Improved learning of Riemannian metrics for exploratory analysis

Authors:
Jaakko Peltonen;Arto Klami;Samuel Kaski
Affiliations:
Neural Network Research Center, Helsinki University of Technology, P.O. Box 5400, FI-02015 HUT, Finland;Neural Network Research Center, Helsinki University of Technology, P.O. Box 5400, FI-02015 HUT, Finland;Neural Network Research Center, Helsinki University of Technology, P.O. Box 5400, FI-02015 HUT, Finland and Department of Computer Science, P.O. Box 68, FI-00014, University of Helsinki, Finland
Venue:
Neural Networks - 2004 Special issue: New developments in self-organizing systems
Year:
2004

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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).