Reducing the Dimensionality of Data: Locally Linear Embedding of Sloan
  Galaxy Spectra
  We introduce Locally Linear Embedding (LLE) to the astronomical community as
a new classification technique, using SDSS spectra as an example data set. LLE
is a nonlinear dimensionality reduction technique which has been studied in the
context of computer perception. We compare the performance of LLE to well-known
spectral classification techniques, e.g. principal component analysis and
line-ratio diagnostics. We find that LLE combines the strengths of both methods
in a single, coherent technique, and leads to improved classification of
emission-line spectra at a relatively small computational cost. We also present
a data subsampling technique that preserves local information content, and
proves effective for creating small, efficient training samples from a large,
high-dimensional data sets. Software used in this LLE-based classification is
made available.
