2015/08/23 by Weicong Ding, Ding, Weicong, Prakash Ishwar +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Complex Network Analysis Techniques #Computation #Computer science #Data Management and Algorithms #Data Mining Algorithms and Applications #Focus (optics) #Graphical model #Key (lock) #Leverage (statistics) #Mathematics #Probabilistic logic #Separable space #Theoretical computer science #Time complexity #Word (group theory) #cs.CL #cs.IR #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1508.05565
published in arXiv (Cornell University) (Cornell University) · Typo corrected; Revised argument in Lemma 3 and 4
openalex publication_date 2015/08/23 · arxiv created 2015/12/04 · arxiv updated 2015/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent factors that have certain properties. Our focus is on the class of topic models in which each shared latent factor contains a novel word that is unique to that factor, a property that has come to be known as separability. Our algorithm is based on the key insight that the novel words correspond to the extreme points of the convex hull formed by the row-vectors of a suitably normalized word co-occurrence matrix. We leverage this geometric insight to establish polynomial computation and sample complexity bounds based on a few isotropic random projections of the rows of the normalized word co-occurrence matrix. Our proposed random-projections-based algorithm is naturally amenable to an efficient distributed implementation and is attractive for modern web-scale distributed data mining applications.