  We demonstrate how galaxy morphologies can be represented by weighted sums of
"eigengalaxies" and how eigengalaxies can be used in a probabilistic framework
to enable principled and simplified approaches in a variety of applications.
Eigengalaxies can be derived from a Principal Component Analysis (PCA) of sets
of single- or multi-band images. They encode the image space equivalent of
basis vectors that can be combined to describe the structural properties of
large samples of galaxies in a massively reduced manner. As an illustration, we
show how a sample of 10,243 galaxies in the Hubble Space Telescope CANDELS
survey can be represented by just 12 eigengalaxies. We show in some detail how
this image space may be derived and tested. We also describe a probabilistic
extension to PCA (PPCA) which enables the eigengalaxy framework to assign
probabilities to galaxies. We present four practical applications of the
probabilistic eigengalaxy framework that are particularly relevant for the next
generation of large imaging surveys: we (i) show how low likelihood galaxies
make for natural candidates for outlier detection (ii) demonstrate how missing
data can be predicted (iii) show how a similarity search can be performed on
exemplars (iv) demonstrate how unsupervised clustering of objects can be
implemented.
