Rotating stellar core-collapse waveform decomposition: a principal component analysis approach

Abstract

This paper introduces the use of principal component analysis (PCA) as a method to decompose the catalogues of gravitational waveforms to produce a set of orthonormal basis vectors. We apply PCA to a set of gravitational waveforms produced by rotating stellar core-collapse simulations and compare its basis vectors with those obtained through Gram–Schmidt decomposition. The comparison is made using the match parameter which quantifies how well each waveform is reconstructed by a set of basis vectors. The performance of the two methods is found to be comparable with 14 Gram–Schmidt basis vectors and 12 principal components required if we require all waveforms in the catalogue to be reconstructed with a match of 0.9 or better. Additionally, we observe that the chosen set of waveforms has very similar features, and a match of at least 0.7 can be obtained by decomposing only waveforms generated from simulations with A = 2. We discuss the implications of this observation and the advantages of eigen-decomposing waveform catalogues with PCA.