vMF Sentence LDA: A Spherical Topic Model over Sentence Embeddings

Ryotaro Kobayashi, Yuri Murayama, Kiyoshi Izumi

Latent Dirichlet Allocation (LDA) and models derived from it remain widely used topic models. LDA observes each document as a bag-of-words and models each topic by a categorical distribution over the vocabulary, so that it uses neither the internal structure of the document nor the similarity in meaning between words. Earlier work has responded to this limitation in two ways: many models have introduced embeddings, and some have assigned topics to sentences rather than to words. Their combination, a topic model that observes sentence embeddings, remains little explored. We propose vMF Sentence LDA (vSLDA), which keeps the admixture structure of LDA, observes each sentence as its L2-normalized embedding and models each topic by a von Mises-Fisher (vMF) distribution, which matches the cosine geometry of sentence embeddings. Its per-topic parameter count and per-iteration cost are linear in the embedding dimension, versus quadratic for the full-covariance Gaussian distribution in the existing model over sentence embeddings. We evaluate vSLDA where the limitation is expected to matter most, among topics that share much of their vocabulary: the topics that subdivide the one subject of…