Low-rank approximations of second-order document representations

Abstract

Document embeddings, created with methods ranging from simple heuristics to statistical and deep models, are widely applicable. Bag-of-vectors models for documents include the mean and quadratic approaches (Torki, 2018). We present evidence that quadratic statistics alone, without the mean information, can offer superior accuracy, fast document comparison, and compact document representations. In matching news articles to their comment threads, low-rank representations of only 3-4 times the size of the mean vector give most accurate matching, and in standard sentence comparison tasks, results are state of the art despite faster computation. Similarity measures are discussed, and the Frobenius product implicit in the proposed method is contrasted to Wasserstein or Bures metric from the transportation theory. We also shortly demonstrate matching of unordered word lists to documents, to measure topicality or sentiment of documents.