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

Daniel Klötzl; Ozan Tastekin; David Hägele; Marina Evers; Daniel Weiskopf

doi:10.1109/uncertaintyvisualization68947.2025.00010

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arXiv · 2508.13990

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

Daniel Klötzl·Ozan Tastekin·David Hägele·Marina Evers·Daniel Weiskopf

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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.

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Daniel Klötzl, Ozan Tastekin, David Hägele, Marina Evers, Daniel Weiskopf. 2025-08-19. Uncertainty-Aware PCA for Arbitrarily Distributed Data Modeled by Gaussian Mixture Models. https://doi.org/10.1109/uncertaintyvisualization68947.2025.00010

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