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Correlation clustering is perhaps the most natural formulation of clustering. Given $n$ objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
The EM algorithm is one of many important tools in the field of statistics. While often used for imputing missing data, its widespread applications include other common statistical tasks, such as clustering. In clustering, the EM algorithm…
Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…
A Copula density estimation method that is based on a finite mixture of heterogeneous parametric copula densities is proposed here. More specifically, the mixture components are Clayton, Frank, Gumbel, T, and normal copula densities, which…
Setting initial values of parameters of mixture distributions estimated by using the EM recursive algorithm is very important to the overall quality of estimation. None of the existing methods is suitable for mixtures with large number of…
The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…
The majority of model-based clustering techniques is based on multivariate Normal models and their variants. In this paper copulas are used for the construction of flexible families of models for clustering applications. The use of copulas…
The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results.…
In this article, we discuss two specific classes of models - Gaussian Mixture Copula models and Mixture of Factor Analyzers - and the advantages of doing inference with gradient descent using automatic differentiation. Gaussian mixture…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…
Bayesian model-based clustering is a widely applied procedure for discovering groups of related observations in a dataset. These approaches use Bayesian mixture models, estimated with MCMC, which provide posterior samples of the model…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there…
Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for…
$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…
In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…