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Automatic classification of galaxy morphology with ZEST+. Mariano - - PowerPoint PPT Presentation

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Automatic classification of galaxy morphology with ZEST+. Mariano Ciccolini Institut fr Astronomie, ETHZ PSI-LTP Theory seminar ETH Zrich - IfA Automatic classification of galaxy morphology with ZEST+. Mariano Ciccolini Institut fr

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Automatic classification of galaxy morphology with ZEST+. Mariano Ciccolini

Institut für Astronomie, ETHZ

PSI-LTP Theory seminar ETH Zürich - IfA

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Automatic classification of galaxy morphology with ZEST+. Mariano Ciccolini

Institut für Astronomie, ETHZ

PSI-LTP Theory seminar ETH Zürich - IfA

Galaxies and their morphologies Support Vector Machines ZEST+

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PSI-LTP Theory seminar ETH Zürich - IfA 2

M109: A barred spiral galaxy

Dale Swanson/Adam Block/NOAO/AURA/NSF

Type: SB(rs)bc

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Early, purely descriptive systems

  • W. Herschel & J. Herschel (1780 -1860)
  • very faint
  • Faint
  • Bright
  • small (with definite borders)
  • exceedingly large
  • J. Dreyer (1888)
  • brightness
  • form
  • concentration

M. Wolf (1908)

  • 17 classes (g) - (w)

PSI-LTP Theory seminar ETH Zürich - IfA 3

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Early, purely descriptive systems

  • W. Herschel & J. Herschel (1780 -1860)
  • very faint
  • Faint
  • Bright
  • small (with definite borders)
  • exceedingly large
  • J. Dreyer (1888)
  • brightness
  • form
  • concentration

M. Wolf (1908)

  • 17 classes (g) - (w)

T.A.Rector and B.A.Wolpa/NOAO/AURA/NSF !!!eeB eL vmE

PSI-LTP Theory seminar ETH Zürich - IfA 3

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Early, purely descriptive systems

  • W. Herschel & J. Herschel (1780 -1860)
  • very faint
  • Faint
  • Bright
  • small (with definite borders)
  • exceedingly large
  • J. Dreyer (1888)
  • brightness
  • form
  • concentration

M. Wolf (1908)

  • 17 classes (g) - (w)

!eB eL R vgbM N Bill Schoening/NOAO/AURA/NSF

PSI-LTP Theory seminar ETH Zürich - IfA 3

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Early, purely descriptive systems

  • W. Herschel & J. Herschel (1780 -1860)
  • very faint
  • Faint
  • Bright
  • small (with definite borders)
  • exceedingly large
  • J. Dreyer (1888)
  • brightness
  • form
  • concentration

M. Wolf (1908)

  • 17 classes (g) - (w)

“Es gibt keine zwei Nebelflecken am Himmel, die sich gleichen. Trotzdem geht das Bestreben der Beobachter seit Herschel dahin, die kleinen Nebelflecken zu klassifizieren.”

PSI-LTP Theory seminar ETH Zürich - IfA 3

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Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

NGC 1132 E5 : n = 10 (1-b/a)

Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA)

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

M51 SAbc

Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA)

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

NGC 1300

Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA)

SB(s)bc

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

NGC 5866

Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA)

S0

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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SLIDE 18

Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

M82 I0

Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA)

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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SLIDE 20

Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

  • E. Hubble (1936): Tuning fork diagram
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Credit: STScI

PSI-LTP Theory seminar ETH Zürich - IfA 4

Early-type Late-type

  • E. Hubble (1936): Tuning fork diagram
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PSI-LTP Theory seminar ETH Zürich - IfA 5

Why classify?

