  The energy sources of nine infrared luminous galaxies (IRLGs) are diagnosed
based on their ground-based 3--4 $\mu$m spectra. Both the equivalent width of
the 3.3 $\mu$m polycyclic aromatic hydrocarbon (PAH) emission feature and the
3.3 $\mu$m PAH to far-infrared luminosity ratio ($L_{3.3}/L_{\rm FIR}$) are
analyzed. Assuming nuclear compact starburst activity in these sources produces
the 3.3 $\mu$m PAH emission as strongly as that in starburst galaxies with
lower far-infrared luminosities, the followings results are found: For six
IRLGs, both the observed equivalent widths and the $L_{3.3}/L_{\rm FIR}$ ratios
are too small to explain the bulk of their far-infrared luminosities by compact
starburst activity, indicating that active galactic nucleus (AGN) activity is a
dominant energy source. For the other three IRLGs, while the 3.3 $\mu$m PAH
equivalent widths are within the range of starburst galaxies, the
$L_{3.3}/L_{\rm FIR}$ ratios after correction for screen dust extinction are a
factor of $\sim$3 smaller. The uncertainty in the dust extinction correction
factor and in the scatter of the intrinsic $L_{3.3}/L_{\rm FIR}$ ratios for
starburst galaxies do not allow a determination of the ultimate energy sources
for these three IRLGs.
