  We present the first principal component analysis (PCA) applied to a sample
of 119 Spitzer Infrared Spectrograph (IRS) spectra of local ultraluminous
infrared galaxies (ULIRGs) at z<0.35. The purpose of this study is to
objectively and uniquely characterise the local ULIRG population using all
information contained in the observed spectra. We have derived the first three
principal components (PCs) from the covariance matrix of our dataset which
account for over 90% of the variance. The first PC is characterised by dust
temperatures and the geometry of the mix of source and dust. The second PC is a
pure star formation component. The third PC represents an anti-correlation
between star formation activity and a rising AGN. Using the first three PCs, we
are able to accurately reconstruct most of the spectra in our sample. Our work
shows that there are several factors that are important in characterising the
ULIRG population, dust temperature, geometry, star formation intensity, AGN
contribution, etc. We also make comparison between PCA and other diagnostics
such as ratio of the 6.2 microns PAH emission feature to the 9.7 micron
silicate absorption depth and other observables such as optical spectral type.
