Check near-Earth asteroid orbit-group labels from orbital elements
This reproducible catalogue benchmark maps eleven orbital and photometric fields to the Amor, Apollo or Aten group. The fixed 11–3 softmax model classifies 317 of 344 held-out records correctly. Its 92.2% accuracy must be read alongside 67.9% balanced accuracy and 22.2% Aten recall.
1. Scientific objective
The objective is to reproduce an existing near-Earth-object orbit-group label from catalogue fields. The learned classifier is useful as a data-pipeline consistency check and as a compact multiclass benchmark. Because Amor, Apollo and Aten classes are defined by explicit orbital-element boundaries, the network does not replace the authoritative rule-based classification.
Flag records whose learned class disagrees with the stored label or with the deterministic orbital-element rule.
Exercise schema validation, feature ordering, multiclass inference and class-level monitoring in a reproducible workflow.
Identify low-margin cases near group boundaries for inspection instead of treating every softmax score as equally certain.
2. Data and provenance
The downloadable orbit_class.csv contains 1,722 complete, non-duplicated records. The target is strongly imbalanced: 1,477 Apollo records (85.8%), 149 Aten records (8.7%) and 96 Amor records (5.6%).
The field names below are the exact names used by the updated CSV and Python export.
| CSV field | Meaning | Unit or scale |
|---|---|---|
semi_major_axis | Semimajor axis, a | AU |
eccentricity | Orbital eccentricity, e | dimensionless |
inclination | Inclination to the reference plane, i | degrees |
argument_of_perihelion | Argument of perihelion, ω | degrees |
longitude_of_ascending_node | Longitude of the ascending node, Ω | degrees |
mean_anomaly | Mean anomaly at the catalogue epoch, M | degrees |
perihelion_distance | Perihelion distance, q | AU |
aphelion_distance | Aphelion distance, Q | AU |
orbital_period | Orbital period | Julian years |
absolute_magnitude | Absolute magnitude, H | magnitude |
earth_moid | Minimum orbit-intersection distance with Earth | AU |
orbit_class | Target group: AMO, APO or ATE | categorical |
Authoritative class boundaries
| Code | Group | JPL orbital-element definition |
|---|---|---|
AMO | Amor | a > 1.0 AU and 1.017 < q < 1.3 AU |
APO | Apollo | a > 1.0 AU and q < 1.017 AU |
ATE | Aten | a < 1.0 AU and Q > 0.983 AU |
| Subset | Rows | Purpose |
|---|---|---|
| Training | 1,034 | Estimate the 36 model parameters |
| Selection | 344 | Monitor generalization during fixed-architecture training |
| Testing | 344 | Report final performance once |
3. Model
All eleven numeric inputs use mean-and-standard-deviation scaling. The fixed model connects them directly to three softmax outputs ordered as AMO, APO and ATE. It has no hidden layer and contains 36 trainable parameters, so it is a multiclass logistic model expressed in Neural Designer’s neural-network framework.
This is both the base and final architecture. No neuron-selection task is used in this example.
4. Training strategy
The model minimizes multiclass cross-entropy with the quasi-Newton method and no explicit regularization. Training stopped at the configured loss goal after 87 completed epochs (88 stored iterations): cross-entropy decreased from 1.1373 to 0.0008 on training data, while selection cross-entropy changed from 0.6998 to 0.1920.
The selection error reached its lowest stored value, 0.0792, at epoch 59 and then increased while training error continued to fall. This divergence is evidence of overfitting after that point; production work should restore the best-selection checkpoint or apply early stopping.
5. Model selection and baseline
No neuron selection was performed, and no architecture selection was performed. The direct 11–3 softmax architecture was fixed before training and retained as the final model. The selection subset was used only to monitor generalization.
