Related papers: Gaussian Mixture Clustering Using Relative Tests o…
This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal…
Generalized linear mixed models (GLMM) are commonly used to analyze clustered data, but when the number of clusters is small to moderate, standard statistical tests may produce elevated type I error rates. Small-sample corrections have been…
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…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to…
In this paper we present a novel iterative multiphase clustering technique for efficiently clustering high dimensional data points. For this purpose we implement clustering feature (CF) tree on a real data set and a Gaussian density…
For many applications, it is critical to interpret and validate groups of observations obtained via clustering. A common validation approach involves testing differences in feature means between observations in two estimated clusters. In…
Cluster analysis is a fundamental research issue in statistics and machine learning. In many modern clustering methods, we need to determine whether two subsets of samples come from the same cluster. Since these subsets are usually…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each…
We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…
In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…
Sum-of-norms clustering is a clustering formulation based on convex optimization that automatically induces hierarchy. Multiple algorithms have been proposed to solve the optimization problem: subgradient descent by Hocking et al., ADMM and…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…
If the same data is used for both clustering and for testing a null hypothesis that is formulated in terms of the estimated clusters, then the traditional hypothesis testing framework often fails to control the Type I error. Gao et al.…
In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection…
In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well…
One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em…
This paper investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM) to treat matrix-valued…