To center or not to center? Hyperspectral data vs. quantum covariance matrices

Abstract

We highlight how the $L^2$ normalization required for embedding data in quantum states affects data centering, which can significantly influence quantum amplitude-encoded covariance matrices in quantum data analysis algorithms. We examine the spectra and eigenvectors of quantum covariance matrices derived from hyperspectral data under various centering scenarios. Surprisingly, our findings reveal that classification performance in problems reduced by principal component analysis remains unaffected, no matter if the data is centered or uncentered, provided that eigenvector filtering is handled appropriately.