Baselines that matter for this scientific task
| Method | Testing accuracy | Balanced accuracy | Interpretation |
|---|---|---|---|
| Always predict Apollo | 87.2% | 33.3% | High apparent accuracy caused by class imbalance |
| Fixed neural model | 92.2% | 67.9% | Improves aggregate classification but misses most Aten records |
| NASA/JPL boundary rules | 100.0% | 100.0% | Expected benchmark because the target is defined from orbital elements |
6. Scientific validation
The held-out subset contains 17 Amor, 300 Apollo and 27 Aten records. The model correctly classifies 317 of 344 records, but the confusion matrix shows that 21 of the 27 Aten records are assigned to Apollo.
| Metric | Value | Interpretation |
|---|---|---|
| Accuracy | 92.15% | 317 correct classifications from 344 testing records |
| Macro precision | 91.63% | Unweighted mean precision across the three groups |
| Balanced accuracy / macro recall | 67.86% | Unweighted mean recall; exposes weak Aten sensitivity |
| Macro-F1 | 71.46% | Unweighted harmonic-mean performance across groups |
| Weighted-F1 | 90.34% | F1 weighted by the imbalanced testing prevalence |
Confusion matrix
| Actual / predicted | Amor | Apollo | Aten | Total |
|---|---|---|---|---|
| Amor | 14 | 3 | 0 | 17 |
| Apollo | 3 | 297 | 0 | 300 |
| Aten | 0 | 21 | 6 | 27 |
| Total | 17 | 321 | 6 | 344 |
Per-class performance
| Group | Testing rows | Precision | Recall | F1 |
|---|---|---|---|---|
| Amor | 17 | 82.35% | 82.35% | 82.35% |
| Apollo | 300 | 92.52% | 99.00% | 95.65% |
| Aten | 27 | 100.00% | 22.22% | 36.36% |
7. Inference and reproducibility
A professional workflow should validate the schema and units, calculate the deterministic NASA/JPL group, optionally run the learned classifier as an independent consistency check, and route disagreements or low-score-margin cases to review. Hazard assessment is a separate workflow that requires more than an orbit-group label.
Representative catalogue-consistency case
This operating point is inside the training ranges and is stored in the Neural Designer project. Its a and q values satisfy the Apollo definition.
| Input | Value | Input | Value |
|---|---|---|---|
| Semimajor axis | 1.52 AU | Eccentricity | 0.34 |
| Inclination | 14.6° | Argument of perihelion | 197° |
| Ascending-node longitude | 200° | Mean anomaly | 118° |
| Perihelion distance | 1.00 AU | Aphelion distance | 2.05 AU |
| Orbital period | 1.88 years | Absolute magnitude | 21.4 |
| Earth MOID | 0.016 AU | Rule-based group | Apollo |
Softmax scores: AMO 4.27%, APO 95.73%, Aten <0.01%. The model and boundary rule agree.
Try the exported orbit classifier
Enter an operating point using the same units and field order as the published CSV. Decimal commas and decimal points are accepted.
Reproduce the calculation
The Python package contains the exact exported model, ordered input schema, representative case and expected softmax scores. The Neural Designer package preserves the 1,034/344/344 split, trained parameters and regenerated analyses.
from model import NeuralNetwork
inputs = [1.52, 0.34, 14.6, 197, 200, 118, 1.00, 2.05, 1.88, 21.4, 0.016]
amo, apo, ate = NeuralNetwork().calculate_outputs(inputs)8. Validity, uncertainty and limitations
- The label is rule-derived. Amor, Apollo and Aten groups are defined from orbital elements. A deterministic implementation is the appropriate production classifier; the learned model is a benchmark or consistency check.
- Class imbalance is substantial. Apollo records are 85.8% of the data. Accuracy therefore overstates performance on the minority Aten class.
- Training continued beyond the best selection epoch. Selection cross-entropy was lowest at epoch 59 and rose to 0.192 by epoch 87. The published export does not restore that earlier checkpoint.
- Random row validation is limited. It measures interpolation within this curated table, not transfer to later catalogue epochs, newly discovered objects or lower-quality orbit solutions.
- Uncertainty is absent. The CSV contains point estimates but no covariance matrices, observational arcs, condition codes or measurement uncertainties.
- The source table lacks object identity. Without catalogue identifiers and epochs, records cannot be independently reconciled with the current JPL Small-Body Database.
- Softmax scores are not calibrated probabilities. They should not be interpreted as scientific confidence or impact risk.
References
- NASA/JPL Center for Near-Earth Object Studies, Near-Earth Object Groups.
- NASA/JPL Solar System Dynamics, Small-Body Database query filters and orbit-class definitions.
- NASA/JPL Solar System Dynamics, Small-Body Database Query API.
- B. Dincer, Orbit Classification For Prediction, Kaggle.