Improved Learning of Riemannian Metrics for Exploratory Analysis

Reference:

Jaakko Peltonen, Arto Klami, and Samuel Kaski. Improved learning of Riemannian metrics for exploratory analysis. Neural Networks, 17:1087–1100, 2004. Invited paper. Preprint postscript file at http://www.cis.hut.fi/projects/mi/papers/nn04_preprint.ps.gz.

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).

Suggested BibTeX entry:

@article{Peltonen04nn,
    author = {Jaakko Peltonen and Arto Klami and Samuel Kaski},
    journal = {Neural Networks},
    note = {Invited paper. Preprint postscript file at \url{http://www.cis.hut.fi/projects/mi/papers/nn04_preprint.ps.gz}},
    pages = {1087-1100},
    title = {Improved Learning of {R}iemannian Metrics for Exploratory Analysis},
    volume = {17},
    year = {2004},
}