Rotating stellar core-collapse waveform decompositon: a Principal Component Analysis approach

TL;DR

This paper applies Principal Component Analysis to decompose supernova waveform catalogues, demonstrating comparable performance to Gram-Schmidt and revealing common features among waveforms for efficient representation.

Contribution

It introduces PCA as an effective method for waveform decomposition and compares it with Gram-Schmidt, highlighting the advantages of eigen-decomposition in waveform analysis.

Findings

PCA and Gram-Schmidt yield similar basis vectors for minimal match 0.9

Few principal components capture most waveform features

Decomposing one third of waveforms achieves minimal match 0.7

Abstract

This paper introduces the use of Principal Component Analysis as a method to decompose the waveform catalogues to produce a set of orthonormal basis vectors. We apply this method to a set of supernova waveforms and compare the basis vectors obtained with those obtained through Gram-Schmidt decomposition. We observe that, for the chosen set of waveforms, the performance of the two methods are comparable for minimal match requirements up to 0.9, with 14 Gram-Schmidt basis vectors and 12 principal components required for a minimal match of 0.9. This implies that there are many common features in the chosen waveforms. Additionally, we observe the chosen waveforms have very similar features and a minimal match of 0.7 can be obtained by decomposing only one third of the entire set of waveforms in the chosen catalogue. We discuss the implications of this observation and the advantages of eigen-decomposing waveform catalogues with Principal Component Analysis.