We can track the physical evolution of massive galaxies over time by characterizing the morphological signatures inherent to different mechanisms of galactic assembly. Structural studies rely on a small set of measurements to bin galaxies into disk, spheroid and irregular classifications. These classes are correlated with colors, SF history and stellar masses. Rare and subtle features that are lost in such a generic classification scheme are important for characterizing the evolution of galaxy morphology. We can connect the Hubble sequence observed for local galaxies to their high redshift progenitors to determine the full distribution of galaxy morphologies as a function of time over the entire lifetime of the Universe. To fully capture the complex morphological transformation of galaxies we need more useful classifications. To accomplish such a feat in a computationally tractable way we will need to convert galaxy images to low-dimensional representations of only a few parameters
