{"ID":2880784,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.13990","arxiv_id":"2508.13990","title":"Uncertainty-Aware PCA for Arbitrarily Distributed Data Modeled by Gaussian Mixture Models","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.","short_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...","url_abs":"https://arxiv.org/abs/2508.13990","url_pdf":"https://arxiv.org/pdf/2508.13990v2","authors":"[\"Daniel Klötzl\",\"Ozan Tastekin\",\"David Hägele\",\"Marina Evers\",\"Daniel Weiskopf\"]","published":"2025-08-19T16:31:41Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.GR\",\"cs.LG\"]","methods":"[]","has_code":false}