Linear Transformations for Cross-lingual Semantic Textual Similarity
Table 4: Skewness of hubness distribution N20.
['[EMPTY]', 'Es', 'Es→En', 'Ar', 'Ar→En', 'Tr', 'Tr→En']
Euclidean distance has been used for searching nearest neighbors. Original semantic spaces before transformation have following skewness: English 3.14, Spanish 2.71, Arabic 3.65, and Turkish 4.02, respectively. The columns with an arrow are for cross-lingual skewness, i.e., for words in source semantic spaces we look for nearest neighbors in the target semantic spaces. Columns without arrow denote the skewness in the space after it is transformed onto English. The hubness in the source space remains the same after the transformation by OT, because it preserves the angles between points. Our nearly orthogonal transformation has slightly worse hubness. Surprisingly, not LS, but CCA transformation leads to the worst hubness in the source space. However, the hubness problem between the semantic spaces is much more important as it affects the cross-lingual performance. In all cases our ORT transformation leads to the lowest hubness. We believe it is because the objective function focused on mapping in both directions.