Morphological Classification of Galaxies by Shapelet Decomposition in   the Sloan Digital Sky Survey II: Multiwavelength Classification
  We describe the application of the `shapelet' linear decomposition of galaxy images to multi-wavelength morphological classification using the $u,g,r,i,$ and $z$-band images of 1519 galaxies from the Sloan Digital Sky Survey. We utilize elliptical shapelets to remove to first-order the effect of inclination on morphology. After decomposing the galaxies we perform a principal component analysis on the shapelet coefficients to reduce the dimensionality of the spectral morphological parameter space. We give a description of each of the first ten principal component's contribution to a galaxy's spectral morphology. We find that galaxies of different broad Hubble type separate cleanly in the principal component space. We apply a mixture of Gaussians model to the 2-dimensional space spanned by the first two principal components and use the results as a basis for classification. Using the mixture model, we separate galaxies into three classes and give a description of each class's physical and morphological properties. We find that the two dominant mixture model classes correspond to early and late type galaxies, respectively. The third class has, on average, a blue, extended core surrounded by a faint red halo, and typically exhibits some asymmetry. We compare our method to a simple cut on $u-r$ color and find the shapelet method to be superior in separating galaxies. Furthermore, we find evidence that the $u-r=2.22$ decision boundary may not be optimal for separation between early and late type galaxies, and suggest that the optimal cut may be $u-r \sim 2.4$. 
B.C. Kelly, T.A. McKay