The Research on Algorithms of Estimating Photometric Redshifts Using

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

• Background
• Various algorithms
• Comparison
• Summary

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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.

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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

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Hyperz
where Fobs,i, Ftemp,i and si 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.
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ANNs
ANN topology
Output Layer
Hidden Layer
Input Layer
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SVMs
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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.

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CMR

• R-magnitude has been divided into 7 subsections
• Build CMRI and CMRII for each sub-sample, CMRI is
  for matrices of u- g- r, and CMRII is for
  matrices of g- r- i
• CMRI and CMRII 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

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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, ci is the test
sample. h is the bandwidth.
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Selection of the Bandwidth
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Bandwidth versus redshift
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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

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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

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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).