ExoProfiler evaluates clustering quality using two complementary metrics — the Elbow method (inertia/WCSS) and the Silhouette coefficient — across K values from 2 to 10. K=2 is selected based on a clear Silhouette peak, and its stability is confirmed through multi-seed perturbation and cross-validation with alternative algorithms.Documentation Index
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Why These Metrics
- Elbow method (Inertia/WCSS): Measures total within-cluster sum of squared distances. The optimal K is at the “elbow” where adding more clusters yields diminishing inertia reduction.
- Silhouette coefficient: Measures how similar each point is to its own cluster versus the nearest cluster. Range: [-1, 1]. Higher = better separation. Cannot be computed for K=1.
K Sweep Results
| K | Inertia | Silhouette |
|---|---|---|
| 2 | 4023.36 | 0.4950 |
| 3 | 2820.81 | 0.3223 |
| 4 | 2392.98 | 0.3238 |
| 5 | ~2100 | < 0.28 |
| 6–10 | — | < 0.28 |
K=2 achieves the highest Silhouette score (0.4950), indicating strong cluster cohesion and separation. K=3 and K=4 show nearly identical Silhouette scores (~0.32), suggesting no natural three- or four-family structure in the data.
Final Model Parameters
Stability Analysis
To confirm that the K=2 solution is not an artifact of centroid initialization, the model is re-run across five different random seeds.| Seed | Inertia | Silhouette | Agreement |
|---|---|---|---|
| 42 | 4023.36 | 0.4950 | baseline |
| 10 | 4023.36 | 0.4950 | 100.00% |
| 2026 | 4023.36 | 0.4950 | 100.00% |
| 9999 | 4023.36 | 0.4950 | 100.00% |
| 100 | 4025.21 | 0.4796 | 99.04% |
4 out of 5 seeds produce identical solutions. Seed 100 differs in 7 assignments (0.96% of 731 planets), with a minor inertia increase of 1.85.
Cross-Validation with Alternative Algorithms
Hierarchical (Agglomerative) Clustering
- Algorithm: Ward linkage,
n_clusters=2 - Agreement with K-Means: 97.13%
- The dendrogram displays two clearly separable primary branches at the top level.
DBSCAN (Density-Based)
- Independently identifies one dense core cluster (majority) and ~60 outlier points (
label = -1). - These outliers correspond closely to Cluster 1 (Exotic Objects) from K-Means.
- Confirms that the Exotic group represents a statistically sparse region of the feature space.
Decision Summary
Interpreting Silhouette Scores
Silhouette scores can be interpreted against the following general benchmarks:
ExoProfiler’s score of 0.4950 approaches the reasonable-structure range, indicating meaningful but not perfectly separated clusters — consistent with a continuous physical distribution rather than discrete populations.
| Range | Interpretation |
|---|---|
| 0.71–1.00 | Strong structure |
| 0.51–0.70 | Reasonable structure |
| 0.26–0.50 | Weak structure (may be artificial) |
| < 0.25 | No substantial structure |