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.

本文介绍了基于跨文档词频模式几何的主题建模算法，并提出了适应数据的算法和随机投影算法，探讨了先验密度对数据相关投影方法的统计保证以及最大和最小值与新颖单词的联系，作者通过在人造数据集和实际数据集上进行的实验表明了该方案的定量和定性优点。