A principal component analysis of gravitational-wave signals from extreme-mass-ratio sources

The Laser Interferometer Space Antenna (LISA) will detect the gravitational wave emissions from a vast number of astrophysical sources, but extracting useful information about individual sources or source types is an extremely challenging prospect; the large number of parameters governing the behaviour of some sources make exhaustively searching this parameter space computationally expensive. We investigate the potential of an alternative approach, with a focus on detecting the presence of particular inspiraling binary source signals within a timeseries of gravitational wave data, and quickly providing estimates of their coalescence times. Specically, we use Principal Component Analysis (PCA) to identify redundancy within the parameter space of Extreme Mass Ratio Inspiral (EMRI) sources and construct a new, smaller parameter space containing only relevant signal information. We then create a simple search method based on how gravitational wave signals project into this new parameter space. Test cases indicate that a small number of principal components span a space occupied by the majority of EMRI spectrograms, but non-EMRI signals (including noise) do not inhabit this space. A PCA-based search method is capable of indicating the presence of gravitational waves from EMRI sources within a new test spectrogram. The results of our PCA-based searches show that the method could be used to provide initial estimates of EMRI coalescence times quickly, to be used as initial data for a more thorough search