We apply instance-based machine learning in the form of a k -nearest neighbor algorithm to the task of estimating photometric redshifts for 55,746 objects spectroscopically classified as quasars in the Fifth Data Release of the Sloan Digital Sky Survey .
We compare the results obtained to those from an empirical color-redshift relation ( CZR ) .
In contrast to previously published results using CZRs , we find that the instance-based photometric redshifts are assigned with no regions of catastrophic failure .
Remaining outliers are simply scattered about the ideal relation , in a similar manner to the pattern seen in the optical for normal galaxies at redshifts z \lesssim 1 .
The instance-based algorithm is trained on a representative sample of the data and pseudo-blind-tested on the remaining unseen data .
The variance between the photometric and spectroscopic redshifts is \sigma ^ { 2 } = 0.123 \pm 0.002 ( compared to \sigma ^ { 2 } = 0.265 \pm 0.006 for the CZR ) , and 54.9 \pm 0.7 \% , 73.3 \pm 0.6 \% , and 80.7 \pm 0.3 \% of the objects are within \Delta z < 0.1 , 0.2 , { \mathrm { and~ { } } } 0.3 respectively .
We also match our sample to the Second Data Release of the Galaxy Evolution Explorer legacy data and the resulting 7,642 objects show a further improvement , giving a variance of \sigma ^ { 2 } = 0.054 \pm 0.005 , and 70.8 \pm 1.2 \% , 85.8 \pm 1.0 \% , and 90.8 \pm 0.7 \% of objects within \Delta z < 0.1 , 0.2 , { \mathrm { and~ { } } } 0.3 .
We show that the improvement is indeed due to the extra information provided by GALEX , by training on the same dataset using purely SDSS photometry , which has a variance of \sigma ^ { 2 } = 0.090 \pm 0.007 .
Each set of results represents a realistic standard for application to further datasets for which the spectra are representative .