Uncertainty-Aware Principal Component Analysis

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 techniqu...

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Vydáno v:IEEE transactions on visualization and computer graphics Ročník 26; číslo 1; s. 822 - 831
Hlavní autoři: Gortler, Jochen, Spinner, Thilo, Streeb, Dirk, Weiskopf, Daniel, Deussen, Oliver
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.01.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Covariance matrices
Covariance matrix
Data visualization
Dimensionality reduction
linear projection
machine learning
Mathematical analysis
Matrix methods
Multivariate analysis
Principal component analysis
Principal components analysis
Probability distribution
Random variables
Reduction
Sensitivity analysis
Uncertainty
Uncertainty analysis
ISSN:1077-2626, 1941-0506, 1941-0506
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Shrnutí: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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ISSN:1077-2626
1941-0506
1941-0506
DOI:10.1109/TVCG.2019.2934812