Closed Form Word Embedding Alignment
This work addresses the challenge of comparing and integrating diverse word embeddings for natural language processing tasks, offering a simple and efficient solution.
The paper tackles the problem of aligning word embeddings from different sources or methods by developing closed-form techniques to optimally rotate, translate, and scale them, minimizing errors or maximizing cosine similarity, and demonstrates that properties like synonyms and analogies are preserved and enhanced through alignment and averaging.
We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize 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, and generalize an approach by Smith etal (ICLR 2017). We prove new results for optimal scaling and for maximizing 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.