Related papers: Semidefinite programming on population clustering:…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is motivated by the application of clustering individuals according to their population…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
In this paper, we consider the problem of partitioning a small data sample drawn from a mixture of $k$ product distributions. We are interested in the case that individual features are of low average quality $\gamma$, and we want to use as…
We consider the problem of clustering partially labeled data from a minimal number of randomly chosen pairwise comparisons between the items. We introduce an efficient local algorithm based on a power iteration of the non-backtracking…
We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this…
The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…
The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across…
We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on $k$-clusters: a random model on $n=km$ vertices, partitioned in $k$ equal sized clusters,…
We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…
We study graph clustering in the Stochastic Block Model (SBM) in the presence of both large clusters and small, unrecoverable clusters. Previous convex relaxation approaches achieving exact recovery do not allow any small clusters of size…
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that…
The well-known clustering algorithm of Miller, Peng, and Xu (SPAA 2013) is useful for many applications, including low-diameter decomposition and low-energy distributed algorithms. One nice property of their clustering, shown in previous…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
In this paper, we develop semi-external and external memory algorithms for graph partitioning and clustering problems. Graph partitioning and clustering are key tools for processing and analyzing large complex networks. We address both…
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…