The scarcity of crossing dependencies: a direct outcome of a specific constraint?
Table 1: Summary of results for each treebank: number of sentences before and after filtering, average values of Ctrue and Δ0, and average, median and standard deviation of the relative error Δ2, over the trees of each treebank. Romanian (Prague) is the only treebank with no crossing dependencies. Languages are sorted decreasingly by average Ctrue according to Stanford dependencies.
['Treebank', '#Sent', '[ITALIC] Stanford annotation #Sent (filtered)', '[ITALIC] Stanford annotation  [ITALIC] Ctrue (avg.)', 'Δ0 (avg.)', 'Δ2 (avg.)', 'Δ2 (median)', 'Δ2 (st. dev.)', '[ITALIC] Prague annotation #Sent (filtered)', '[ITALIC] Prague annotation  [ITALIC] Ctrue (avg.)', 'Δ0 (avg.)', 'Δ2 (avg.)', 'Δ2 (median)', 'Δ2 (st. dev.)']
The average number of crossings per sentence does not exceed 1 for most of the treebanks. See Ferrer -i-Cancho et al. Here we adopt the convention of sorting languages in tables not alphabetically but decreasingly by number of crossings, measured according to the average number of crossings (the average Ctrue) with Stanford dependencies. On the other hand, agglutinating languages like Basque, Japanese, Turkish, the Uralic languages Estonian and Finnish, and the Dravidian languages Tamil and Telugu, are placed rather to the bottom of the table. Agglutinating languages are languages where certain information is often integrated into words as morphemes (not leading to new vertices in the tree, except in the Turkish treebank) while non-agglutinating languages would instead place it in separate words (leading to separate vertices). Therefore, one expects fewer chances for dependency crossings in agglutinating languages, as equivalent information is expressed with fewer vertices, and the number of crossings tends to increase with the length of the sentence Ferrer -i-Cancho et al. Thus, the average Δ2 is at least 6 times smaller than the baseline Δ0≈33%. This is potentially problematic because the results might be heavily determined by the distribution of sentence lengths Ferrer-i-Cancho and Liu