Before revision: Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. th\v{e } or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed.
After revision: Despite strong stability properties, the persistent homology of filtrations classically used in Topological Data Analysis, such as, e.g. th\v{e }ech or Vietoris-Rips filtrations, are very sensitive to the presence of outliers in the data from which they are computed.