If tr xy () is a translation function that maps a concept c i ∈ C x into the concept c i ∈ C y via the interlanguage links, we can write: The projection of the ESA vector t from language x onto y can be written as: Using equations 5, 7, and 9, we can calculate the cross-lingual semantic relatedness between any two content terms a x and b y in given languages x and y as: Note that the weights assigned to Wikipedia concepts inside the concept vectors are language specific.
two Wikipedia concepts from different languages, mapped via an interlanguage link, can, and often do have different weights.