  In recent years, topological data analysis has been utilized for a wide range
of problems to deal with high dimensional noisy data. While text
representations are often high dimensional and noisy, there are only a few work
on the application of topological data analysis in natural language processing.
In this paper, we introduce a novel algorithm to extract topological features
from word embedding representation of text that can be used for text
classification. Working on word embeddings, topological data analysis can
interpret the embedding high-dimensional space and discover the relations among
different embedding dimensions. We will use persistent homology, the most
commonly tool from topological data analysis, for our experiment. Examining our
topological algorithm on long textual documents, we will show our defined
topological features may outperform conventional text mining features.
