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

arXiv: https://arxiv.org/abs/2508.13990 · HTML: https://mlsanity.com/paper/2508.13990/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [Sliced Wasserstein Distance for Learning Gaussian Mixture Models](https://mlsanity.com/paper/1711.05376/) (2017)
- [Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Study](https://mlsanity.com/paper/2110.02894/) (2021)
- [Uncertainty-Aware Principal Component Analysis](https://mlsanity.com/paper/1905.01127/) (2019)
- [Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models](https://mlsanity.com/paper/2407.18015/) (2024)
- [UADAPy: An Uncertainty-Aware Visualization and Analysis Toolbox](https://mlsanity.com/paper/2409.10217/) (2024)

## Abstract (arXiv)

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.