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

• URL: http://arxiv.org/abs/2508.13990v1
• Date: Tue, 19 Aug 2025 16:31:41 GMT
• Title: Uncertainty-Aware PCA for Arbitrarily Distributed Data Modeled by Gaussian Mixture Models
• Authors: Daniel Klötzl, Ozan Tastekin, David Hägele, Marina Evers, Daniel Weiskopf,
• Abstract summary: Multidimensional data is often associated with uncertainties that are not well-described by normal distributions.<n>We show how multidimensional distributions can be projected to a low-dimensional space using uncertainty-aware principal component analysis (UAPCA)<n>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.
• Score: 7.664298995468921
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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