Extracting Stellar Population Parameters of Galaxies from Photometric Data Using Evolution Strategie

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Extracting Stellar Population Parameters of
Galaxies from Photometric Data Using Evolution
Strategies and Locally Weighted Linear Regression

• 1Luis Alvarez,1Olac Fuentes and
• 1,2Roberto Terlevich

1Instituto Nacional de Astrofísica Óptica y
Electrónica, Mexico 2Institute of Astronomy,
University of Cambridge, U.K.
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Content

• Problem definition
• Data
• Methods
• Evolution strategies
• Hybrid algorithm ES-LWLR
• Experiments
• Results
• Conclusions
• Future work

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Problem definition

• Nowadays, there is a great amount of high
  quality photometric data that are being analyzed
  by different methods, with the aim of obtaining a
  better understanding of the structure and
  evolution of the Universe.
• Among the important information that can be
  extracted from galactic photometric data are
  ages and proportions of stellar populations,
  redshift and reddening.
• The goal of this work is to develop fast and
  accurate algorithms for extracting stellar
  population parameters from photometric data of
  galaxies.
• We are interested in using photometric instead of
  spectroscopic data because photometric can be
  obtained from very weak galaxies.

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Photometric vs. Spectroscopic Data
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Data

• The data are spectra of artificial galaxies
  formed by combining three spectra of synthetic
  stellar populations of different ages (F1, F2
  and F3). Each artificial galaxy is reddened (R)
  and redshifted (z). The photometric data are
  obtained after applying filters to the galaxy.
• The experiments use a set of nine synthetic
  stellar population spectra of high resolution.
  Also, another set with nine low resolution
  spectra is obtained from the original one by
  sampling.

combination
p1, p2, R, z
F2, F3
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Data (in detail)
1. To combine three spectra Fi , where each
spectrum belong
to a different stellar age, according to
percentages Pi.
2. To apply the reddening
Reddening (R) is the preferential scattering of
the shorter wavelengths of light due to gas and
interstellar dust.
3. To apply the redshift
Redshift (z) is a shift toward longer wavelengths
of the radiation caused by the emitting object
moving away from the observer. It is to the
expanssion of the Universe.
4. To filter the spectrum
Finally, from the redshifted spectrum we
calculate fifteen photometric filter values by
averaging the fluxes in fiftten windows of equal
width distributed uniformly along the spectrum.
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Optimization approach

• The problem is posed as an optimization task. The
  objective function is the sum of cuadratic
  differences between photometric query data (pd)
  and photometric data predicted by a
  model.

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Methods

• Traditional methods
• Template fitting (used for estimating age and
  reddening)
• Neural networks (photometric redshifts)
• Nearest Neighbors (photometric redshifts)
• Evolution Strategies
• They implement biological evolution concepts by
  means of genetic operators combination, mutation
  and selection.
• They optimize parameters by generating a random
  population of solutions that is evolved using
  genetic operators. The evolved population
  contains candidate solutions that are closer to
  an acceptable solution.
• They are appropriate for this problem because
  they are noise tolerant, work well in high
  dimensional spaces and they do not get stuck in
  local minima.

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Solution Diagram using ES
Evolution Strategies
no
Input PD
Generation of n random SPP, by means of genetic
operators
Selection of the SPP that best describe input PD
Acceptable solution ?
Creation of pairs (SPP, PD)
SPP
YES
SPP
Pair creation (SPP, PD)
Synthetic spectra database
Application of N filters
Combination
PD
1 2 N
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Hybrid algorithm ES-LWLR

• Key Idea We can use the individuals created in
  previous generations as training data for a
  learning algorithm.
• Use the best individuals of each generation to
  build a local linear model (M PD-gtSPP) to
  generate a new individual, possibly closer to the
  global solution than the best in the current
  population.
• The model is built using Locally Weighted Linear
  Regression (LWLR), an instance-based learning
  algorithm.
• The resulting hybrid algorithm ES-LWLR converges
  faster than ES alone to an acceptable solution.

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Using LWLR

• Evolution strategies create individuals encoding
  parameters of stellar populations SPP
  (F2,F3,P1,P2,,R, z), these are used to obtain the
  corresponding photometric data, then the
  objective function is evaluated for each
  individual.
• If the relation SPP-gtPD is reversed, a linear
  model can be created for estimating the SPP from
• This model is used for predicting a new set of
  parameters for the query photometric data pd.
  LWLR estimates the coeficcients of the relation
  Y-1.

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Experiments

• Performance measures
• Time (in seconds, using a PC Pentium 4 2.4Ghz
  RAM 128Kb)
• Mean absolute error (MAE) of SPP.
• Evolution strategies parameters
• µ 50, ?100, ?s0.25, generations50
• The test set of pd for ES algorithm is formed
  from
• - 100 SPP using high resolution spectra,
• - 100 SPP using low resolution spectra,
• - 100 SPP using high resolution noisy spectra,
  and
• - 100 SPP using low resolution noisy spectra.
• (all random)
• Another set test of equal size is formed for
  ES-LWLR algorithm.

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Results
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Results (2)
Objective function

pd query photometric data, pd photometric data
predicted by the model.
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Conclusions

• The problem of extracting stellar population
  parameters from photometric data is posed as an
  optimization problem and then solved using
  Evolution Strategies.
• The idea of
• forming a linear model, using the solutions in
  each evolution-estrategy generation, that
  predicts a new individual
• accelerates the convergence and increases the
  accuracy.
• In spectra with Gaussian noise, the performance
  of ES and the hybrid algorithm (ES-LWLR) is
  similar.

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Future Work

• Improvement of the hybrid algorithm
• Use ES-(µ,?) version to possibly improve the
  performance in noisy spectra.
• Design a strategy that stores the best
  individuals of each generation, then forms the
  linear model after n generations, because the
  solutions of (µ,?) version are more sparse than
  the solutions of the (µ?) version used in this
  work.
• Improve the population by adding more than one
  individual by means of a weighted average between
  the query pd and the best pd predicted.

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Future Work

• Improvement of the application
• Refine the models used reddening, filters,
  method of combining spectra.
• Experiment with different filter sets.
• Form a training set of real spectra with the aid
  of an expert in the domain who would have to
  verify the labeling of the test set.
• Experiment with real data.

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Thanks!Questions?