Subspace-based Set Operations on a Pre-trained Word Embedding Space

Word embedding is a fundamental technology in natural language processing. It is often exploited for tasks using sets of words, although standard methods for representing word sets and set operations remain limited. If we can leverage the advantage of word embedding for such set operations, we can calculate sentence similarity and find words that effectively share a concept with a given word set in a straightforward way. In this study, we formulate representations of sets and set operations in a pre-trained word embedding space. Inspired by \textit{quantum logic}, we propose a novel formulation of set operations using subspaces in a pre-trained word embedding space. Based on our definitions, we propose two metrics based on the degree to which a word belongs to a set and the similarity between embedding two sets. Our experiments with Text Concept Set Retrieval and Semantic Textual Similarity tasks demonstrated the effectiveness of our proposed method.