Letters: ISOLLE: LLE with geodesic distance

Authors:
Claudio Varini;Andreas Degenhard;Tim W. Nattkemper
Affiliations:
Applied Neuroinformatics Group, Faculty of Technology, University of Bielefeld, Universitätsstrasse 25, 33615 Bielefeld, Germany and Condensed Matter Theory Group, Department of Physics, Univ ...;Condensed Matter Theory Group, Department of Physics, University of Bielefeld, Universitätsstrasse 25, 33615 Bielefeld, Germany;Applied Neuroinformatics Group, Faculty of Technology, University of Bielefeld, Universitätsstrasse 25, 33615 Bielefeld, Germany
Venue:
Neurocomputing
Year:
2006

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Abstract

We propose an extension of the algorithm for nonlinear dimensional reduction locally linear embedding (LLE) based on the usage of the geodesic distance (ISOLLE). 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 show that the search for the neighbors performed with respect to the geodesic distance can lead to a more accurate preservation of the data structure. This is confirmed by experiments on both real-world and synthetic data.