Spherical embeddings for non-euclidean dissimilarities

Elzbieta Pekalska, Richard C. Wilson, Edwin R. Hancock, Elzbieta Pȩkalska, Robert P W Duin

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    Many computer vision and pattern recognition problems may be posed by defining a way of measuring dissimilarities between patterns. For many types of data, these dissimilarities are not Euclidean, and may not be metric. In this paper, we provide a means of embedding such data. We aim to embed the data on a hypersphere whose radius of curvature is determined by the dissimilarity data. The hypersphere can be either of positive curvature (elliptic) or of negative curvature (hyperbolic). We give an efficient method for solving the elliptic and hyperbolic embedding problems on symmetric dissimilarity data. This method gives the radius of curvature and a method for approximating the objects as points on a hyperspherical manifold. We apply our method to a variety of data including shape-similarities, graph-similarity and gesture-similarity data. In each case the embedding maintains the local structure of the data while placing the points in a metric space. ©2010 IEEE.
    Original languageEnglish
    Title of host publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition|Proc IEEE Comput Soc Conf Comput Vision Pattern Recognit
    Pages1903-1910
    Number of pages7
    DOIs
    Publication statusPublished - 2010
    Event2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010 - San Francisco, CA
    Duration: 1 Jul 2010 → …

    Conference

    Conference2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2010
    CitySan Francisco, CA
    Period1/07/10 → …

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