title: Multiresolution Topological Simplification.
abstract: 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.
authors.affiliation: 1 Department of Mathematics, Michigan State University , East Lansing, Michigan.
authors.forename: Kelin
authors.initials: K
authors.lastname: Xia
authors.affiliation: 1 Department of Mathematics, Michigan State University , East Lansing, Michigan.
authors.forename: Zhixiong
authors.initials: Z
authors.lastname: Zhao
authors.affiliation: 1 Department of Mathematics, Michigan State University , East Lansing, Michigan.|2 Department of Electrical and Computer Engineering, Michigan State University , East Lansing, Michigan.|3 Department of Biochemistry and Molecular Biology, Michigan State University , East Lansing, Michigan.
authors.forename: Guo-Wei
authors.initials: GW
authors.lastname: Wei
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D062126:Databases, Chemical; D008853:Microscopy / Q000379:methods; D012313:RNA / Q000235:genetics*; D017385:Sequence Homology; D013223:Statistics as Topic
chemical_list: D012313:RNA
keywords: big data; multiresolution topology; persistent homology; rigidity function