Understanding Galaxy Evolution
through Machine Learning
First Stars and First Galaxies Workshop 2019 @ Nagoya U

Suchetha Cooray
Collaborators:
Tsutomu T. Takeuchi (Nagoya U.), Shuntaro Yoshida (Nagoya U.), Kai Kono (Nagoya U.)

Formation and Evolution of Galaxies

Important!

http://map.gsfc.nasa.gov/m_mm.html

Formation and Evolution of Galaxies

Evolving Galaxies

Important!

http://map.gsfc.nasa.gov/m_mm.html

Final Aim of Galaxy Evolution Studies
The theoretical model to explain galaxy evolution would look like thisClearly, it is a very complicated problem!
It is high time to define the evolution of galaxies
with a more objective point of view
Credit: T. Takeuchi

Conventional Method (Derived Physical Quantities)

Grootes et al. 2013

Color (u - g)Color (NUV - r)

Color (u - g)

Traditional Methods (Color-Magnitude Diagrams)MK
Absolute magnitude Mg
Blanton (2006)

MKArnouts et al. (2007)

These plots show clear
bimodality / multimodality
Do they have a physical meaning?

Color (u - g)Color (NUV - r)

Color (u - g)

Traditional Methods (Color-Magnitude Diagrams)MK
Absolute magnitude Mg

MKRedder Galaxies: Red Sequence, Bluer galaxies: Blue Cloud, Boundary: Green Valley

Potential Problems with Color Based Methods➤ Colors are basically ratios of two luminosities

Selection effect is always too entangled and messy
Completeness test is almost impossible in a simple way

Suggestion: forget about colors!
Credit: T. Takeuchi

Question 1
Can we ﬁnd intrinsic groups ofgalaxies without selection eﬀects?

Multidimensional Luminosity Space
Instead of colors, can we just use the distribution of galaxies in a
multidimensional luminosity (absolute magnitude) space?

ColorLuminosity

If we have a bimodality in color-color space,
we must have equivalent peaks inthe multidimensional luminosity space

ColorytisoinmuLLuminosity
Credit: T. Takeuchi

Multidimensional Luminosity Space
Instead of colors, can we just use the distribution of galaxies in a
multidimensional luminosity (absolute magnitude) space?

If we have a bimodality in color-color space,
we must have equivalent peaks inthe multidimensional luminosity space
The boundaries can be automatically defined by amachine-learning type method
Advantage of this idea is that we simply deal with the selection
at each band, not as an entangled multiple selection.
Credit: T. TakeuchiData➤ Reference Catalog of galaxy Spectral Energy Distributions(RCSED) (Chilingarian et al. 2016)➤ Catalog of galaxies produced as join between GALEX, SDSS,and UKIDSS catalogs, and processed with state-of-the-art
spectral analysis methods➤ Covers approximately 25% of the sky and contains k-corrected ultraviolet-to-near-infrared photometry (11bands of FUV, NUV, u, g, r, i, z, Y, J, H, K) of some 1 million
galaxies, as well as some of their physical properties
http://rcsed.sai.msu.ru

Classification in Luminosity Space
Generate a subsample with all 11 rest-frame magnitudes (FUV,NUV, u, g, r, i, z, Y, J, H, K) -> ~800,000 galaxies=> Find a volume limited sample that is representative of thewhole galaxy sample -> ~30,000 galaxies
Can you then classify these galaxies by intuition?

…
…

Credit: T. Takeuchi

Unsupervised Machine Learning of Galaxy Groups➤ Fisher Expectation-Maximization(FisherEM) algorithm (Bouveryron& Brunet 2012)

InitialIteration 1

Iteration 3

Iteration 5

Iteration 7

Iteration 14➤ Subspace clustering method for high-dimensional data.
➤ Based on the Gaussian Mixture

Model (GMM) and estimates both
the discriminative subspace and theparameters of the mixture model

Projected clusters onto estimatedlatent discriminative sub-space atcertain iterations

Machine Learnt Galaxy Classes
We classified the whole galaxy sample into 11 classes

NUV - r(based on Siudek et al. 2018)

Davidzon et al. 2016

r-K
NUVrK diagram (Arnouts et al. 2013)

Machine Learnt Galaxy Classes
We classified the whole galaxy sample into 11 classes(based on Siudek et al. 2018)

Cross-matched with GSWLC (Salim, Boquien & Lee 2018)

FisherEMくん is so smart that helearnt about these groups all by himself!

The power of unsupervisedmachine learning algorithms!

Machine Learnt Galaxy Classes
We classified the whole galaxy sample into 11 classes(based on Siudek et al. 2018)

NUV - rHowever, the groups
don’t seem to be
separated in thisprojection!

Davidzon et al. 2016

Intrinsic smooth distribution?

Possibly amanifold (多様体)?

r-KNUVrK diagram (Arnouts et al. 2013)Galaxy Manifold?
Studies have claimed a smooth relation of galaxies in the 3D colour–colour–magnitude spacesmoothly continuing from the ‘blue cloud’ to the ‘red sequence’ (e.g. Chilingarian et al. 2012)

Chilingarian et al. (2012)

Suggests a low dimensional space existing
within a higher dimensional space (Manifold)What is the Best Representation of the Manifold?
If the manifold is 2D (surface), only two parameters are sufficient to fully describe it

β1M1 + β2 M2 + β3M3 + . . .
Linear combination of luminosities

α1M1 + α2 M2 + α3M3 + . . .
The parameters that best describes the manifold will be a
combination of the parameters in the higher dimensional space

However, we mostly only care about magnitudes and colors…

Question 2Can we ﬁnd the magnitudes orcolors that best describes a galaxy
in the manifold?

Feature Selection
Can we use a machine learning technique to identify which
magnitudes/colors (features) best represent the manifold?
Yes! We just need to ask the right question…

What features separates the 11 galaxyclasses we identified, the most?

β1M3 + β2 M4Magnitudes or colors

α1M1 + α2 M2

Random Forests for Feature Selection➤ Random Forests or random decision

forests are clustering algorithms thatgenerates random decision trees basedon the given features➤ Many of such trees produce a randomforest➤ By providing the answer (classmembership), the random forest will“learn” the important features
https://towardsdatascience.com/from-a-single-decision-tree-to-a-random-forest-b9523be65147

Feature Selection for Galaxy Manifold
Input all the magnitudes
and colors with class info

Features ranked based

Random Foreston importance
Most Important Features

Correlation Heat Map
MYFeature Importance

MNUVCorrelation

Mu

Remove highly
correlated features

Feature ImportanceMNUV (Near Ultraviolet)

2 Dimensional Galaxy Manifold

MY (Near Infrared)

MNUV (Near Ultraviolet)

2 Dimensional Galaxy Manifold
Star forming bluer galaxies
toquenched redder galaxies

MY (Near Infrared)

Comparison to SM-SFR Relation

Cross-matched with GSWLC (Salim, Boquien & Lee 2018)

3 Dimensional Galaxy Manifold

Mu(Short Optical)(3500 Å)MNUV
(Near Ultraviolet)(1700~2800 Å)

MY (Near Infrared)(10000 Å)Implications of the Results
The distribution in MNUV - MY can be
explained intuitively by a SSP evolution➤

Surprisingly, luminosities and notcolors are the best discriminators➤

Flux (normalized)➤Multimodalities and dispersions areeffects of suboptimal projections

Wavelength [Å]Bruzual & Charlot (1993)

We should rethink how we classify galaxies. Maybe we should
characterize the evolution in terms of a continuous parameterSummary➤ We demonstrated how machine learning methods can aid ourunderstanding of galaxy evolution➤ Finding unobvious patterns in the multidimensional luminosity space➤ Determining the “Galaxy Manifold” and the best projection

Machine Learning algorithms have allowed us
to do an unbiased study of galaxy evolution.
The results suggest we fundamentallyrethink our galaxy studies

Thanks!
Looking forward to the banquet!