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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.
This article was published in the following journal.
Name: IEEE transactions on visualization and computer graphics
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One of three principal openings in the SUBARACHNOID SPACE. They are also known as cerebellomedullary cistern, and collectively as cisterns.
Mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components.
The condition in which reasonable knowledge regarding risks, benefits, or the future is not available.
A minichromosome maintenance protein that is a key component of the six member MCM protein complex. It is also found in tightly-bound trimeric complex with MINICHROMOSOME MAINTENANCE COMPLEX COMPONENT 4 and MINICHROMOSOME MAINTENANCE COMPLEX COMPONENT 7.
A minichromosome maintenance protein that is a key component of the six member MCM protein complex. It is also found in tightly-bound trimeric complex with MINICHROMOSOME MAINTENANCE COMPLEX COMPONENT 4 and MINICHROMOSOME MAINTENANCE COMPLEX COMPONENT 6.