Uncertainty-Aware PCA for Arbitrarily Distributed Data Modeled by Gaussian Mixture Models

2025/08/19 by Klötzl, Daniel, Tastekin, Ozan, Hägele, David +2
#FOS: Computer and information sciences #Graphics (cs.GR) #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2508.13990

Abstract

Multidimensional data is often associated with uncertainties that are not well-described by normal distributions. In this work, we describe how such distributions can be projected to a low-dimensional space using uncertainty-aware principal component analysis (UAPCA). We propose to model multidimensional distributions using Gaussian mixture models (GMMs) and derive the projection from a general formulation that allows projecting arbitrary probability density functions. The low-dimensional projections of the densities exhibit more details about the distributions and represent them more faithfully compared to UAPCA mappings. Further, we support including user-defined weights between the different distributions, which allows for varying the importance of the multidimensional distributions. We evaluate our approach by comparing the distributions in low-dimensional space obtained by our method and UAPCA to those obtained by sample-based projections.

Citations

• UADAPy: An Uncertainty-Aware Visualization and Analysis Toolbox
• Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models
• Sliced Wasserstein Distance for Learning Gaussian Mixture Models

Related

• Mixture of Bilateral-Projection Two-dimensional Probabilistic Principal Component Analysis
• Stochastic Subspace via Probabilistic Principal Component Analysis for Characterizing Model Error
• Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles
• Principal component analysis for max-stable distributions
• Exact Dimensionality Selection for Bayesian PCA