Related papers: On Perfect Classification and Clustering for Gauss…

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 Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…

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…

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…

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…

We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…

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…

Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…

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…

Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a…

Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…

We introduce a model-free relax-and-round algorithm for k-means clustering based on a semidefinite relaxation due to Peng and Wei. The algorithm interprets the SDP output as a denoised version of the original data and then rounds this…

Gaussian process is an indispensable tool in clustering functional data, owing to it's flexibility and inherent uncertainty quantification. However, when the functional data is observed over a large grid (say, of length $p$), Gaussian…

We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same…

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 models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…

This paper considers the clustering problem for large data sets. We propose an approach based on distributed optimization. The clustering problem is formulated as an optimization problem of maximizing the classification gain. We show that…

A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…

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…