Principal Component Analysis as a Tool for Characterizing Black Hole Images and Variability

TL;DR

This paper demonstrates how principal component analysis (PCA) can effectively characterize black hole images and variability, linking spatial and Fourier domains, and providing insights into physical processes.

Contribution

It introduces a PCA-based framework for analyzing black hole images and their variability, including a mathematical link between spatial and Fourier PCA, and methods for model comparison and physical diagnostics.

Findings

Eigenimages in spatial and Fourier domains are mathematically equivalent.

PCA eigenvalues spectrum reveals the physical power spectrum of structures.

PCA basis allows compact representation and outlier detection in time series images.

Abstract

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show mathematically that the Fourier transforms of eigenimages derived from PCA applied to an ensemble of images in the spatial-domain are identical to the eigenvectors of PCA applied to the ensemble of the Fourier transforms of the images, which suggests that this approach may be applied to modeling the sparse interferometric Fourier-visibilities produced by an array such as the Event Horizon Telescope (EHT). We also show that the simulations in the spatial domain themselves can be compactly represented with a PCA-derived basis of eigenimages allowing for detailed comparisons between variable observations and time-dependent models, as well as for detection of outliers or rare events within a time series of images. Furthermore, we demonstrate that the spectrum of PCA eigenvalues is a diagnostic of the power spectrum of the structure and, hence, of the underlying physical processes in the simulated and observed images.