On principal component analysis of the convex combination of two data matrices and its application to acoustic metamaterial filters

TL;DR

This paper derives a matrix perturbation bound for PCA eigenvalues when data is a convex combination of two matrices, with applications to optimizing acoustic metamaterial filters.

Contribution

It introduces a novel perturbation bound for PCA eigenvalues in convex combination data matrices and discusses its application to acoustic metamaterial filter design.

Findings

Derived a new eigenvalue perturbation bound for convex combination data matrices

Applied the theoretical results to multi-objective optimization in acoustic metamaterials

Discussed potential extensions of the analysis

Abstract

In this short paper, a matrix perturbation bound on the eigenvalues found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of two data matrices. The application of the theoretical analysis to multi-objective optimization problems (e.g., those arising in the design of acoustic metamaterial filters) is briefly discussed, together with possible extensions.