Schrödinger Principal-Component Analysis: on the Duality Between Principal-Component Analysis and the Schrödinger Equation.

Ziming Liu,Sitian Qian,Yixuan Wang,Yuxuan Yan,Tianyi Yang

Physical Review E（2021）SCI 3区

Cited 7|Views14

Abstract

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.

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