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.