object classification in sdss dr12 - cosmostat · farhang habibi lal - université paris sud-11....
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Object classification in SDSS DR12
Farhang Habibi LAL - Université Paris SUD-11
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Aim
To automatically separate stars, galaxies and Quasars by using the colour indices in
the absence of spectroscopic data.
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Cosmological surveysAll sky surveys —> cosmic structures
Deep surveys —> structures formation & evolution
To know about the nature of Dark Matter & Dark Energy
Galaxies are units of cosmic structures
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Object classification
• Cosmic structures contain galaxies.
• Images taken by surveys include galaxies, QSOs and foreground stars.
• How to separate these three objects?
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Nearby galaxies
luminosity spread on CCD: stars ~ 1 arcsec
galaxies ~ 10 arcsec
full moon ~1800 arcsec
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1.2 GLy 2.2 GLy 3 GLy 3.6 GLy 4.2 GLy
Change in galaxies angular size by distance
(SDSS)
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Far galaxies luminosity spread on CCD:
stars, QSOs ~ 1 arcsec
galaxies ~ 1 arcsec
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Stellar energy spectrum
RedBlue
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Galactic energy spectrum
RedBlue
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QSO energy spectrum
RedBlue
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Photometric systemsMagnitude in a filter
~ -Log (Flux in the same filter)
Colour = Mag(filter 1) - Mag(filter 2)
higher colour index: Redder object
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Stellar colour-magnitude diagram
Brighter stars
Fainter stars
SDSS completeness
limit
RedBlue
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galactic colour-magnitude diagram
S. Salim 2015
colo
ur
Absolute Magnitude
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Colour indices can be used to classify the celestial objects
Stars Galaxies
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SDSS survey (Sloan digital sky survey)
.2 m class telescope.complete up to ~ 2.6 GLy
~ 4 million spectroscopically classified objects
Galactic coordinates
Equatorial coordinates
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SDSS DR12 photo-spec sample ~ 2,100,000 objects (after data cleaning)
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SDSS DR12 photo-spec sample ~ 2,100,000 objects (after data cleaning)
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Colour indices as “features” for classification
Black: stars Red: galagies
u-g
g-r
i-z
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Colour indices as “features” for classification
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Colour indices as “features” for classification
Stars Galaxies
QSOs
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Object’s size as “feature” for classification
disk size ~ 8 kpc disk size ~ 2 kpc
with good seeing MW-like galaxies can be resolved by morphology
but not for faint galaxies (dwarfs)
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Object’s size as “feature” for classification
Stars Galaxies
QSOs
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Supervised Classification
Logistic regression
Parameters of the separating curve are derived by the logistic regression method.
0 0 0 0
1 1
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h✓
=1
1� e�✓
Tx
J(✓) = � 1
m
[⌃y
(i)log(h✓(x
(i))) + (1� y
(i)) log(1� h✓(x
(i))) + (1� y
(i)) log(1� h✓(x
(i)))]
Logistic regression (thanks to Andrew Ng)
xi : vector of features of an object
yi : object’s label, 0 for stars, 1 for galaxies
✓ : vector of parameters to be fitted
i : object’s index
m : total number of objects in the training set
Cost function to be minimised
Sigmoid (logistic) function
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Logistic regression• We take into account size of objects and10 colours
(c1=u-g, c2=u-r, …) plus one magnitude (u) and their quadratic function (ci.cj) to have 77 features.
• The separation region is constrained by a 12 dimension hyper parabola defined by 79 parameters.
• From ~670,000 stars, ~1,100,000 galaxies and 250,000 QSOs we randomly put 20000 form each object into the training sample.
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Results from the L.R. fit
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Results from the classification• Classification efficiency for the
whole sample: 94% galaxies: 96% stars: 92%QSOs: 88%
• Mean size of the galaxies classified wrongly: 0.5 arcseccorrectly: 3 arcsec
• Mean magnitude (extinction corrected) of the stars classified wrongly: z = 19 (fainter stars)correctly: z = 17
• Mean redshift of the QSOs classifiedwrongly: redshift = 2 (further QSOs)correctly: redshift = 1.5
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Wrongly and correctly classified galaxies
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Wrongly and correctly classified stars
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Wrongly and correctly classified QSOs
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Ongoing workComparison with other classifiers
1. Random forest technique: Whole sample efficiency ~ 95%
efficiency per object to be investigated (special thanks to Mehdi Cherti)
A basic classifier works nicely so far!
2. Go deeper in finding the sources of the misclassifications.
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• in SDSS DR12, ~ 94% of galaxies, stars and QSOs can be correctly separated using their colours and size by implementing Logistic Regression.
• 4% of galaxies (small angular size) can be mis-classified as point-like sources.
• 9% of (faint) stars can be mis-classified as galaxy-QSO.
• 12% of (further) QSOs can be mis-classified as galaxy-star.
• Classifying the simulated objects according to the LSST observation ability (higher redshifts and fainter objects).
• What is the effect of misclassified objects on photo-z determination of galaxies and cosmological parameters?
Conclusions & Perspectives