Closed form word embedding alignment

We develop a family of techniques to align word embeddings which are derived from different source datasets or created using mechanisms (e.g., GloVe word2vec). Our methods simple and have closed form optimally rotate, translate, scale minimize root mean squared errors maximize the average cosine similarity between two same vocabulary into dimensional space. extend approaches known as absolute orientation, popular for aligning objects in three dimensions, generalize an approach by Smith et al. (ICLR 2017). prove new results optimal scaling maximizing similarity. Then, we demonstrate how evaluate sources mechanisms, that certain properties like synonyms analogies preserved across can be enhanced simply averaging ensembles embeddings.