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We present algorithms for topic modeling based on the geometry ofcross-document word-frequency patterns. This perspective gains significanceunder the so called separability condition. This is a condition on existence ofnovel-words that are unique to each topic. We present a suite of highlyefficient algorithms based on data-dependent and random projections ofword-frequency patterns to identify novel words and associated topics. We willalso discuss the statistical guarantees of the data-dependent projectionsmethod based on two mild assumptions on the prior density of topic documentmatrix. Our key insight here is that the maximum and minimum values ofcross-document frequency patterns projected along any direction are associatedwith novel words. While our sample complexity bounds for topic recovery aresimilar to the state-of-art, the computational complexity of our randomprojection scheme scales linearly with the number of documents and the numberof words per document. We present several experiments on synthetic andreal-world datasets to demonstrate qualitative and quantitative merits of ourscheme.

Topic Discovery through Data Dependent and Random Projections