  While the strength of Topological Data Analysis has been explored in many
studies on high dimensional numeric data, it is still a challenging task to
apply it to text. As the primary goal in topological data analysis is to define
and quantify the shapes in numeric data, defining shapes in the text is much
more challenging, even though the geometries of vector spaces and conceptual
spaces are clearly relevant for information retrieval and semantics. In this
paper, we examine two different methods of extraction of topological features
from text, using as the underlying representations of words the two most
popular methods, namely word embeddings and TF-IDF vectors. To extract
topological features from the word embedding space, we interpret the embedding
of a text document as high dimensional time series, and we analyze the topology
of the underlying graph where the vertices correspond to different embedding
dimensions. For topological data analysis with the TF-IDF representations, we
analyze the topology of the graph whose vertices come from the TF-IDF vectors
of different blocks in the textual document. In both cases, we apply
homological persistence to reveal the geometric structures under different
distance resolutions. Our results show that these topological features carry
some exclusive information that is not captured by conventional text mining
methods. In our experiments we observe adding topological features to the
conventional features in ensemble models improves the classification results
(up to 5\%). On the other hand, as expected, topological features by themselves
may be not sufficient for effective classification. It is an open problem to
see whether TDA features from word embeddings might be sufficient, as they seem
to perform within a range of few points from top results obtained with a linear
support vector classifier.
