an estimated…
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…
Clustering is a fundamental data processing task used for grouping records based on one or more features. In the vertically partitioned setting, data is distributed among entities, with each holding only a subset of those features. A key…
In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a…
We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
Community detection approaches resolve complex networks into smaller groups (communities) that are expected to be relatively edge-dense and well-connected. The stochastic block model (SBM) is one of several approaches used to uncover…
In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in…
We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…
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)…
Recent work of Erlingsson, Feldman, Mironov, Raghunathan, Talwar, and Thakurta [EFMRTT19] demonstrates that random shuffling amplifies differential privacy guarantees of locally randomized data. Such amplification implies substantially…
Spectral clustering is one of the most popular, yet still incompletely understood, methods for community detection on graphs. This article studies spectral clustering based on the Bethe-Hessian matrix $H_r = (r^2-1)I_n + D-rA$ for sparse…
Motivated by the prevalent data science applications of processing large-scale graph data such as social networks and biological networks, this paper investigates lossless compression of data in the form of a labeled graph. Particularly, we…
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…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…