“The ultimate purpose of the classification is to understand galaxy formation and evolution.” A. Sandage

HEP example: Eight-fold way Quark model & QCD Hadrons classification scheme

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PSI-LTP Theory seminar ETH Zürich - IfA 6

Sérsic profile:

Parametric approach

Light decomposition: Fit a 1D/2D model to surface brightness profile Other approaches:

  • Isophote fitting
  • Fourier decomposition
  • Shapelets

n=1 : Exponential profile n=4 : de Vaucouleurs profile

  • I(R) = I4(R) + I1(R)

⇒ B D =

∞

0 I4(R)

∞

0 I1(R)

I(R) = Ie exp

  • −bn

R

Re

1/n

− 1

  • Re

I(R) = 1 2

∞

I(R) ⇒ Γ(2n) = 2γ(2n, bn)

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PSI-LTP Theory seminar ETH Zürich - IfA 7

Parametric approach limitations

Redshift Lookback time (Gy) Morphology

z < 0.3 < ~3.5 Hubble scheme applies in full detail. z ~ 0.5 ~5 Barred spirals rare Underdeveloped arms z > 0.6 ~6 Mergers and Irr increase z~1 : 30% off HS

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PSI-LTP Theory seminar ETH Zürich - IfA 7

Parametric approach limitations

Nearby galaxy (z ~ 0.001) Distant galaxy (z ~ 1.2)

COSMOS HST

  • ACS survey

Hillary Mathis, N.A.Sharp/NOAO/AURA/NSF

M94

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PSI-LTP Theory seminar ETH Zürich - IfA 8

Non-parametric approach: Concentration

r20 :

  • i:r(i)≤r20

Ii < 0.20 Itot r80 :

  • i:r(i)≤r80

Ii < 0.80 Itot C = log

r20

r80

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PSI-LTP Theory seminar ETH Zürich - IfA 8

Non-parametric approach: Concentration

r20 :

  • i:r(i)≤r20

Ii < 0.20 Itot r80 :

  • i:r(i)≤r80

Ii < 0.80 Itot C = log

r20

r80

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PSI-LTP Theory seminar ETH Zürich - IfA 9

Non-parametric approach: Asymmetry

A0 = 1 2

  • ij |I(i, j) − I180(i, j)|
  • ij |I(i, j)|

, A = A0 − Abkg

I( i , j ) I180( i , j ) I( i , j ) - I180( i , j )

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PSI-LTP Theory seminar ETH Zürich - IfA 9

Non-parametric approach: Asymmetry

A0 = 1 2

  • ij |I(i, j) − I180(i, j)|
  • ij |I(i, j)|

, A = A0 − Abkg

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PSI-LTP Theory seminar ETH Zürich - IfA 10

Non-parametric approach: Clumpiness

I( i , j ) IS( i , j ) I( i , j ) - IS( i , j )

S0 = 1 2

′

ij I(i, j) − IS(i, j)

  • ij |I(i, j)|

, S = S0 − Sbkg

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PSI-LTP Theory seminar ETH Zürich - IfA 10

Non-parametric approach: Clumpiness

S0 = 1 2

′

ij I(i, j) − IS(i, j)

  • ij |I(i, j)|

, S = S0 − Sbkg

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PSI-LTP Theory seminar ETH Zürich - IfA 11

Non-parametric approach: Gini coefficient

G = 1 2I N (N − 1)

N

  • i=1

N

  • j=1

|Ii − Ij|

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PSI-LTP Theory seminar ETH Zürich - IfA 12

Non-parametric approach: M20

xc =

  • i∈E xiIi
  • i∈E Ii

yc =

  • i∈E yiIi
  • i∈E Ii

Mi = Ii[(xi − xc)2 + (yi − yc)2] Mtot =

  • i∈E

Mi

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PSI-LTP Theory seminar ETH Zürich - IfA 12

Non-parametric approach: M20

xc =

  • i∈E xiIi
  • i∈E Ii

yc =

  • i∈E yiIi
  • i∈E Ii

M20 = log

  • i∈E20 Mi

Mtot

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PSI-LTP Theory seminar ETH Zürich - IfA 13

Non-parametric approach: Towards automatic classification

Can these results be generalized?

