Open AccessConvex combination of data matrices: PCA perturbation bounds for multi-objective optimal design of mechanical metafilters
Author(s) -
Giorgio Gnecco,
Andrea Bacigalupo
Publication year - 2021
Publication title -
mathematical foundations of computing
Language(s) - English
Resource type - Journals
ISSN - 2577-8838
DOI - 10.3934/mfc.2021014
Subject(s) - principal component analysis , eigenvalues and eigenvectors , linear subspace , perturbation (astronomy) , mathematics , convex optimization , regular polygon , invariant (physics) , algorithm , sparse pca , combinatorics , mathematical optimization , pure mathematics , geometry , physics , statistics , quantum mechanics , mathematical physics
In the present study, matrix perturbation bounds on the eigenvalues and on the invariant subspaces 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 mechanical metamaterial filters – is also discussed, together with possible extensions.