ISOLLE: locally linear embedding with geodesic distance

Authors:
Claudio Varini;Andreas Degenhard;Tim Nattkemper
Affiliations:
Applied Neuroinformatics Group, Faculty of Technology, University of Bielefeld, Bielefeld, Germany;Condensed Matter Theory Group, Faculty of Physics, University of Bielefeld, Bielefeld, Germany;Applied Neuroinformatics Group, Faculty of Technology, University of Bielefeld, Bielefeld, Germany
Venue:
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
Year:
2005

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Abstract

Locally Linear Embedding (LLE) has recently been proposed as a method for dimensional reduction of high-dimensional nonlinear data sets. In LLE each data point is reconstructed from a linear combination of its n nearest neighbors, which are typically found using the Euclidean Distance. We propose an extension of LLE which consists in performing the search for the neighbors with respect to the geodesic distance (ISOLLE). In this study we show that the usage of this metric can lead to a more accurate preservation of the data structure. The proposed approach is validated on both real-world and synthetic data.