ANNz: estimating photometric redshifts using artificial neural networks

TL;DR

ANNz presents a freely available software package that uses artificial neural networks to estimate photometric redshifts from broad-band photometry by learning a mapping from observed magnitudes to redshift using a labeled training set. The method employs multilayer perceptrons, regularized training, and validation to minimize squared-error, with a committee mechanism to reduce variance and provide uncertainty estimates. Applied to SDSS data, ANNz achieves photometric redshift rms around $\sigma_{rms}\approx 0.02$–0.024, outperforming several template-based approaches and enabling extensions such as incorporating additional inputs and predicting spectral-type. The paper discusses limitations due to training-set representativeness and highlights strategies like using simulated catalogs to improve coverage and extrapolation, illustrating the practical impact for large photometric surveys.

Abstract

We introduce ANNz, a freely available software package for photometric redshift estimation using Artificial Neural Networks. ANNz learns the relation between photometry and redshift from an appropriate training set of galaxies for which the redshift is already known. Where a large and representative training set is available ANNz is a highly competitive tool when compared with traditional template-fitting methods. The ANNz package is demonstrated on the Sloan Digital Sky Survey Data Release 1, and for this particular data set the r.m.s. redshift error in the range 0 < z < 0.7 is 0.023. Non-ideal conditions (spectroscopic sets which are small, or which are brighter than the photometric set for which redshifts are required) are simulated and the impact on the photometric redshift accuracy assessed.

Figures (6)

• Figure 1: A schematic diagram of a multi-layer perceptron, as implemented by annz, with input nodes taking, for example, magnitudes $m_i = -2.5\log_{10}f_i$ in various filters, a single hidden layer, and a single output node giving, for example, redshift $z$. The architecture is $n$:$p$:1 in the notation used in this paper. Each connecting line carries a weight $w_{ij}$. The bias node allows for an additive constant in the network function defined at each node. More complex networks can have additional hidden layers and/or outputs.
• Figure 2: Spectroscopic vs. photometric redshifts for annz applied to 10,000 galaxies randomly selected from the SDSS EDR.
• Figure 3: A subset of 200 galaxies randomly selected from the results of Fig. \ref{['fig.edr.5']}, and with the error bars calculated by annz shown. These are a combination of contributions from photometric noise (§\ref{['sec.noise']}) and network variance (§\ref{['sec.netvar']}).
• Figure 4: Photometric redshift estimation using hyperz with the CWW template SEDs. This uses the same 10,000 galaxy sample as figure \ref{['fig.edr.5']}. There are obvious systematic deviations, with bands apparent above and below the $z_\mathrm{phot} = z_\mathrm{spec}$ line.
• Figure 5: Results from using annz to predict the spectral type (in the form of the eClass parameter) simultaneously with the redshift for 64,175 galaxies from the SDSS Data Release 1.