arXiv research

Study finds the cutoff for exact recovery in Gaussian mixture models.

A new clustering method improves recovery guarantees by re-embedding data.

Paper proposes a new clustering model that preserves cluster recovery with fewer dimensions.

Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.

Paper explores limits of high-order clustering with planted structures.

BalLOT uses optimal transport for balanced k-means clustering.

Exact cluster recovery with same-cluster queries for arbitrary ellipsoidal clusters.

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and…

Geometric framework links clustering accuracy to structural recovery.

KSS method converges and recovers correct clustering under certain conditions.

Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community structure under the binary stochastic block model of two equal-sized clusters. The s…

New bounds for convex clustering under graph connectivity.

We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs of regression coefficients, cyclic shifts, and even group elements from a unified…

We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity graph with vertices as data points randomly sampled on the manifolds and edges as …

New algorithms recover clusters with minimal queries, connecting margins to recoverability.

We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with $k$ blocks of equal size. More precisely, we consider a random $d$-uniform hypergraph $H$ with $n$ vertices partitioned into $k$ clusters of size $s = n / k$. Hyperedges $e$ are added independently with probability $p$ if $e$ is…

In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many applications, which exhibit both row and column cluster structure, and our goal is …

New method recovers clusters in non-convex finite metric spaces with oracle queries.

Spectral clustering for geometric graphs achieves strong consistency in community recovery.

This paper tackles exact recovery of clusters in a stochastic Ising model on a SBM graph.

Study exact partition recovery with same-cluster oracle, bounded error.

We suggest using the max-norm as a convex surrogate constraint for clustering. We show how this yields a better exact cluster recovery guarantee than previously suggested nuclear-norm relaxation, and study the effectiveness of our method, and other related convex relaxations, compared to other clustering approaches.

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 clusters. In the asymptotic regime of $p=a \log n/n$ and $q=b \log n/n$ for fixe…

For a certain class of distributions, we prove that the linear programming relaxation of $k$-medoids clustering---a variant of $k$-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn a…

New clustering method recovers hidden tree structure from data.

Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.

New spectral clustering method handles discrete covariates for better community detection.

There is a recent surge of interest in identifying the sharp recovery thresholds for cluster recovery under the stochastic block model. In this paper, we address the more refined question of how many vertices that will be misclassified on average. We consider the binary form of the stochastic block model, where $n$ ver…

Flexible model captures varying scales in data clusters.

Develops an ℓ_p theory for PCA and spectral clustering.

One-bit clustering method for two-component sub-Gaussian mixture models

Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling Euclidean distances between data points, in a growing number of applications, the dat…

Functional neuroimaging can measure the brain?s response to an external stimulus. It is used to perform brain mapping: identifying from these observations the brain regions involved. This problem can be cast into a linear supervised learning task where the neuroimaging data are used as predictors for the stimulus. Brai…

New algorithm IAC recovers hidden communities in labeled SBM with optimal performance.

LCRSR recovers latent row space for multi-view clustering.

For the degree corrected stochastic block model in the presence of arbitrary or even adversarial outliers, we develop a convex-optimization-based clustering algorithm that includes a penalization term depending on the positive deviation of a node from the expected number of edges to other inliers. We prove that under m…

This work tackles community detection in networks with node attributes, achieving exact recovery.

Solves complex clustering and rotation synchronization problem.

Bottom-up algorithms outperform top-down in hierarchical community detection at intermediate levels.

Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to construct a consistent modal regression algorithm.

New SDP algorithm recovers large clusters in SBM with small clusters of any size.

The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in recovering communities in the SBM from statistical and computational points of view, there are still gaps in understanding the fundamental information theoretic and computational l…

We propose and analyze a generic method for community recovery in stochastic block models and degree corrected block models. This approach can exactly recover the hidden communities with high probability when the expected node degrees are of order $\log n$ or higher. Starting from a roughly correct community partition …

In this paper we make two novel contributions to hierarchical clustering. First, we introduce an anomalous pattern initialisation method for hierarchical clustering algorithms, called A-Ward, capable of substantially reducing the time they take to converge. This method generates an initial partition with a sufficiently…

Proposes methods to recover labels from shuffled networks using graph averages.

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 sufficiently large (in particular, $\tildeΩ(\sqrt{n})$ where $n$ is the number of nodes …

SMM improves signal recovery from noisy data.

Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.