Methodology

Overview of the research methods used in the paper

Example of the S-curve:

2D manifold embedded in 3D

Compute \(k\)-nearest neighbors
→ edges of a graph

Draw a point
→ find shortest path to all others

Take a radius
→ count number of points in \([r, r+\Delta r]\)

\(r\)

\(\#(<r)\)

How well does it perform?

Methodology

1. Draw
   • \(N\) points
   • from \(D\)-sphere
   • embed in 14 dimensions
   • fill \(14-D\) dims with small (\(<10^{-2}\)) noise
2. Measure \(D\) vs. \(N\)

Results

Summary of the key findings and conclusions presented in the paper

COSMOS dataset

COSMOS dataset

HAGN

Both datasets broadly agree

HAGN

w/out noise

HAGN

w/out noise
abs. magnitudes

HAGN

w/out noise
passive only

HAGN

w/out noise
\(10^{10}<M_\star/\mathrm{M_\odot} < 10^{10.5}\)

How complex are galaxies?

How complex are galaxies?

*From wide-band photometry

Galaxies are not that complex

Wide-band photometry is 4-dimensional:

• noise
• redshift
• stellar mass
• SFR

Important to guide dimensionality reduction techniques (UMAP, SOM, VAE)

Physical underlying params?

• halo mass
• local density?
• gravitational shear (Paranjape+18)?
• tidal misalignment (Moon&Lee 24, Cadiou+22)?