Related papers: Parametric density-based optimization of partition…
Clustering algorithms are fundamental tools across many fields, with density-based methods offering particular advantages in identifying arbitrarily shaped clusters and handling noise. However, their effectiveness is often limited by the…
In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
A new characterization of the multivariate so-called "quasi-Gaussian distribution" (the authors dared to coin a new term) by means of independence their Cartesian and polar coordinates proposed. The authors try to show that these…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
Mixture models are a natural choice in many applications, but it can be difficult to place an a priori upper bound on the number of components. To circumvent this, investigators are turning increasingly to Dirichlet process mixture models…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
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…
Clustering is widely used in different field such as biology, psychology, and economics. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes. However, datasets with…
Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing…
We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…
This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio,…
In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…
We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partition of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each…
In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…