Related papers: Weak Separation, Pure Domains and Cluster Distance

This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it…

Clustering in high-dimensions poses many statistical challenges. While traditional distance-based clustering methods are computationally feasible, they lack probabilistic interpretation and rely on heuristics for estimation of the number of…

We present the results of a weak lensing survey of six high-redshift (z > 0.5), X-ray selected clusters of galaxies. We have obtained ultra-deep R-band images of each cluster with the Keck Telescope, and have measured a weak lensing signal…

In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…

Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering $\sigma_8$ and matter density parameter $\Omega_m$. The main nuisance parameter in a cluster weak lensing cosmological analysis is the…

We report the weak lensing discovery, spectroscopic confirmation, and weak lensing tomography of a massive cluster of galaxies at $z=0.68$, demonstrating that shear selection of clusters works at redshifts high enough to be cosmologically…

In this study, we explore how a non-minimal coupling between dark matter and gravity can affect the behavior of dark matter in galaxy clusters. We have considered the case of a disformal coupling, which leads to a modification of the…

In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that…

In this work we show that combining different cluster data sets is a powerful tool to constrain both, the cosmology and cluster properties. We assume a model with 9 parameters and fit them to 5 cluster data sets. From that fit, we conclude…

An impurity measures $I:{R}^k \to {R}^+$ maps a $k$-dimensional vector ${\bf v}$ to a non-negative value $I({\bf v})$ so that the more homogeneous ${\bf v}$, the larger its impurity. We study clustering based on impurity measures: given a…

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…

Weak gravitational lensing has been used extensively in the past decade to constrain the masses of galaxy clusters, and is the most promising observational technique for providing the mass calibration necessary for precision cosmology with…

We report the detection of weak gravitational lensing of distant background galaxies by two rich, X-ray luminous clusters of galaxies, MS 1137+66 at z=0.783 and RXJ 1716+67 at z=0.813. We detect a shear signal in each cluster over the…

The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter…

In this paper, we introduce a new parameter of a code, referred to as the remoteness, which can be viewed as a dual to the covering radius. Indeed, the remoteness is the minimum radius needed for a single ball to cover all codewords. After…

Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no…

AIMS. While weak lensing cannot resolve cluster cores and strong lensing is almost insensitive to density profiles outside the scale radius, combinations of both effects promise to constrain density profiles of galaxy clusters well, and…

We discuss the variation of cosmological upper bounds on $M_\nu$, the sum of the neutrino masses, with the choice of data sets included in the analysis, pointing out a few oddities not easily seen when all data sets are combined. For…

For a permutation $\omega\in S_n$, Leclerc and Zelevinsky \cite{LZ} introduced a concept of $\omega$-{\em chamber weakly separated collection} of subsets of $\{1,2,...,n\}$ and conjectured that all inclusion-wise maximal collections of this…