title: Improved learning of Riemannian metrics for exploratory analysis.
abstract: We have earlier introduced a principle for learning metrics, which shows how metric-based methods can be made to focus on discriminative properties of data. The main applications are in supervising unsupervised learning to model interesting variation in data, instead of modeling all variation as plain unsupervised learning does. The metrics are derived by approximations to an information-geometric formulation. In this paper, we review the theory, introduce better approximations to the distances, and show how to apply them in two different kinds of unsupervised methods: prototype-based and pairwise distance-based. The two examples are self-organizing maps and multidimensional scaling (Sammon's mapping).
authors.affiliation: Neural Networks Research Centre, Helsinki University of Technology, PO Box 5400, FI-02015 HUT, Finland.
authors.forename: Jaakko
authors.initials: J
authors.lastname: Peltonen
authors.forename: Arto
authors.initials: A
authors.lastname: Klami
authors.forename: Samuel
authors.initials: S
authors.lastname: Kaski
mesh_terms: D016477:Artifacts; D001185:Artificial Intelligence; D016571:Neural Networks, Computer