Using $k$-way Co-occurrences for Learning Word Embeddings

Co-occurrences between two words provide useful insights into the semantics of those words. Consequently, numerous prior work on word embedding learning have used co-occurrences between two words as the training signal for learning word embeddings. However, in natural language texts it is common for multiple words to be related and co-occurring in the same context. We extend the notion of co-occurrences to cover k(≥2)-way co-occurrences among a set of k-words. Specifically, we prove a theoretical relationship between the joint probability of k(≥2) words, and the sum of `2 norms of their embeddings. Next, we propose a learning objective motivated by our theoretical result that utilises k-way co-occurrences for learning word embeddings. Our experimental results show that the derived theoretical relationship does indeed hold empirically, and despite data sparsity, for some smaller k values, k-way embeddings perform comparably or better than 2-way embeddings in a range of tasks.