# Uncertainty-Aware Principal Component Analysis

arXiv: https://arxiv.org/abs/1905.01127 · HTML: https://mlsanity.com/paper/1905.01127/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2019.

## Built on by (most cited first, 3 of 3)

- [The State of the Art in Enhancing Trust in Machine Learning Models with the Use of Visualizations](https://mlsanity.com/paper/2212.11737/) (2022)
- [DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy](https://mlsanity.com/paper/2508.12145/) (2025)
- [Uncertainty-Aware PCA for Arbitrarily Distributed Data Modeled by Gaussian Mixture Models](https://mlsanity.com/paper/2508.13990/) (2025)

## Abstract (arXiv)

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach.