Extending Sammon mapping with Bregman divergences

Jigang Sun; Colin Fyfe; Malcolm Crowe

doi:10.1016/j.ins.2011.10.013

Extending Sammon mapping with Bregman divergences

Jigang Sun, Colin Fyfe, Malcolm Crowe

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	72-92
Journal	Information Sciences
Volume	187
DOIs	https://doi.org/10.1016/j.ins.2011.10.013
Publication status	Published - 15 Mar 2012

Keywords

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

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10.1016/j.ins.2011.10.013Licence: Unspecified

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AU - Fyfe, Colin

AU - Crowe, Malcolm

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AB - 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.

KW - Metric multidimensional scaling

KW - Sammon mapping

KW - LeftSammon

KW - RightSammon

KW - Bregman divergence

KW - Visualisation quality assessment criterion

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DO - 10.1016/j.ins.2011.10.013

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SN - 0020-0255

VL - 187

SP - 72

EP - 92

JO - Information Sciences

JF - Information Sciences

ER -

Extending Sammon mapping with Bregman divergences

Abstract

Keywords

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