Work

Physical meaning of principal component analysis for classical lattice systems with translational invariance

Year: 2025

Type: article

Abstract: We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a d-dimensional hypercubic lattice. Using Rayleigh-Schrödinger perturbation theory, we demonstrate that the principal components are related to the reciprocal lattice vectors of the hypercubic lattice, and the corresponding eigenvalues are connected to the discrete Fourier transform of the sampled configurations. From a different perspective, we show that the PCA in question can be viewed as a numerical method for computing the ensemble average of the squared moduli of the Fourier transform of physical quantities. Our results also provide a way to determine approximately the principal components of a classical system with translational invariance without the need for matrix diagonalization.

Source: Physical review. E

DOI: 10.1103/physreve.111.045301

Author: Su-Chan Park

Institution: Catholic University of Korea

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea

Awards: G3812690899, G7061100273, G8166738082