Related papers: Mixture Probabilistic Principal Geodesic Analysis

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…

We develop a robust data fusion algorithm for field reconstruction of multiple physical phenomena. The contribution of this paper is twofold: First, we demonstrate how multi-spatial fields which can have any marginal distributions and…

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…

Matrix factor model has been growing popular in scientific fields such as econometrics, which serves as a two-way dimension reduction tool for matrix sequences. In this article, we for the first time propose the matrix elliptical factor…

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Principal component analysis (PCA) is a widely used technique for dimension reduction. As datasets continue to grow in size, distributed-PCA (DPCA) has become an active research area. A key challenge in DPCA lies in efficiently aggregating…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…

In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…

In probabilistic principal component analysis (PPCA), an observed vector is modeled as a linear transformation of a low-dimensional Gaussian factor plus isotropic noise. We generalize PPCA to tensors by constraining the loading operator to…

Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It primary objective is to identify a subset of disease-causing genes from a vast pool of…

Data augmentation for deep learning benefits model training, image transformation, medical imaging analysis and many other fields. Many existing methods generate new samples from a parametric distribution, like the Gaussian, with little…

We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted…