Homological Coordinatization
  In this paper, we review a method for computing and parameterizing the set of homotopy classes of chain maps between two chain complexes. This is then applied to finding topologically meaningful maps between simplicial complexes, which in the context of topological data analysis, can be viewed as an extension of conventional unsupervised learning methods to simplicial complexes. 
Andrew Tausz and Gunnar Carlsson
cs.CG