Multiresolution Topological Simplification.

Persistent homology has been advocated as a new strategy for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for tackling large datasets. Our basic idea is to match the resolution with the scale of interest so as to create a topological microscopy for the underlying data. We adjust the resolution via a rigidity density-based filtration. The proposed multiresolution topological analysis is validated by the study of a complex RNA molecule.