Related papers: Stability of Density-Based Clustering

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…

For a density $f$ on ${\mathbb R}^d$, a {\it high-density cluster} is any connected component of $\{x: f(x) \geq \lambda\}$, for some $\lambda > 0$. The set of all high-density clusters forms a hierarchy called the {\it cluster tree} of…

Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

Identifying possible clusters in datasets and estimating their overall modularity are central tasks in pattern recognition. In the present work, concepts and methodologies are described for performing these tasks while considering only the…

The idea underlying the modal formulation of density-based clustering is to associate groups with the regions around the modes of the probability density function underlying the data. This correspondence between clusters and dense regions…

A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…

This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…

We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based…

Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often…

The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an…

We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…

Turing instability in complex networks have been shown in the literature to be dominated by the distribution of the nodal degrees. The conditions for Turing instability have been derived with an explicit dependence on the eigenvalues of the…

We improve current instability-based methods for the selection of the number of clusters $k$ in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously…

We review a range of stastistical methods for analyzing the structures of star clusters, and derive a new measure ${\cal Q}$ which both quantifies, and distinguishes between, a (relatively smooth) large-scale radial density gradient and…

Classically, Bayesian clustering interprets each component of a mixture model as a cluster. The inferred clustering posterior is highly sensitive to any inaccuracies in the kernel within each component. As this kernel is made more flexible,…

We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…

A rank-invariant clustering of variables is introduced that is based on the predictive strength between groups of variables, i.e., two groups are assigned a high similarity if the variables in the first group contain high predictive…

We study the problem of optimal estimation of the density cluster tree under various assumptions on the underlying density. Building up from the seminal work of Chaudhuri et al. [2014], we formulate a new notion of clustering consistency…

The mass spectra of gas-phase clusters in cluster beams have a rich structure where the relative heights of the peaks compared to peaks corresponding to clusters of neighbor sizes reveal the stability of the clusters as a function of the…