Related papers: PCA Reduced Gaussian Mixture Models with Applicati…

Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis which, since its formulation in 2006, has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable…

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…

In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random inputs. Gaussian process (GP) is a widely used surrogate…

We consider the problem of estimating the parameters a Gaussian Mixture Model with K components of known weights, all with an identity covariance matrix. We make two contributions. First, at the population level, we present a sharper…

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…

Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…

Color transfer, which plays a key role in image editing, has attracted noticeable attention recently. It has remained a challenge to date due to various issues such as time-consuming manual adjustments and prior segmentation issues. In this…

To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parameterisations with Weak Lensing (WL) and Large-Scale Structure (LSS) data, we introduce a novel alternative method…

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…

Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its…

In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Pansharpening techniques aim at fusing low-resolution multispectral (MS) images and high-resolution panchromatic (PAN) images to produce high-resolution MS images. Despite significant progress in the field, spectral and spatial distortions…

Gaussian Mixture Models (GMMs) are a standard tool in data analysis. However, they face problems when applied to high-dimensional data (e.g., images) due to the size of the required full covariance matrices (CMs), whereas the use of…

Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…

Principal component analysis (PCA) is a commonly used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…