  • Parameter space dimensionality.
  • Automatic, non-linear, region detection.
  • Number of classes.
  • Prediction.
  • R. Abraham et al. (1996):

C-A plane separation

  • C. J. Concelice (2003):

C-A-S volume separation

  • J. Lotz et al. (2004):

C-A and G-M20 separation

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SLIDE 36

PSI-LTP Theory seminar ETH Zürich - IfA 13

Non-parametric approach: Towards automatic classification

Can these results be generalized?

  • Parameter space dimensionality.
  • Automatic, non-linear, region detection.
  • Number of classes.
  • Prediction.
  • R. Abraham et al. (1996):

C-A plane separation

  • C. J. Concelice (2003):

C-A-S volume separation

  • J. Lotz et al. (2004):

C-A and G-M20 separation

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SLIDE 37

PSI-LTP Theory seminar ETH Zürich - IfA 13

Non-parametric approach: Towards automatic classification

Can these results be generalized?

  • Parameter space dimensionality.
  • Automatic, non-linear, region detection.
  • Number of classes.
  • Prediction.
  • R. Abraham et al. (1996):

C-A plane separation

  • C. J. Concelice (2003):

C-A-S volume separation

  • J. Lotz et al. (2004):

C-A and G-M20 separation

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PSI-LTP Theory seminar ETH Zürich - IfA 14

Pattern Recognition: Supervised Learning

Patterns Equations & Graphics rate Label / Target Astronomer: +1 Particle Physicist:

  • 1

Data = Pattern + Label Algorithms:

  • Principal component analysis
  • Artificial neural networks
  • κ-nearest neighbours
  • Support

Vector Machines

Toy example:

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PSI-LTP Theory seminar ETH Zürich - IfA 15

Pattern Recognition: Supervised Learning

Training sample

Patterns (x1 , x2) Label (y) Equations Images 0.05 0.23 +1 0.08 0.33 +1 0.10 0.30 +1 0.13 0.20 +1 0.25 0.05

  • 1

0.23 0.18

  • 1

0.33 0.15

  • 1

0.33 0.05

  • 1

… … …

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 15

Pattern Recognition: Supervised Learning

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 15

Pattern Recognition: Supervised Learning

?

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 15

Pattern Recognition: Supervised Learning

?

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 15

Pattern Recognition: Supervised Learning

?

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 15

Pattern Recognition: Supervised Learning

?

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 15

Pattern Recognition: Supervised Learning

?

x ∈ Π ⇔ w · x + b = 0 f(x) = sgn (w · x + b) (xi, yi) in training sample ⇒ yi = f(xi)

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

δ

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 16

Pattern Recognition: Separating hyperplanes

δ

x ∈ Π ⇔ w · x + b = 0 x ∈ Π± ⇔ w · x + b = ±1 ⇒ Margin : δ = 2 w f(x) = sgn (w · x + b) (xi, yi) in training sample ⇒ yi = f(xi) w · xi + b ≤ −1 i : hep w · xj + b ≥ +1 j : astro

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PSI-LTP Theory seminar ETH Zürich - IfA 17

Optimal hyperplane: Formal approach

x ∈ Π ⇔ w · x + b = 0 x ∈ Π± ⇔ w · x + b = ±1 ⇒ Margin : δ = 2 w f(x) = sgn (w · x + b) (xi, yi) in training sample ⇒ yi = f(xi) w · xi + b ≤ −1 i : hep w · xj + b ≥ +1 j : astro

(x1, y1), . . . , (xm, ym) ∈ X × {±1} with X ⊂ ℜN (xi, yi) ← → P(x, y) f : X → {±1} : f(xi) = yi P(x, y) − → (x, y) ∈ X ⇒ f(x) = y

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PSI-LTP Theory seminar ETH Zürich - IfA 18

