Uncertainty-Aware PCA for Arbitrarily Distributed Data Modeled by Gaussian Mixture Models
This work addresses the challenge of handling arbitrarily distributed data with uncertainties for applications in data analysis and visualization, representing an incremental improvement over prior methods.
The paper tackles the problem of projecting multidimensional data with non-normal uncertainties to low-dimensional spaces by proposing an uncertainty-aware PCA method that models data using Gaussian mixture models, resulting in more detailed and faithful representations compared to existing UAPCA mappings.
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.