1. The Research on Algorithms of Estimating Photometric Redshifts Using SDSS Galaxy Data Wang Dan China-VO group Chinese Virtual Observatory

2. 11/29-12/03China-VO 2006, Guilin2 Outline Background Various algorithms Comparison Summary

3. 11/29-12/03China-VO 2006, Guilin3 Background The redshift of a galaxy is measured spectroscopically For those large and faint sets of galaxies, spectra of galaxies are not quick and easy to obtain Photometric redshift technique concentrates on medium- or broadband color features Photometric redshifts have been regarded as an efficient and effective measure for studying the statistical properties of galaxies and their evolution.

4. 11/29-12/03China-VO 2006, Guilin4 Methods Template fitting approach  Real observation (CWW)  Population synthesis models (Bruzual & Charlot) Training set approach  Artificial Neural Networks (ANNs)  Support Vector Machines ( SVMs)  Multivariable Polynomial Regression (MPR)  Color-Magnitude-Redshift Relation (CMR)  Nonparametric Regression

5. 11/29-12/03China-VO 2006, Guilin5 Hyperz where F obs,i, F temp,i and σ i are the observed and template fluxes and their uncertainty in filter i, respectively, and b is a normalization constant. Do not reply on having any spectroscopic redshifts, need only a few templates.

6. 11/29-12/03China-VO 2006, Guilin6 ANN topology: Input Layer Hidden Layer Output Layer ANNs

7. 11/29-12/03China-VO 2006, Guilin7 Principal ：利用结构风险最小化的原理，即 最小化预期风险的上限。通过最大化超平 面与任意类训练样本的最小距离或最大化 分类边界的距离，从而得到最优超平面。 SVMs

8. 11/29-12/03China-VO 2006, Guilin8

9. 11/29-12/03China-VO 2006, Guilin9 MPR Generate logical relationships between several independent variables and a dependent variable Training set containing the values of the independent and dependent variables MPR performs the regression and presents the result as a mathematical expression The more complete and representative training data we provide, the more accurate the estimate of redshifts will be Easy to communicate with astronomers.

10. 11/29-12/03China-VO 2006, Guilin10

11. 11/29-12/03China-VO 2006, Guilin11 CMR R-magnitude has been divided into 7 subsections Build CMR I and CMR II for each sub-sample, CMR I is for matrices of u- g- r, and CMR II is for matrices of g- r- i CMR I and CMR II have been separated into 400 × 400 bins. Compute the median redshift if the number of galaxies exceeds 25 Achieve a color-redshift matrix, and compute the redshifts from the matrices

12. 11/29-12/03China-VO 2006, Guilin12

13. 11/29-12/03China-VO 2006, Guilin13 Nonparametric Regression No (or very little) a priori knowledge Selecting an appropriate bandwidth (smoothing parameter) is a key part of nonparametric regression fitting Where c is training sample, c i is the test sample. h is the bandwidth.

14. 11/29-12/03China-VO 2006, Guilin14 Selection of the Bandwidth

15. 11/29-12/03China-VO 2006, Guilin15 Bandwidth versus redshift

16. 11/29-12/03China-VO 2006, Guilin16 Accuracies of Different Methods CWW 0.0666 Bruzual - Charlot 0.0552 ANNs 0.0229 SVMs 0.027 CMR 0.032 Nonparametric Regression 0.0236 MPR 0.0256

17. 11/29-12/03China-VO 2006, Guilin17 Summary Empirical photometric redshift estimators do rely on the existence of a sufficiently large and representative training set Difficulty in extrapolating to regions that are not well sampled by the training data. Well suited to problems that require the redshift distribution rather than accurate redshift of individual galaxy

18. 11/29-12/03China-VO 2006, Guilin18 Prospect With the large and deep sky survey projects carried out, more large and representive samples will be obtained. The development of new statistical analysis algorithms. Feature selection/extraction while data reprocessing More ensemble algorithms (e.g. least-square SVMs).