Uncertainty-Aware Principal Component Analysis

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IEEE Transactions on Visualization and Computer Graphics. Institute of Electrical and Electronics Engineers (IEEE). 2020, 26(1), pp. 822-831. ISSN 1077-2626. eISSN 1941-0506. Available under: doi: 10.1109/TVCG.2019.2934812
Zusammenfassung

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.

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ISO 690GÖRTLER, Jochen, Thilo SPINNER, Dirk STREEB, Daniel WEISKOPF, Oliver DEUSSEN, 2020. Uncertainty-Aware Principal Component Analysis. In: IEEE Transactions on Visualization and Computer Graphics. Institute of Electrical and Electronics Engineers (IEEE). 2020, 26(1), pp. 822-831. ISSN 1077-2626. eISSN 1941-0506. Available under: doi: 10.1109/TVCG.2019.2934812
BibTex
@article{Gortler2020-01Uncer-47963,
  year={2020},
  doi={10.1109/TVCG.2019.2934812},
  title={Uncertainty-Aware Principal Component Analysis},
  number={1},
  volume={26},
  issn={1077-2626},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  pages={822--831},
  author={Görtler, Jochen and Spinner, Thilo and Streeb, Dirk and Weiskopf, Daniel and Deussen, Oliver}
}
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