Spectral clustering has received a lot of attention due to its ability to separate nonconvex, non-intersecting manifolds, but its high computational complexity has significantly limited its applicability. Motivated by the document-term co-clustering framework by Dhillon (2001), we propose a landmark-based scalable spectral clustering approach in which we first use the selected landmark set and the given data to form a bipartite graph and then run a diffusion process on it to obtain a family of diffusion coordinates for clustering. We show that our proposed algorithm can be implemented based on very efficient operations on the affinity matrix between the given data and selected landmarks, thus capable of handling large data. Finally, we demonstrate the excellent performance of our method by comparing with the state-of-the-art scalable algorithms on several benchmark data sets.

Sequence to sequence (seq2seq) models are often employed in settings where the target output is natural language. However, the syntactic properties of the language generated from these models are not well understood. We explore whether such output belongs to a formal and realistic grammar, by employing the English Resource Grammar (ERG), a broad coverage, linguistically precise HPSG-based grammar of English. From a French to English parallel corpus, we analyze the parseability and grammatical constructions occurring in output from a seq2seq translation model. Over 93% of the model translations are parseable, suggesting that it learns to generate conforming to a grammar. The model has trouble learning the distribution of rarer syntactic rules, and we pinpoint several constructions that differentiate translations between the references and our model.