These plots compare Manhattan (L1) and Euclidean (L2) distances for a single data set.
| Data set | Curse factor | Minimum distance and difference to maximum |
| All-Relevant | all-relevant-factor.pdf | all-relevant.pdf |
| 10-Relevant | 10-relevant-factor.pdf | 10-relevant.pdf |
| Cyc-Relevant | cyc-relevant-factor.pdf | cyc-relevant.pdf |
| Half-Relevant | half-relevant-factor.pdf | half-relevant.pdf |
| All-Dependent | all-dependent-factor.pdf | all-dependent.pdf |
| 10-Dependent | 10-dependent-factor.pdf | 10-dependent.pdf |
These plots compare all artificial data sets for a single distance function.
| Manhattan | Euclidean | L0.6 | L0.8 | Arccosine |
Curse factor: The common formulation (Beyer et al.) of the curse of dimensionality states that the contrast between the farthest neighbor and the closest neighbor diminish. As it can be seen, all of these data sets are to be considered "cursed" using this formula.
Minimum distance and difference to maximum: By separating the two factors, minimum distance and difference between minimum and maximum distance, one can see that the minimum distance is growing quickly for all of these data sets.
Lp norms with p < 1 ("fractional Lp norms") are no longer metric: they do not satisfy the triangle equality.
Manhattan = L1, Euclidean = L2.
