A Provably Efficient Algorithm for Separable Topic Discovery

作者：Ding Weicong^*; Ishwar Prakash^*; Saligrama Venkatesh^*

来源：IEEE Journal of Selected Topics in Signal Processing, 2016, 10(4): 712-725.

DOI：10.1109/JSTSP.2016.2555240

• Topic Modeling
• Separability
• Random Projection
• Solid Angle
• Necessary and Sufficient Conditions

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 computational 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.

• 出版日期2016-6