Related papers: M-decomposability, elliptical unimodal densities, …
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a…
A kernel density is an aggregate of kernel functions, which are itself densities and could be kernel densities. This is used to decompose a kernel into its constituent parts. Pearson's test for equality of proportions is applied to…
A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity…
We address the question of how well the density profile of galaxy clusters can be determined by combining strong lensing and velocity dispersion data. We use cosmological dark matter simulations of clusters to test the reliability of the…
This paper considers coresets for the robust $k$-medians problem with $m$ outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension $d$, the coreset size…
This paper investigates the application of consensus clustering and meta-clustering to the set of all possible partitions of a data set. We show that when using a "complement" of Rand Index as a measure of cluster similarity, the…
Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…
In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering…
The completeness axiom renders the explanation of a post-hoc XAI method only locally faithful to the model, i.e. for a single decision. For the trustworthy application of XAI, in particular for high-stake decisions, a more global model…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
Variational autoencoder (VAE) and generative adversarial networks (GAN) have found widespread applications in clustering and have achieved significant success. However, the potential of these approaches may be limited due to VAE's mediocre…
This paper presents a comprehensive analysis of simple models useful to analyze the growth of nanostructures obtained by cluster deposition. After detailing the potential interest of nanostructures, I extensively study the first stages of…
This paper presents a unified framework for uncertainty propagation in dynamical systems involving hybrid aleatory and epistemic uncertainties. The framework accommodates precise probabilistic, imprecise probabilistic, and non-probabilistic…
Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues.…
The increasing needs of clustering massive datasets and the high cost of running clustering algorithms poses difficult problems for users. In this context it is important to determine if a data set is clusterable, that is, it may be…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
Research on cluster analysis for categorical data continues to develop, with new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. In this paper, we propose a…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…