  A new geometrically-motivated algorithm for nonnegative matrix factorization
is developed and applied to the discovery of latent "topics" for text and image
"document" corpora. The algorithm is based on robustly finding and clustering
extreme points of empirical cross-document word-frequencies that correspond to
novel "words" unique to each topic. In contrast to related approaches that are
based on solving non-convex optimization problems using suboptimal
approximations, locally-optimal methods, or heuristics, the new algorithm is
convex, has polynomial complexity, and has competitive qualitative and
quantitative performance compared to the current state-of-the-art approaches on
synthetic and real-world datasets.