Optimal hyperplane: Formal approach

minimize τ(w) = 1 2w2 s.t. yi ((w · xi) + b) ≥ 1, i = 1, . . . , m αi ≥ 0 i = 1, . . . , m L(w, b, α) = 1 2w2 −

m

  • i=1

αi(yi ((w · xi) + b) − 1)

m

  • i=1

αi yi = 0, w =

m

  • i=1

αi yi xi ≤ αi ≤ (yi (w · xi + b) − 1) = αi (yi (w · xi + b) − 1) f(x) = sgn m

  • i=1

yi αi(x · xi) + b

  • Karush-Kuhn-Tucker
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PSI-LTP Theory seminar ETH Zürich - IfA 19

maximize W(α) =

m

  • i=1

αi − 1 2

m

  • i,j=1

αi αj yi yj (xi · xj) s.t. αi ≥ 0 i = 1, . . . , m and

m

  • i=1

αiyi = 0 f(x) = sgn m

  • i=1

yi αi(x · xi) + b

  • b

= 1 −

m

  • i=1

αi yi (xi · xj) with αj = 0

Wolfe dual problem

Optimal hyperplane: Formal approach

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 20

Optimal hyperplane: Non-linear separable data

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 20

Optimal hyperplane: Non-linear separable data

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 20

Optimal hyperplane: Non-linear separable data

ξi ξj

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0.1 0.2 0.3 0.4 0.5 Equations rate 0.1 0.2 0.3 0.4 0.5 Graphics rate

hep astro

PSI-LTP Theory seminar ETH Zürich - IfA 20

Optimal hyperplane: Non-linear separable data

ξi ξj

w · xi + b ≤ −1 i : hep w · xj + b ≥ +1 j : astro yi (w · xi + b) ≥ +1 ξi ≥ 0 i = 1 . . . m yi (w · xi + b) ≥ 1 − ξi

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PSI-LTP Theory seminar ETH Zürich - IfA 21

minimize τ(w) = 1 2w2 + C

m

  • i=1

ξi s.t. ξ ≥ 0 and yi (w · xi + b) ≥ 1 − ξi, i = 1, . . . , m maximize W(α) =

m

  • i=1

αi − 1 2

m

  • i,j=1

αi αj yi yj (xi · xj) s.t. 0 ≤ αi ≤ C i = 1, . . . , m and

m

  • i=1

αiyi = 0 f(x) = sgn m

  • i=1

yi αi(x · xi) + b

  • b

= 1 −

m

  • i=1

αi yi (xi · xj) with 0 < αj < C ⇒ ξj = 0

Optimal hyperplane: Non-linear separable data

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PSI-LTP Theory seminar ETH Zürich - IfA 22 x 1 x 2 x 1 x 2

~ ~

Φ

Support vector machines: Mapping data

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PSI-LTP Theory seminar ETH Zürich - IfA 23

Support Vector Machines: Kernel methods

(x1, y1), . . . , (xm, ym) ∈ X × {±1} with X ⊂ ℜN (xi, yi) ← → P(x, y) f : X → {±1} : f(xi) = yi P(x, y) − → (x, y) ∈ X ⇒ f(x) = y k : X × X − → ℜ (x, x′) − → k(x, x′) If x, x′ ∈ ℜN ⇒ k(x, x′) = x · x′ Φ : X − → F ⊂ ℜN x − → x k(x, x′) ≡ x · x′ = Φ(x) · Φ(x′)

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PSI-LTP Theory seminar ETH Zürich - IfA 23

Support Vector Machines: Kernel methods

(x1, y1), . . . , (xm, ym) ∈ X × {±1} with X ⊂ ℜN (xi, yi) ← → P(x, y) f : X → {±1} : f(xi) = yi P(x, y) − → (x, y) ∈ X ⇒ f(x) = y k : X × X − → ℜ (x, x′) − → k(x, x′) If x, x′ ∈ ℜN ⇒ k(x, x′) = x · x′ Φ : X − → F ⊂ ℜN x − → x k(x, x′) ≡ x · x′ = Φ(x) · Φ(x′)

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PSI-LTP Theory seminar ETH Zürich - IfA 23

