Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddings

We propose a novel manifold based geometric approach for learning\nunsupervised alignment of word embeddings between the source and the target\nlanguages. Our approach formulates the alignment learning problem as a domain\nadaptation problem over the manifold of doubly stochastic matrices. This\nviewpoint arises from the aim to align the second order information of the two\nlanguage spaces. The rich geometry of the doubly stochastic manifold allows to\nemploy efficient Riemannian conjugate gradient algorithm for the proposed\nformulation. Empirically, the proposed approach outperforms state-of-the-art\noptimal transport based approach on the bilingual lexicon induction task across\nseveral language pairs. The performance improvement is more significant for\ndistant language pairs.\n