Multi-Scale Local Shape Analysis and Feature Selection in Machine   Learning Applications
  We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of granularity to capture diverse types of local information for subsequent machine learning algorithms operating on the dataset. Using synthetic and real dataset examples, we demonstrate significant performance improvement of classification algorithms constructed for these datasets with correspondingly augmented features. 
Paul Bendich, Ellen Gasparovic, John Harer, Rauf Izmailov, and Linda   Ness
cs.CG cs.LG math.AT stat.ML