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We propose a novel manifold based geometric approach for learningunsupervised alignment of word embeddings between the source and the targetlanguages. Our approach formulates the alignment learning problem as a domainadaptation problem over the manifold of doubly stochastic matrices. Thisviewpoint arises from the aim to align the second order information of the twolanguage spaces. The rich geometry of the doubly stochastic manifold allows toemploy efficient Riemannian conjugate gradient algorithm for the proposedformulation. Empirically, the proposed approach outperforms state-of-the-artoptimal transport based approach on the bilingual lexicon induction task acrossseveral language pairs. The performance improvement is more significant fordistant language pairs.

Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddings