Cross-lingual Word Analogies using Linear Transformations between Semantic Spaces
Table 2: The average accuracies across all combinations of language pairs for different linear transformations and post-processing techniques. The size of bilingual dictionary was set to n=20,000. No trans. denotes the monolingual experiments without transforming the spaces.
['[EMPTY]', '[EMPTY]', '[BOLD] -  [BOLD] Acc@1', '[BOLD] -  [BOLD] Acc@5', '[BOLD] -c  [BOLD] Acc@1', '[BOLD] -c  [BOLD] Acc@5', '[BOLD] -u  [BOLD] Acc@1', '[BOLD] -u  [BOLD] Acc@5', '[BOLD] -cu  [BOLD] Acc@1', '[BOLD] -cu  [BOLD] Acc@5']
The columns represent different post-processing techniques and rows different transformations. The upper part of the table shows the monolingual experiments with original spaces without transformation (No trans.) compared with the unified multilingual space for all six languages. The orthogonal transformation provides same results as the original semantic space. Canonical correlation analysis leads to slightly lower accuracies and least squares method is worst. The most interesting is the lower part of the table, i.e., cross-lingual experiments, showing the average accuracies over all language pairs, but where source a and target b languages differ a≠b. We can see that canonical correlation analysis performs best for bilingual cases, while orthogonal transformation yields better accuracies in multilingual spaces. In all cases, the mean centering followed by vector normalization led to the best results.