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

Liu, Ziming and Qian, Sitian and Wang, Yixuan and Yan, Yuxuan and Yang, Tianyi (2021) Schrödinger principal-component analysis: On the duality between principal-component analysis and the Schrödinger equation. Physical Review E, 104 (2). Art. No. 025307. ISSN 2470-0045. doi:10.1103/physreve.104.025307. https://resolver.caltech.edu/CaltechAUTHORS:20210927-213256290

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physreve.104.025307DOIArticle
https://arxiv.org/abs/2006.04379arXivDiscussion Paper
ORCID:
AuthorORCID
Qian, Sitian0000-0001-9053-2809
Wang, Yixuan0000-0001-7305-5422
Yan, Yuxuan0000-0002-4293-8270
Alternate Title:Schrödinger PCA: On the Duality between Principal Component Analysis and Schrödinger Equation
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.
Issue or Number:2
DOI:10.1103/physreve.104.025307
Record Number:CaltechAUTHORS:20210927-213256290
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210927-213256290
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111064
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:27 Sep 2021 21:46
Last Modified:28 Sep 2021 20:41

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