Spectral principal component analysis of mid-infrared spectra of a
  sample of PG QSOs
  A spectral principal component analysis (SPCA) of a sample of 87 PG QSOs at
$z < 0.5$ is presented for their mid-infrared spectra from Spitzer Space
Telescope. We have derived the first five eigenspectra, which account for
85.2\% of the mid-infrared spectral variation. It is found that the first
eigenspectrum represents the mid-infrared slope, forbidden emission line
strength and $9.7~\mu m$ silicate feature, the 3rd and 4th eigenspectra
represent the silicate features at $18~ \mu m$ and $9.7~\mu m$, respectively.
With the principal components (PC) from optical PCA, we find that there is a
medium strong correlation between spectral SPC1 and PC2 (accretion rate). It
suggests that more nuclear contribution to the near-IR spectrum leads to the
change of mid-IR slope. We find mid-IR forbidden lines are suppressed with
higher accretion rate. A medium strong correlation between SPC3 and PC1
(Eddington ratio) suggests a connection between the silicate feature at $18~\mu
m$ and the Eddington ratio. For the ratio of the silicate strength at 9.7 $\mu
m$ to that at 18 $\mu m$, we find a strong correlation with PC2 (accretion rate
or QSO luminosity). We also find that there is a medium strong correlation
between the star formation rate (SFR) and PC2. It implies a correlation between
star formation rate and the central accretion rate in PG QSOs.
