Assuming we are able to compute a M × Ndimensional bilingual word co-occurrence matrix Σ from the SMT parallel corpus, the matrix-vector productû = Σv is a projection of the target sentence in the source vector space.
those source terms of the M -dimensional vectorû will be emphasized that most frequently co-occur with the target terms in v. ,û can be interpreted as a "bagof-words" translation of v. the cross-lingual similarity between the candidate source and target sentences then reduces to the cosine similarity between the source term-frequency vector u and the projected target term-frequency vectorû, as shown in Equation 2.1: In the above equation, we ensure that both u and u are normalized to unit L 2 -norm.