Kernel Regression For Determining Photometric Redshifts From Sloan Broadband Photometry

TL;DR

This paper introduces a kernel regression method to estimate photometric redshifts for a large galaxy dataset from SDSS, optimizing bandwidth selection via cross-validation, and achieving low rms errors.

Contribution

The study applies kernel regression with optimized bandwidth to photometric redshift estimation, demonstrating improved accuracy over traditional methods on SDSS data.

Findings

Optimal bandwidth varies with input pattern.

Achieved rms error of 0.019 with color+eClass inputs.

Rms scatter as low as 0.021 with color+r inputs.

Abstract

We present a new approach, kernel regression, to determine photometric redshifts for 399,929 galaxies in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS). In our case, kernel regression is a weighted average of spectral redshifts of the neighbors for a query point, where higher weights are associated with points that are closer to the query point. One important design decision when using kernel regression is the choice of the bandwidth. We apply 10-fold cross-validation to choose the optimal bandwidth, which is obtained as the cross-validation error approaches the minimum. The experiments show that the optimal bandwidth is different for diverse input patterns, the least rms error of photometric redshift estimation arrives at 0.019 using color+eClass as the inputs, the less rms error amounts to 0.020 using ugriz+eClass as the inputs. Here eClass is a galaxy spectra type. Then the little rms scatter is 0.021 with color+r as the inputs.