  We examine a number of methods to compute a dense vector embedding for a
document in a corpus, given a set of word vectors such as those from word2vec
or GloVe. We describe two methods that can improve upon a simple weighted sum,
that are optimal in the sense that they maximizes a particular weighted cosine
similarity measure.
  We consider several weighting functions, including inverse document frequency
(idf), smooth inverse frequency (SIF), and the sub-sampling function used in
word2vec. We find that idf works best for our applications. We also use common
component removal proposed by Arora et al. as a post-process and find it is
helpful in most cases.
  We compare these embeddings variations to the doc2vec embedding on a new
evaluation task using TripAdvisor reviews, and also on the CQADupStack
benchmark from the literature.
