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Uncertainty-Aware Principal Component Analysis.

08:00 EDT 10th October 2019 | BioPortfolio

Summary of "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 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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This article was published in the following journal.

Name: IEEE transactions on visualization and computer graphics
ISSN: 1941-0506
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One of three principal openings in the SUBARACHNOID SPACE. They are also known as cerebellomedullary cistern, and collectively as cisterns.

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