Vector representations of words have heralded a transformational approach to
classical problems in NLP; the most popular example is word2vec. However, a
single vector does not suffice to model the polysemous nature of many
(frequent) words, i.e., words with multiple meanings. In this paper, we propose
a three-fold approach for unsupervised polysemy modeling: (a) context
representations, (b) sense induction and disambiguation and (c) lexeme (as a
word and sense pair) representations. A key feature of our work is the finding
that a sentence containing a target word is well represented by a low rank
subspace, instead of a point in a vector space. We then show that the subspaces
associated with a particular sense of the target word tend to intersect over a
line (one-dimensional subspace), which we use to disambiguate senses using a
clustering algorithm that harnesses the Grassmannian geometry of the
representations. The disambiguation algorithm, which we call $K$-Grassmeans,
leads to a procedure to label the different senses of the target word in the
corpus -- yielding lexeme vector representations, all in an unsupervised manner
starting from a large (Wikipedia) corpus in English. Apart from several
prototypical target (word,sense) examples and a host of empirical studies to
intuit and justify the various geometric representations, we validate our
algorithms on standard sense induction and disambiguation datasets and present
new state-of-the-art results.

本文提出了一种三倍增的方法来进行无监督的多义词建模，其中使用低秩子空间来表示包含目标单词的句子，通过对表示的格拉斯曼几何进行聚类算法对目标单词的不同义项进行消歧辨别，最后基于英文维基百科语料库得出了多个词和词义对的表示，这些算法在标准意义识别和消歧辨别数据集上带来了新的最佳成果。