  Topological data analysis (TDA) has been widely used to make progress on a
number of problems. However, it seems that TDA application in natural language
processing (NLP) is at its infancy. In this paper we try to bridge the gap by
arguing why TDA tools are a natural choice when it comes to analysing word
embedding data. We describe a parallelisable unsupervised learning algorithm
based on local homology of datapoints and show some experimental results on
word embedding data. We see that local homology of datapoints in word embedding
data contains some information that can potentially be used to solve the word
sense disambiguation problem.
