VIPurPCA: Visualizing and Propagating Uncertainty in Principal Component Analysis

Area of Science:

• Data Science
• Statistics
• Machine Learning

Background:

• Experimental measurements and statistical inference often yield data with inherent uncertainties.
• Propagating these uncertainties through algorithms like principal component analysis (PCA) is crucial for accurate interpretation.
• Uncertainty in input data can significantly affect the reliability of PCA-derived lower-dimensional representations.

Purpose of the Study:

• To develop a method for quantifying and visualizing the uncertainty in PCA embeddings.
• To provide researchers with a tool to assess the reliability of PCA results when applied to uncertain data.
• To enhance the interpretability of PCA outputs in the presence of measurement or inference errors.

Main Methods:

• Utilizing automatic differentiation to linearize the nonlinear functionality of PCA.
• Approximating the propagation of input uncertainties to the PCA output.
• Developing an animation technique to visualize the uncertainty of the lower-dimensional PCA map.

Main Results:

• Demonstrated a method to approximate uncertainty propagation in PCA.
• Developed an effective animation technique for visualizing PCA embedding uncertainty.
• Implemented the methodology as an open-source software package.

Conclusions:

• The developed method allows for the assessment of uncertainty in PCA embeddings.
• The open-source software facilitates researchers' evaluation of PCA result reliability.
• Visualizing uncertainty improves the interpretability and trustworthiness of PCA applications with imperfect data.