where C m denotes the centering matrix This equivalence reveals that the method proposed by <cite>Faruqui and Dyer (2014)</cite> is closely related to our framework. More concretely, <cite>Faruqui and Dyer (2014)</cite> use Canonical Correlation Analysis (CCA) to project the word embeddings in both languages to a shared vector space. Therefore, the only fundamental difference between both methods is that, while our model enforces monolingual invariance, <cite>Faruqui and Dyer (2014)</cite> do change the monolingual embeddings to meet this restriction.