L1 Norm
For the disagreement maps interpretation
L1 vs L2 Disagreement Metrics
When computing disagreement between two maps, L1 and L2 represent different distance metrics that measure how different the values are. Here's the key difference:
L1 (Manhattan Distance)
L1 = Σ |difference_i|
- Sums the absolute differences directly across all parameters
- Each parameter's disagreement is added linearly
- Less sensitive to outliers because large differences don't get magnified
- Result is in the same units as the original differences
- Better for detecting consistent, distributed disagreement across parameters
Example: If you have 3 parameters with differences (1, 2, 3):
- L1 = |1| + |2| + |3| = 6
L2 (Euclidean Distance)
L2 = √(Σ difference_i²)
- Squares differences before summing, then takes the square root
- Large disagreements get heavily weighted (squared term)
- More sensitive to outliers — a few large differences dominate
- Result is the geometric distance in multi-dimensional space
- Better for detecting localized, extreme disagreement
Example: Same 3 parameters with differences (1, 2, 3):
- L2 = √(1² + 2² + 3²) = √14 ≈ 3.74
Visual Comparison
| Aspect | L1 | L2 |
|---|---|---|
| Formula | Sum of absolute values | Square root of sum of squares |
| Outlier sensitivity | Low | High |
| When to use | Distributed disagreement | Extreme disagreement |
| Interpretation | Total cumulative difference | Geometric distance |
| Result scale | Larger values | Smaller values (due to square root) |
In Your Code Context
In compute_composite_disagreement():
- L1 method: Each pixel shows the sum of all parameter differences → highlights regions where many parameters disagree
- L2 method: Each pixel shows the Euclidean norm → emphasizes regions where at least one parameter disagrees significantly
Choose L1 if you want to see overall cumulative disagreement; choose L2 if you want to highlight hotspots of severe disagreement in specific parameters.