Absolute Orientation for Word Embedding Alignment
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We propose a new technique to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). We design a simple, closed-form solution to find the optimal rotation and optionally scaling which minimizes the root mean squared error or maximizes the average cosine similarity between two embeddings of the same vocabulary into the same dimensional space. Our methods extend approaches known as Absolute Orientation, which are popular for aligning objects in three-dimensions. We extend them to arbitrary dimensions, and show that a simple scaling solution can be derived independent of the rotation, and also that it optimizes cosine similarity. Then we demonstrate how to evaluate the similarity of embeddings from different sources or mechanisms, and that certain properties like synonyms and analogies are preserved across the embeddings and can be enhanced by simply aligning and averaging ensembles of embeddings.
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