title: Geometric diffusions for the analysis of data from sensor networks.
abstract: Harmonic analysis on manifolds and graphs has recently led to mathematical developments in the field of data analysis. The resulting new tools can be used to compress and analyze large and complex data sets, such as those derived from sensor networks or neuronal activity datasets, obtained in the laboratory or through computer modeling. The nature of the algorithms (based on diffusion maps and connectivity strengths on graphs) possesses a certain analogy with neural information processing, and has the potential to provide inspiration for modeling and understanding biological organization in perception and memory formation.
authors.affiliation: Program of Applied Mathematics, Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT 06520, USA. coifman@math.yale.edu
authors.forename: Ronald R
authors.initials: RR
authors.lastname: Coifman
authors.forename: Mauro
authors.initials: M
authors.lastname: Maggioni
authors.forename: Steven W
authors.initials: SW
authors.lastname: Zucker
authors.forename: Ioannis G
authors.initials: IG
authors.lastname: Kevrekidis
mesh_terms: D000465:Algorithms; D008959:Models, Neurological; D008962:Models, Theoretical; D016571:Neural Networks, Computer