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In this short paper, a matrix perturbation bound on the eigenvalues found byprincipal component analysis is investigated, for the case in which the datamatrix on which principal component analysis is performed is a convexcombination of two data matrices. The application of the theoretical analysisto multi-objective optimization problems (e.g., those arising in the design ofacoustic metamaterial filters) is briefly discussed, together with possibleextensions.

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