Extending metric multidimensional scaling with Bregman divergences

Jigang Sun, Malcolm Crowe, Colin Fyfe

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Sum of weighted square distance errors has been a popular way of defining stress function for metric multidimensional scaling (MMDS) like the Sammon mapping. In this paper we generalise this popular MMDS with Bregman divergences, as an example we show that the Sammon mapping can be thought of as a truncated Bregman MMDS (BMMDS) and we show that the full BMMDS improves upon the Sammon mapping on some standard data sets and investigate the reasons underlying this improvement. We then extend a well known family of MMDS, that deploy a strategy of focusing on small distances, with BMMDS and investigate limitations of the strategy empirically. Then an opposite strategy is introduced to create another family of BMMDS that gives increasing mapping quality. A data preprocessing method and a distance matrix preprocessing are introduced.
Original languageEnglish
Pages (from-to)1137-1154
JournalPattern Recognition
Volume44
Issue number5
DOIs
Publication statusPublished - May 2011

Keywords

  • Multidimensional scaling
  • Sammon mapping
  • Bregman divergence
  • Distance matrix preprocessing
  • Strategy focusing on small distances
  • Stress function definition

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