Support Vector Machines: Kernel methods

(x1, y1), . . . , (xm, ym) ∈ X × {±1} with X ⊂ ℜN (xi, yi) ← → P(x, y) f : X → {±1} : f(xi) = yi P(x, y) − → (x, y) ∈ X ⇒ f(x) = y k : X × X − → ℜ (x, x′) − → k(x, x′) If x, x′ ∈ ℜN ⇒ k(x, x′) = x · x′ Φ : X − → F ⊂ ℜN x − → x k(x, x′) ≡ x · x′ = Φ(x) · Φ(x′) maximize W(α) =

m

  • i=1

αi − 1 2

m

  • i,j=1

αi αj yi yj (xi · xj) s.t. 0 ≤ αi ≤ C i = 1, . . . , m and

m

  • i=1

αiyi = 0 f(x) = sgn m

  • i=1

yi αi(x · xi) + b

  • b

= 1 −

m

  • i=1

αi yi (xi · xj) with 0 < αj < C ⇒ ξj = 0

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PSI-LTP Theory seminar ETH Zürich - IfA 23

Support Vector Machines: Kernel methods

(x1, y1), . . . , (xm, ym) ∈ X × {±1} with X ⊂ ℜN (xi, yi) ← → P(x, y) f : X → {±1} : f(xi) = yi P(x, y) − → (x, y) ∈ X ⇒ f(x) = y k : X × X − → ℜ (x, x′) − → k(x, x′) If x, x′ ∈ ℜN ⇒ k(x, x′) = x · x′ Φ : X − → F ⊂ ℜN x − → x k(x, x′) ≡ x · x′ = Φ(x) · Φ(x′) maximize W(α) =

m

  • i=1

αi − 1 2

m

  • i,j=1

αi αj yi yj (xi · xj) s.t. 0 ≤ αi ≤ C i = 1, . . . , m and

m

  • i=1

αiyi = 0 f(x) = sgn m

  • i=1

yi αi(x · xi) + b

  • b

= 1 −

m

  • i=1

αi yi (xi · xj) with 0 < αj < C ⇒ ξj = 0

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PSI-LTP Theory seminar ETH Zürich - IfA 24

linear : K(xi, xj) = xi · xj RBF : K(xi, xj) = exp

  • −γ xi − xj2

polynomial : K(xi, xj) = (γ xi · xj + r0)d sigmoid : K(xi, xj) = tanh (γ xi · xj + r0)

Support Vector Machines: Kernel methods

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linear : K(xi, xj) = xi · xj RBF : K(xi, xj) = exp

  • −γ xi − xj2

polynomial : K(xi, xj) = (γ xi · xj + r0)d sigmoid : K(xi, xj) = tanh (γ xi · xj + r0)

Support Vector Machines: Kernel methods

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linear : K(xi, xj) = xi · xj RBF : K(xi, xj) = exp

  • −γ xi − xj2

polynomial : K(xi, xj) = (γ xi · xj + r0)d sigmoid : K(xi, xj) = tanh (γ xi · xj + r0)

Support Vector Machines: Kernel methods

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PSI-LTP Theory seminar ETH Zürich - IfA 24

linear : K(xi, xj) = xi · xj RBF : K(xi, xj) = exp

  • −γ xi − xj2

polynomial : K(xi, xj) = (γ xi · xj + r0)d sigmoid : K(xi, xj) = tanh (γ xi · xj + r0)

Support Vector Machines: Kernel methods

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Remp [ f ] = 1 m

m

  • i=1

1 2|f(xi) − yi| , R [ f ] = 1 2|f(x) − y|dP(x, y) R [ f ] ≤ Remp [ f ] + φ h m, log(η) m

  • φ

h m, log(η) m

  • =
  • h
  • log 2m

h + 1

  • − log(η/4)

m

Capacity:

Support Vector Machines: Error constraints

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2-class SVM generalization to k classes.

Multiclass Support Vector Machines

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  • ne-versus-one:
  • Train k (k+1)/2 SVM
  • Classification: Poll

2-class SVM generalization to k classes.

Multiclass Support Vector Machines

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PSI-LTP Theory seminar ETH Zürich - IfA 26

  • ne-versus-all:
  • Train k SVM
  • Classification: max{d.f.}

2-class SVM generalization to k classes.

