Extending Sammon mapping with Bregman divergences

Jigang Sun, Colin Fyfe, Malcolm Crowe

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Scopus)

    Abstract

    The Sammon mapping has been one of the most successful nonlinear metric multidimensional scaling methods since its advent in 1969, but effort has been focused on algorithm improvement rather than on the form of the stress function. This paper further investigates using left Bregman divergences to extend the Sammon mapping and by analogy develops right Bregman divergences and reveals the mechanism that improves the performance of scaling over the Sammon mapping. The influence of data space distance preprocessing on optimisation speed is noticed. Non-stress visualisation quality measures are used to compare the configuration quality of the Sammon mapping and its extensions using both Euclidean distance and graph distance on three data sets.
    Original languageEnglish
    Pages (from-to)72-92
    JournalInformation Sciences
    Volume187
    DOIs
    Publication statusPublished - 15 Mar 2012

    Keywords

    • Metric multidimensional scaling
    • Sammon mapping
    • LeftSammon
    • RightSammon
    • Bregman divergence
    • Visualisation quality assessment criterion

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