title: Locally learning biomedical data using diffusion frames.
abstract: Diffusion geometry techniques are useful to classify patterns and visualize high-dimensional datasets. Building upon ideas from diffusion geometry, we outline our mathematical foundations for learning a function on high-dimension biomedical data in a local fashion from training data. Our approach is based on a localized summation kernel, and we verify the computational performance by means of exact approximation rates. After these theoretical results, we apply our scheme to learn early disease stages in standard and new biomedical datasets.
authors.affiliation: Helmholtz Zentrum München, Institute of Biomathematics and Biometry, Ingolstädter Landstrasse 1, D-85764 Neuherberg, Germany. martin.ehler@helmholtz-muenchen.de
authors.forename: M
authors.initials: M
authors.lastname: Ehler
authors.forename: F
authors.initials: F
authors.lastname: Filbir
authors.forename: H N
authors.initials: HN
authors.lastname: Mhaskar
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D006801:Humans; D015233:Models, Statistical; D016571:Neural Networks, Computer; D012984:Software