REDUCING THE DIMENSIONALITY OF DATA: LOCALLY LINEAR EMBEDDING OF SLOAN GALAXY SPECTRA

Abstract

We introduce Locally Linear Embedding (LLE) to the astronomical community as\na new classification technique, using SDSS spectra as an example data set. LLE\nis a nonlinear dimensionality reduction technique which has been studied in the\ncontext of computer perception. We compare the performance of LLE to well-known\nspectral classification techniques, e.g. principal component analysis and\nline-ratio diagnostics. We find that LLE combines the strengths of both methods\nin a single, coherent technique, and leads to improved classification of\nemission-line spectra at a relatively small computational cost. We also present\na data subsampling technique that preserves local information content, and\nproves effective for creating small, efficient training samples from a large,\nhigh-dimensional data sets. Software used in this LLE-based classification is\nmade available.\n