Multiclass Support Vector Machines

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Support Vector Machines in HEP

A. Vaiciulis, SVM in analysis of Top quark production (Nucl. Instrum. Meth. A502 (2003) 492) P . Vannerem et al., Classifying LEP data with support vector algorithms (hep-ex/9905027) TMVA: Toolkit for Multivariate Analysis In e+ e- → q qbar:

  • Charm-tagging.
  • Muon identification.

ANN and SVM give consistent results Signal and background efficiency consistent with best set of cuts Integrated machine learning environment for CERN’s ROOT http://tmva.sourceforge.net

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Non-parametric coefficients: C, A, S... Support Vector Machines: M = M(C, A, S, G, M20, . . .) Class M Early 1 Late 2 Irregular 3

Very large catalogue Training ? ? ? ?

SVM

Summary

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SLIDE 80

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The evolution of ZEST+ General Approach Details Applications: COSMOS Challenges ahead

ZEST+: The Zurich estimator of structural types

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SLIDE 81

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The evolution of ZEST+

ZEST+:

  • First C++ version, without classification (E. Weihs).
  • Further modifications (T. Bschorr).
  • Complete rewrite, new features, SVM classification (M.C.)

ZEST: C. Scarlata & M. Carollo (2007)

  • C, A, G, M20, ε, and Sérsic n.
  • PCA analysis: 3D classification grid.
  • IDL application, no public release.
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ZEST+ Architecture

Initialisation Pre-processing Characterisation Classification Catalogue Coefficients Morphologies

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ZEST+: Pre-processing

Pre-processing Image cleaning Segmentation refinement Basic segmentation

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ZEST+: Pre-processing

Pre-processing Image cleaning Segmentation refinement Basic segmentation Basic segmentation

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SLIDE 85

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ZEST+: Pre-processing

Pre-processing Image cleaning Segmentation refinement Basic segmentation Image cleaning

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SLIDE 86

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ZEST+: Pre-processing

Pre-processing Image cleaning Segmentation refinement Basic segmentation Segmentation refinement

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SLIDE 87

ZEST+: Segmentation refinement

PSI-LTP Theory seminar ETH Zürich - IfA 33

Galaxy’s center: Center of asymmetry Galaxy’s size: Petrosian radius

η(R) = 2π

R

0 I(R′)dR′

πR2I(R) 1 η(Rαp) = α Rp ≡ R0.2

p

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SLIDE 88

Save results

PSI-LTP Theory seminar ETH Zürich - IfA 34

ZEST+: Characterisation

Characterisation Substructure analysis Diagnostics Structure analysis

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SLIDE 89

Save results

PSI-LTP Theory seminar ETH Zürich - IfA 34

ZEST+: Characterisation

Characterisation Substructure analysis Diagnostics Structure analysis Center iterations Rp roots Background Signal-to-noise Negative pixels Contamination

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SLIDE 90

Save results

PSI-LTP Theory seminar ETH Zürich - IfA 34

ZEST+: Characterisation

Characterisation Substructure analysis Diagnostics Structure analysis C, A, S, G, M20

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SLIDE 91

Save results

PSI-LTP Theory seminar ETH Zürich - IfA 34

ZEST+: Characterisation

Characterisation Substructure analysis Diagnostics Structure analysis Selection ε, C, A, G, M20

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Save results

PSI-LTP Theory seminar ETH Zürich - IfA 34

ZEST+: Characterisation

Characterisation Substructure analysis Diagnostics Structure analysis

Id … C A S M20 G

ε

C A G M20 Err.

