Published August 2021
| Published + Accepted Version
Journal Article
Open
Schrödinger principal-component analysis: On the duality between principal-component analysis and the Schrödinger equation
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.
Additional Information
© 2021 American Physical Society. (Received 13 February 2021; revised 30 July 2021; accepted 4 August 2021; published 20 August 2021) We thank Zhihan Li, Yifan Chen, Huichao Song, Houman Owhadi and Max Tegmark for valuable discussions.Attached Files
Published - PhysRevE.104.025307.pdf
Accepted Version - 2006.04379.pdf
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PhysRevE.104.025307.pdf
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Additional details
- Alternative title
- Schrödinger PCA: On the Duality between Principal Component Analysis and Schrödinger Equation
- Eprint ID
- 111064
- Resolver ID
- CaltechAUTHORS:20210927-213256290
- Created
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2021-09-27Created from EPrint's datestamp field
- Updated
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2021-09-28Created from EPrint's last_modified field