Photometric redshift estimation using spectral connectivity analysis

Abstract

The development of fast and accurate methods of photometric redshift estimation is a vital step towards being able to fully utilize the data of next‐generation surveys within precision cosmology. In this paper, we apply a specific approach to spectral connectivity analysis (SCA) called diffusion map. SCA is a class of non‐linear techniques for transforming observed data (e.g. photometric colours for each galaxy, where the data lie on a complex subset of p‐dimensional space) to a simpler, more natural coordinate system wherein we apply regression to make redshift predictions. In previous applications of SCA to other astronomical problems, we demonstrate its superiority vis‐a‐vis the principal components analysis, a standard linear technique for transforming data. As SCA relies upon eigen‐decomposition, our training set size is limited to ≲104 galaxies; we use the Nyström extension to quickly estimate diffusion coordinates for objects not in the training set. We apply our method to 350 738 Sloan Digital Sky Survey (SDSS) main sample galaxies, 29 816 SDSS luminous red galaxies and 5223 galaxies from DEEP2 with Canada–France–Hawaii Telescope Legacy Survey ugriz photometry. For all three data sets, we achieve prediction accuracies at par with previous analyses, and find that the use of the Nyström extension leads to a negligible loss of prediction accuracy relative to that achieved with the training sets. As in some previous analyses, we observe that our predictions are generally too high (low) in the low (high) redshift regimes. We demonstrate that this is a manifestation of attenuation bias, wherein measurement error (i.e. uncertainty in diffusion coordinates due to uncertainty in the measured fluxes/magnitudes) reduces the slope of the best‐fitting regression line. Mitigation of this bias is necessary if we are to use photometric redshift estimates produced by computationally efficient empirical methods in precision cosmology.

The rise-time of Type II supernovae

“…A small fraction of the SNe IIP were used in Nugent et al (2006) for distance estimation analyses. The full dataset of photometric transients consists of more than 6000 objects, for which a fraction also have spectroscopic (Davis et al 2003;Le Fèvre et al 2005;Lilly et al 2007) or photometric (Ilbert et al 2006;Freeman et al 2009) redshifts from their host galaxies.…”

A catalogue of photometric redshifts for the SDSS-DR9 galaxies

“…Among the various interpolative methods, we shall just quote a few: i) polynomial fitting (Connolly et al 1995); ii) nearest neighbours (Csabai et al 2003); iii) neural networks (D'Abrusco et al 2007;Yéche et al 2010 and references therein); iv) support vector machines (Wadadekar 2005); v) regression trees (Carliles et al 2010); vi) Gaussian processes (Way & Srivastava 2006;Bonfield et al 2010); and vii) diffusion maps (Freeman et al 2009).…”

A new method to improve photometric redshift reconstruction

“…underestimation at high redshifts, shown by the downward slope in the bias, can be attributed to attenuation bias. This is the effect of the measurement errors in the observed fluxes, resulting in the measured slope of the linear regression to be underestimated on average; see Freeman et al (2009) for a full discussion of this bias. We note that the photo-z bias obtained from the templatefitting method has an opposite sign and is of the same amplitude to that obtained from the neural network method.…”