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ZEST+: Coefficients revisited

Differences from ideal case:

  • Negative pixels
  • Low signal-to-noise ratio
  • Background artefacts

A = A0 − Abkg S = S0 − Sbkg G = G(Ij) → G(|Ij|)

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PSI-LTP Theory seminar ETH Zürich - IfA 35

ZEST+: Coefficients revisited

Differences from ideal case:

  • Negative pixels
  • Low signal-to-noise ratio
  • Background artefacts

A = A0 − Abkg S = S0 − Sbkg G = G(Ij) → G(|Ij|)

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SLIDE 95

PSI-LTP Theory seminar ETH Zürich - IfA 35

ZEST+: Coefficients revisited

Differences from ideal case:

  • Negative pixels
  • Low signal-to-noise ratio
  • Background artefacts

A = A0 − Abkg S = S0 − Sbkg G = G(Ij) → G(|Ij|)

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ZEST+: Substructure analysis

  • 1. Self-subtract smoothed image.
  • 2. Threshold and eliminate isolated pixels.
  • 3. Measure all morphological coefficients.
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SLIDE 97

ZEST+: Classification

PSI-LTP Theory seminar ETH Zürich - IfA 37

  • SVM stand-alone C applications.
  • SVM library
  • Kernels: Linear, polynomial, RBF, sigmoid and user provided.
  • Multiclass algorithm: one-versus-one.
  • Supports SVM probabilities.

Algorithm: Support Vector Machines Implementation: libSVM-3.88 (C. Chang & C. Lin 2001)

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SLIDE 98

ZEST+: Classification

PSI-LTP Theory seminar ETH Zürich - IfA 38

libSVM Preprocessing Characterization Interface Catalogue C, A, S, G, M20 External Data (z, B/D,etc.) SVM info. Morphologies

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SLIDE 99

Recent ZEST+ applications

PSI-LTP Theory seminar ETH Zürich - IfA 39

  • Automatic preprocessing of large datasets.
  • Mask preparation to use with external fitting programs.
  • Petrosian radius calculation in simulated galaxies.
  • Morphological data calculation for a recent

VLT proposal.

  • Star-forming E/S0 galaxies study.
  • Substructure identification for tidal features study.
  • Morphological analysis in the COSMOS survey.
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SLIDE 100

PSI-LTP Theory seminar ETH Zürich - IfA 40

  • HST Treasury Project with ACS
  • Largest HST survey
  • 2 square degrees equatorial field
  • 2 million objects IAB > 27 mag
  • Up to z ~ 5

NASA

Objective Probe galaxy formation and evolution as a function of z and LSS environment

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SLIDE 101

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Image courtesy of ESA Subaru Telescope, NAOJ ESO/H.Zodet NASA/JPL-Caltech

Chandra, UKIRT, NOAO,CFHT, and others

NASA/JPL-Caltech Image courtesy of NRAO/AUI

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The COSMOS field

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HST - ACS camea

PSI-LTP Theory seminar ETH Zürich - IfA 43

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HST - ACS camea

PSI-LTP Theory seminar ETH Zürich - IfA 43

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HST - ACS camea

PSI-LTP Theory seminar ETH Zürich - IfA 43

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SLIDE 106

HST - ACS camea

PSI-LTP Theory seminar ETH Zürich - IfA 43

Visual ~ 4000 Å - 7000 Å

7000 8000 9000 10000 ! [Å] 0.2 0.4 0.6 0.8 1

Filter Throughput

F814W

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HST - ACS Data

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HST - ACS Data

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HST

  • ACS data: From the instrument to ZEST+
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SLIDE 110

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HST

  • ACS data: From the instrument to ZEST+
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HST

  • ACS data: From the instrument to ZEST+
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ZEST+ results

N ~ 120 000

  • IAB > 24
  • 1-b/a < 0.85
  • Stamp size < 1200 px.
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ZEST+ results

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Challenges: Cleaning errors tolerance

Bright nearby objects

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Challenges: Cleaning errors tolerance

Object truncation

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Challenges: Cleaning errors tolerance

Object truncation

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Challenges: Cleaning errors tolerance

Background features

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SLIDE 118

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Challenges: Cleaning errors tolerance

Background features

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SLIDE 119

PSI-LTP Theory seminar ETH Zürich - IfA 48

Challenges: Point Spread Function

˜ I(x, y) = I(x, y) F(x, y) + n(x, y)

No PSF With PSF

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SLIDE 120

PSI-LTP Theory seminar ETH Zürich - IfA 48

Challenges: Point Spread Function

˜ I(x, y) = I(x, y) F(x, y) + n(x, y)

No PSF With PSF

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PSI-LTP Theory seminar ETH Zürich - IfA 48

Challenges: Point Spread Function

˜ I(x, y) = I(x, y) F(x, y) + n(x, y)

No PSF With PSF

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SLIDE 122

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Challenges: Point Spread Function

Problem 1: PSF effects

  • Parametric Approach
  • Richardson-Lucy Deconvolution
  • Simulations

Problem I1: PSF determination

  • Analytic PSF
  • PSF fitting
  • HST: TinyTim
  • Blind deconvolution

˜ I(x, y) = I(x, y) F(x, y) + n(x, y)

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Conclusions

ZEST+:

  • uses a comprehensive set of non-parametric morphology descriptors.
  • analyses substructure.
  • uses a state-of-the-art classification algorithm.
  • supports the use of ad-hoc external data.
  • is flexible and fast.
  • is fully documented and its source is freely available.
  • is a portable, modular, standalone application written in C++.

More information:

  • http://www.astro.phys.ethz.ch
  • http://cosmos.astro.caltech.edu
  • http://www.kernel-machines.org
  • http://www.csie.ntu.edu/~cjlin/libsvm
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Top quark SVM analysis (A. Vaiciulis, 2003)

(GeV)

T

Jet 1 E

50 100 150 200

0.02 0.04 0.06 0.08 0.1 0.12 0.14

top WW

(GeV)

T

max lepton E

50 100 150 200

0.02 0.04 0.06 0.08 0.1 0.12

top WW

(GeV)

T

sum jet E

100 200 300

0.05 0.1 0.15

top WW

(GeV)

T

missing E

100 200

0.02 0.04 0.06 0.08 0.1 0.12

top WW

background eff.

0.2 0.4 0.6 0.8 1

signal eff.

0.2 0.4 0.6 0.8 1 SVM cuts

t t

–

q q

–

b b

–

W+ W- l+ , q

–

!l , q, l- , q, !

– l , q –

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SLIDE 125

Revised Hubble system

PSI-LTP Theory seminar ETH Zürich - IfA 52

  • Narrowing of the bins
  • Extension: Sd, Im, Am
  • Arm attachment: (r) and (s)
  • Rings
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SLIDE 126

Revised Hubble system

PSI-LTP Theory seminar ETH Zürich - IfA 52

  • Narrowing of the bins
  • Extension: Sd, Im, Am
  • Arm attachment: (r) and (s)
  • Rings

Modern Notation E - S0 - S0a - Sab - Sb - Sbc - Sc - Scd - Sd - Sd/m - Sm - Im

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Revised Hubble system

PSI-LTP Theory seminar ETH Zürich - IfA 52

  • Narrowing of the bins
  • Extension: Sd, Im, Am
  • Arm attachment: (r) and (s)
  • Rings

NGC 2523: Sbr NGC 1300: Sbs

Kormendy, J. 1979a, Ap.J., 227, 714.

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Revised Hubble system

PSI-LTP Theory seminar ETH Zürich - IfA 52

  • Narrowing of the bins
  • Extension: Sd, Im, Am
  • Arm attachment: (r) and (s)
  • Rings

NGC 1291: RSb0

Kormendy, J. 1979a, Ap.J., 227, 714.

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Visualization of the revised system

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Visualization of the revised system

Hodge (1966)

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Visualization of the revised system

de Vaucouleurs (1959)

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Visualization of the revised system

de Vaucouleurs (1959)

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The Universe large scale structure Text

Volker Springel, Carlos S. Frenk and Simon D. M. White Nature 440, 1137-1144 (27 April 2006)

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Galaxies: The hierarchical formation model

  • R. G. Abraham, Science 293, 1273 (2001)
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Galaxies: The hierarchical formation model

  • R. G. Abraham, Science 293, 1273 (2001)