Topological Data Analysis in smart manufacturing processes -- A survey
  on the state of the art
Martin Uray Barbara Giunti Michael Kerber Stefan Huber
Topological Data Analysis (TDA) is a mathematical method using techniques
from topology for the analysis of complex, multi-dimensional data that has been
widely and successfully applied in several fields such as medicine, material
science, biology, and others. This survey summarizes the state of the art of
TDA in yet another application area: industrial manufacturing and production in
the context of Industry 4.0. We perform a rigorous and reproducible literature
search of applications of TDA on the setting of industrial production and
manufacturing. The resulting works are clustered and analyzed based on their
application area within the manufacturing process and their input data type. We
highlight the key benefits of TDA and their tools in this area and describe its
challenges, as well as future potential. Finally, we discuss which TDA methods
are underutilized in (the specific area of) industry and the identified types
of application, with the goal of prompting more research in this profitable
area of application.