  Comparing document semantics is one of the toughest tasks in both Natural
Language Processing and Information Retrieval. To date, on one hand, the tools
for this task are still rare. On the other hand, most relevant methods are
devised from the statistic or the vector space model perspectives but nearly
none from a topological perspective. In this paper, we hope to make a different
sound. A novel algorithm based on topological persistence for comparing
semantics similarity between two documents is proposed. Our experiments are
conducted on a document dataset with human judges' results. A collection of
state-of-the-art methods are selected for comparison. The experimental results
show that our algorithm can produce highly human-consistent results, and also
beats most state-of-the-art methods though ties with NLTK.
