Related papers: Gaussian Mixture Clustering Using Relative Tests o…
Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM),…
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…
The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…
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…
Clustering methods have led to a number of important discoveries in bioinformatics and beyond. A major challenge in their use is determining which clusters represent important underlying structure, as opposed to spurious sampling artifacts.…
Gaussian mixture models with eigen-decomposed covariance structures make up the most popular family of mixture models for clustering and classification, i.e., the Gaussian parsimonious clustering models (GPCM). Although the GPCM family has…
Sum-of-norms clustering is a method for assigning $n$ points in $\mathbb{R}^d$ to $K$ clusters, $1\le K\le n$, using convex optimization. Recently, Panahi et al.\ proved that sum-of-norms clustering is guaranteed to recover a mixture of…
We propose a hybrid method for accurately estimating the score function, i.e., the gradient of the log steady-state density, using a Gaussian Mixture Model (GMM) in conjunction with a bisecting K-means clustering step. Our approach, which…
Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have…
We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…
Clustering methods are popular for revealing structure in data, particularly in the high-dimensional setting common to contemporary data science. A central statistical question is, "are the clusters really there?" One pioneering method in…
We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…
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…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
Deep clustering as an important branch of unsupervised representation learning focuses on embedding semantically similar samples into the identical feature space. This core demand inspires the exploration of contrastive learning and…
Constrained clustering has gained significant attention in the field of machine learning as it can leverage prior information on a growing amount of only partially labeled data. Following recent advances in deep generative models, we…
Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…
Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability…