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radius_norm p=4: n = max(1, round((Re/8)^4)) sobre h2f_delight_autolabeling_1pct
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---
license: cc-by-4.0
task_categories:
- image-to-image
tags:
- astronomy
- supernovae
- panstarrs
- delight
size_categories:
- 10K<n<100K
---
## Description
This is the dataset from DELIGHT [1], a model that locates the host galaxy of a
transient from multi-resolution images. The difference with the original is that
the images are **not** the cutouts used in the paper: they were regenerated from
[hips2fits](https://alasky.cds.unistra.fr/hips-image-services/hips2fits)
(PanSTARRS DR1 HiPS, served by CDS).
It contains **12,610 examples**, built by **autolabeling**: transient positions are
**simulated**, not observed. For each of the 7,093 host galaxies in
[h2f_delight_train](https://huggingface.co/datasets/PRISM-Astro/h2f_delight_train),
positions are drawn **uniformly** inside the elliptical footprint of its r-band
Sérsic fit, truncated at 3·Re.
This is exactly how
[h2f_delight_autolabeling_1pct](https://huggingface.co/datasets/PRISM-Astro/h2f_delight_autolabeling_1pct)
was built. **The only difference is how many positions each galaxy gets**, and
that is what the `radius_norm` name refers to.
This variant uses the exponent `p = 4`. Its sibling
[h2f_delight_radius_norm](https://huggingface.co/datasets/PRISM-Astro/h2f_delight_radius_norm)
uses `p = 6`; see the comparison at the end.
## How many examples per galaxy: `radius_norm`
### The problem
A galaxy can only place a transient as far as **3·Re** from its own center. A
small galaxy simply cannot produce a large transient–host distance.
Most galaxies are small. So if every galaxy contributes roughly the same number
of examples, nearly all of them land at short distances and the long ones are
almost missing. In `1pct`, the fullest distance bin holds **338 times** more
examples than the emptiest one.
### The rule
Bigger galaxies generate more examples:
```
n = max(1, round((Re / Re0) ** p)) Re0 = 8 arcsec, p = 4
```
`Re0` is the size at which a galaxy starts generating more than one example.
Below it, a galaxy contributes exactly one. **No galaxy is ever dropped**: all
7,093 are present, and 90.6 % of them contribute a single example. Only 667
galaxies (9.4 %) contribute more, up to 95 for the largest one.
### Why those numbers
The count of galaxies large enough to reach a given distance drops very fast:
2,912 reach 10 arcsec, 499 reach 30, and only 27 reach 60. Raising the count to
a power compensates that drop, and `p = 4` with `Re0 = 8` is the pair that
flattened the histogram best in a grid search over both.
They are **not universal constants**: they were fitted to the size distribution
of this catalog and must be recomputed for a different survey.
### Result
| | `1pct` | `radius_norm_p4` |
|---|---|---|
| examples | 535,743 | 12,610 |
| examples per galaxy | 75.5 avg | 1.78 avg |
| median distance | 13.85″ | 9.69″ |
| 90th percentile | 30.42″ | 35.79″ |
| fullest / emptiest distance bin | **147×** | **43×** |
Measured over 5 linear bins between 0″ and 70″, the grid used to report
per-distance metrics. Neither dataset leaves an empty bin.
### `p = 4` versus `p = 6`
| | `radius_norm` (p=6, Re0=12) | `radius_norm_p4` (p=4, Re0=8) |
|---|---|---|
| examples | 9,246 | 12,610 |
| fullest / emptiest bin | 56× | **43×** |
| same, after balanced sampling | 8× | **7×** |
| effective sample size kept by that sampler | 63.4 % | **70.6 %** |
| worst-case repeats per epoch | 15 | **12** |
`p = 4` is better on every measure; it just costs 3,364 more examples. The
balanced sampler referenced above is the KDE sampler in `prism/sampler.py`
(`configs/sampler/distance_kde.yaml`).
### How it was built
Every row here is a row of `1pct`, copied unchanged. Because both use the same
uniform-in-area law, keeping a **random subset** of each galaxy's rows is a
valid sample of that same law, so nothing had to be regenerated or re-downloaded.
Every cutout is centered on the **simulated** transient position, and the
`host_pos` label is the offset from there to the host galaxy. The `fold` column
is inherited from `h2f_delight_train`, so the 5-fold cross-validation split is
preserved and no host galaxy leaks between training and validation.
Note that folds are balanced by galaxy count, not by galaxy size, and `Re**4`
amplifies any size asymmetry between them: fold 4 ends up with 2,934 examples
and fold 5 with 2,250.
## Image format
`image` has shape `(12610, 5, 1, 30, 30)`, which maps to
`(examples, resolution levels, photometric bands, height, width)`. Only the
**r band** was downloaded, hence the size-1 band dimension.
## Columns
<div style="font-family:-apple-system,BlinkMacSystemFont,'Segoe UI',Roboto,sans-serif;max-width:1000px;margin:0 auto;padding:16px 0">
<table style="width:100%;border-collapse:collapse;font-size:13px">
<thead><tr>
<th style="padding:10px 7px;text-align:left;font-weight:600;border-bottom:2px solid #4a6fb5;color:#4a6fb5;font-size:14px;width:18%">Column</th>
<th style="padding:10px 7px;text-align:left;font-weight:500;border-bottom:2px solid #4a6fb5;color:#4a6fb5;font-size:14px;width:20%">Type</th>
<th style="padding:10px 7px;text-align:left;font-weight:500;border-bottom:2px solid #4a6fb5;color:#4a6fb5;font-size:14px">Description</th>
</tr></thead>
<tbody>
<tr><td colspan="3" style="padding:8px 12px;font-weight:600;color:#4a6fb5;border-bottom:1px solid rgba(74,111,181,0.25);background:rgba(74,111,181,0.12)">Image and label</td></tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>image</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>(5,1,30,30)</code> float32</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Multi-resolution PanSTARRS r-band cutout, centered on the simulated transient position.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>host_pos</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float32 &times; 2</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Offset <code>[x, y]</code> from the simulated transient to the host galaxy, in level-0 pixels.</td>
</tr>
<tr><td colspan="3" style="padding:8px 12px;font-weight:600;color:#4a6fb5;border-bottom:1px solid rgba(74,111,181,0.25);background:rgba(74,111,181,0.12)">Identification</td></tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>oid</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">string</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Identifier of the real transient this galaxy came from. Repeats across the draws of the same galaxy.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>host_name</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">string</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Catalog name of the host galaxy.</td>
</tr>
<tr><td colspan="3" style="padding:8px 12px;font-weight:600;color:#4a6fb5;border-bottom:1px solid rgba(74,111,181,0.25);background:rgba(74,111,181,0.12)">Host galaxy</td></tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>host_redshift</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Redshift of the host; <code>NaN</code> when unknown.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>hostsize</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Angular size of the host galaxy from the catalog.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>host_ra</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Right ascension of the host, in degrees.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>host_dec</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Declination of the host, in degrees.</td>
</tr>
<tr><td colspan="3" style="padding:8px 12px;font-weight:600;color:#4a6fb5;border-bottom:1px solid rgba(74,111,181,0.25);background:rgba(74,111,181,0.12)">Real transient position</td></tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>meanra</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Mean right ascension of the real transient, in degrees. Not the center of this cutout.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>meandec</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Mean declination of the real transient, in degrees. Not the center of this cutout.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>sn_ra</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Right ascension of the real supernova, in degrees.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>sn_dec</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Declination of the real supernova, in degrees.</td>
</tr>
<tr><td colspan="3" style="padding:8px 12px;font-weight:600;color:#4a6fb5;border-bottom:1px solid rgba(74,111,181,0.25);background:rgba(74,111,181,0.12)">S&eacute;rsic fit &mdash; r band, from CasJobs</td></tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>rSerRadius</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Effective radius Re of the r-band S&eacute;rsic fit, in arcsec. Defines the sampling region.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>rSerMag</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Magnitude of the r-band S&eacute;rsic fit.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>rSerAb</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Axis ratio b/a of the fitted ellipse, between 0 and 1. Defines the sampling region.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>rSerPhi</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Position angle of the fitted ellipse, in degrees. Defines the sampling region.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>rSerRa</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Right ascension of the S&eacute;rsic fit center, in degrees.</td>
</tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>rSerDec</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">float64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Declination of the S&eacute;rsic fit center, in degrees.</td>
</tr>
<tr><td colspan="3" style="padding:8px 12px;font-weight:600;color:#4a6fb5;border-bottom:1px solid rgba(74,111,181,0.25);background:rgba(74,111,181,0.12)">Cross-validation</td></tr>
<tr>
<td style="padding:7px 7px;padding-left:20px;border-bottom:1px solid rgba(128,128,128,0.15)"><code>fold</code></td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">int64</td>
<td style="padding:7px 7px;border-bottom:1px solid rgba(128,128,128,0.15)">Cross-validation fold, from 1 to 5, inherited from the source galaxy.</td>
</tr>
</tbody>
</table>
</div>
## References
[1] F&ouml;rster, F., Mu&ntilde;oz Arancibia, A. M., Reyes-Jainaga, I., et al. 2022,
*DELIGHT: Deep Learning Identification of Galaxy Hosts of Transients using
Multiresolution Images*, The Astronomical Journal, 164, 195.
[doi:10.3847/1538-3881/ac912a](https://doi.org/10.3847/1538-3881/ac912a)
```bibtex
@article{Forster_2022,
doi = {10.3847/1538-3881/ac912a},
url = {https://doi.org/10.3847/1538-3881/ac912a},
year = {2022},
month = {oct},
publisher = {The American Astronomical Society},
volume = {164},
number = {5},
pages = {195},
author = {F\"orster, Francisco and Mu\~noz Arancibia, Alejandra M. and Reyes-Jainaga, Ignacio and Gagliano, Alexander and Britt, Dylan and Cuellar-Carrillo, Sara and Figueroa-Tapia, Felipe and Polzin, Ava and Yousef, Yara and Arredondo, Javier and Rodr\'iguez-Mancini, Diego and Correa-Orellana, Javier and Bayo, Amelia and Bauer, Franz E. and Catelan, M\'arcio and Cabrera-Vives, Guillermo and Dastidar, Raya and Est\'evez, Pablo A. and Pignata, Giuliano and Hern\'andez-Garc\'ia, Lorena and Huijse, Pablo and Reyes, Esteban and S\'anchez-S\'aez, Paula and Ram\'irez, Mauricio and Grand\'on, Daniela and Pineda-Garc\'ia, Jonathan and Chabour-Barra, Francisca and Silva-Farf\'an, Javier},
title = {DELIGHT: Deep Learning Identification of Galaxy Hosts of Transients using Multiresolution Images},
journal = {The Astronomical Journal},
}
```