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

被引：4

作者：

Liu, Ziming ^{[1
]}

Qian, Sitian ^{[2
]}

Wang, Yixuan ^{[3
]}

Yan, Yuxuan ^{[2
]}

Yang, Tianyi ^{[2
]}

机构：

[1] MIT, Dept Phys, Cambridge, MA 02139 USA

[2] Peking Univ, Sch Phys, Beijing 100871, Peoples R China

[3] CALTECH, Appl & Computat Math, Pasadena, CA 91125 USA

来源：

PHYSICAL REVIEW E | 2021年 / 104卷 / 02期

关键词：

RANDOM-FIELDS; PCA; APPROXIMATION; ALGORITHMS;

D O I：

10.1103/PhysRevE.104.025307

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

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.

引用

页数：13

共 33 条

[1] Multiscale principal component analysis [J].