  We present algorithms for topic modeling based on the geometry of
cross-document word-frequency patterns. This perspective gains significance
under the so called separability condition. This is a condition on existence of
novel-words that are unique to each topic. We present a suite of highly
efficient algorithms based on data-dependent and random projections of
word-frequency patterns to identify novel words and associated topics. We will
also discuss the statistical guarantees of the data-dependent projections
method based on two mild assumptions on the prior density of topic document
matrix. Our key insight here is that the maximum and minimum values of
cross-document frequency patterns projected along any direction are associated
with novel words. While our sample complexity bounds for topic recovery are
similar to the state-of-art, the computational complexity of our random
projection scheme scales linearly with the number of documents and the number
of words per document. We present several experiments on synthetic and
real-world datasets to demonstrate qualitative and quantitative merits of our
scheme.
