Reducing the Dimensionality of Data: Locally Linear Embedding of Sloan Galaxy Spectra

TL;DR

This paper introduces Locally Linear Embedding (LLE) as a nonlinear dimensionality reduction method for classifying Sloan Galaxy Spectra, demonstrating improved accuracy and efficiency over traditional techniques like PCA.

Contribution

The paper applies LLE to astronomical spectra, compares it with existing methods, and presents a data subsampling technique to enhance classification efficiency.

Findings

LLE improves classification of emission-line spectra.

LLE combines strengths of PCA and line-ratio diagnostics.

Efficient data subsampling preserves local information.

Abstract

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.