__Persistent homology__ is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to represent true features of the underlying space rather than artifacts of sampling, noise, or particular choice of parameters - wikipedia 
To find the persistent homology of a space, the space must first be represented as a simplicial complex. A distance function on the underlying space corresponds to a Filtration (mathematics) of the simplicial complex, that is a nested sequence of increasing subsets.
# Sections
See homology (mathematics) for an introduction to the notation.
# See also