Improved learning of Riemannian metrics for exploratory analysis
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 train 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). (C) 2004 Elsevier Ltd. All rights reserved.
learning metrics self-organizing map multidimensional scaling information geometry information visualization