Related papers: Skewed Distributions or Transformations? Modelling…
Finite mixture models, typically Gaussian mixtures, are well known and widely used as model-based clustering. In practical situations, there are many non-Gaussian data that are heavy-tailed and/or asymmetric. Normal inverse Gaussian (NIG)…
Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…
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…
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…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
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…
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…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
Handling missing data is a major challenge in model-based clustering, especially when the data exhibit skewness and heavy tails. We address this by extending the finite mixture of scale mixtures of multivariate skew-normal (FMSMSN) family…
We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…
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…
Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier…
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is…
In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this paper, we study a class of skewed distributions by invoking arguments as described by Ferreira…
Skewness is a common occurrence in statistical applications. In recent years, various distribution families have been proposed to model skewed data by introducing unequal scales based on the median or mode. However, we argue that the point…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…