**Joseph W. Richards, Peter E. Freeman, Ann B. Lee, Chad M. Schafer**

Dimension-reduction techniques can greatly improve statistical inference
in astronomy. A standard approach is to use Principal Components Analysis
(PCA). In this letter we apply a recently-developed technique, diffusion
maps, to astronomical spectra, and develop a robust, eigenmode-based
framework for regression and data parameterization. We show how our
framework provides a computationally efficient means by which to predict
redshifts of galaxies, and thus could inform more expensive redshift
estimators such as template cross-correlation. It also provides a natural
means by which to identify outliers (e.g., misclassified spectra). We
analyze 3846 SDSS spectra and show how our framework yields an approximately
99% percent reduction in dimensionality. Finally, we show that the prediction
error of the diffusion map-based regression approach is markedly smaller
than that of a similar approach based on PCA, clearly demonstrating the
superiority of diffusion maps over PCA and traditional linear data reduction
techniques.

Heidi Sestrich 2008-06-02 Here is the full PDF text for this technical report. It is 1406617 bytes long.