Schrodinger principal-component analysis: On the duality between principal-component analysis and the Schrodinger equation

Principal component analysis (PCA) has been applied to analyze random fields in various scientific disciplines. However, the explainability of PCA remains elusive unless strong domain-specific knowledge is available. This paper provides a theoretical framework that builds a duality between the PCA eigenmodes of a random field and eigenstates of a Schrodinger equation. Based on the duality we propose the Schrodinger PCA algorithm to replace the expensive PCA solver with a more sample-efficient Schrodinger equation solver. We verify the validity of the theory and the effectiveness of the algorithm with numerical experiments.