  Great progress has been made in unsupervised bilingual lexicon induction
(UBLI) by aligning the source and target word embeddings independently trained
on monolingual corpora. The common assumption of most UBLI models is that the
embedding spaces of two languages are approximately isomorphic. Therefore the
performance is bound by the degree of isomorphism, especially on etymologically
and typologically distant languages. To address this problem, we propose a
transformation-based method to increase the isomorphism. Embeddings of two
languages are made to match with each other by rotating and scaling. The method
does not require any form of supervision and can be applied to any language
pair. On a benchmark data set of bilingual lexicon induction, our approach can
achieve competitive or superior performance compared to state-of-the-art
methods, with particularly strong results being found on distant languages.
