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 Schrödinger equation. Based on the duality we propose the Schrödinger PCA algorithm to replace the expensive PCA solver with a more sample-efficient Schrödinger equation solver. We verify the validity of the theory and the effectiveness of the algorithm with numerical experiments.
1 More- Received 13 February 2021
- Revised 30 July 2021
- Accepted 4 August 2021
DOI:https://doi.org/10.1103/PhysRevE.104.025307
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