Mapping the Similarities of Spectra: Global and Locally-biased Approaches to SDSS Galaxy Data.

We present a novel approach to studying the diversity of galaxies. It is based on a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors. Our method introduces new coordinates that summarize an entire spectrum, similar to but going well beyond the widely used Principal Component Analysis ( PCA). Unlike PCA, however, this technique does not assume that the Euclidean distance between galaxy spectra is a good global measure of similarity. Instead, we relax that condition to only the most similar spectra, and we show that doing so yields more reliable results for many astronomical questions of interest. The global variant of our approach can identify very finely numerous astronomical phenomena of interest. The locally-biased variants of our basic approach enable us to explore subtle trends around a set of chosen objects. The power of the method is demonstrated in the Sloan Digital Sky Survey Main Galaxy Sample, by illustrating that the derived spectral coordinates carry an unprecedented amount of information.