  We propose a novel manifold based geometric approach for learning
unsupervised alignment of word embeddings between the source and the target
languages. Our approach formulates the alignment learning problem as a domain
adaptation problem over the manifold of doubly stochastic matrices. This
viewpoint arises from the aim to align the second order information of the two
language spaces. The rich geometry of the doubly stochastic manifold allows to
employ efficient Riemannian conjugate gradient algorithm for the proposed
formulation. Empirically, the proposed approach outperforms state-of-the-art
optimal transport based approach on the bilingual lexicon induction task across
several language pairs. The performance improvement is more significant for
distant language pairs.
