Normalization¶
Overview¶
METIS normalizes all raw metric values to [0, 1] where 1 = best quality. This enables:
- Comparison across metrics with different scales
- Aggregation into composite scores
- Cross-dataset comparability
Normalization Types¶
Each metric has a normalization type that determines how the raw value is transformed:
| Type | Raw interpretation | Formula |
|---|---|---|
| Distance | Lower = better | 1 - clip((raw - lower) / (upper - lower)) |
| Similarity | Higher = better | clip((raw - lower) / (upper - lower)) |
| Bounded [0,1] | Already in [0,1] | clip(raw) or calibrated |
Metric Normalization Map¶
All 48 metrics are pre-classified:
Distance metrics (lower raw = better synthetic quality)¶
- KS, Wasserstein, Anderson-Darling, Hellinger, KDE-ISE
- Delta Mean, Delta Median, Delta IQR, Delta MAD, Cohen's d
- TVD, JS, KL, PSI, Entropy Delta, Gini Delta
- Pearson delta, Spearman delta, MI delta, dCor delta
- Eta², Point-Biserial, Kruskal ε²
- Cramér's V delta, Theil's U delta, χ² statistic delta
- Correlation Matrix, MMD, Energy Distance
- DCR (inverted), NNAA, MIA, Record Linkage, Inference Attack
Similarity metrics (higher raw = better)¶
- Outliers Coverage
- TSTR, TRTS, TTS, TTRS, ML Efficiency
- k-Anonymity, l-Diversity, t-Closeness
- Differential Privacy, Delta Exceedance
Stochastic Dominance Aggregation¶
After normalization, scores are aggregated using First-Order Stochastic Dominance (FSD):
- Per-column scores are computed for each metric
- FSD determines if one distribution of scores dominates another
- Family scores (fidelity, utility, privacy) are computed
- A composite score combines all three dimensions
This is more robust than simple averaging because it respects the ordinal structure of scores.