Exponential Curvilinear Components Analysis and Bregman divergence

Jigang Sun, Malcolm Crowe, Colin Fyfe

Research output: Contribution to journalArticle

Abstract

Curvilinear Component Analysis (CCA) is an interesting flavour of metric multidimen-sional scaling (MMDS) in that, unlike the classical Sammon mapping whose stress function uses weights which are function of distances in data space, it uses weights of distances in output space. In this paper some discrepancies in one version of CCA are brought to light and its real stress function is proved to be a specific Bregman divergence. The “neighbourhood radius” parameter is explained differently. We examine the Bregmanised stress function and its features are theoretically analysed. Common rank-based visualisation quality measures are reviewed. Finally the version of CCA together with other MMDS methods are tested on three standard data sets.
Original languageEnglish
JournalComputing and Information Systems Technical Reports
Publication statusPublished - 2012

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Bregman Divergence
Scaling
Metric
Quality Measures
Discrepancy
Visualization
Radius
Output

Cite this

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title = "Exponential Curvilinear Components Analysis and Bregman divergence",
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Exponential Curvilinear Components Analysis and Bregman divergence. / Sun, Jigang; Crowe, Malcolm; Fyfe, Colin.

In: Computing and Information Systems Technical Reports, 2012.

Research output: Contribution to journalArticle

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AU - Crowe, Malcolm

AU - Fyfe, Colin

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AB - Curvilinear Component Analysis (CCA) is an interesting flavour of metric multidimen-sional scaling (MMDS) in that, unlike the classical Sammon mapping whose stress function uses weights which are function of distances in data space, it uses weights of distances in output space. In this paper some discrepancies in one version of CCA are brought to light and its real stress function is proved to be a specific Bregman divergence. The “neighbourhood radius” parameter is explained differently. We examine the Bregmanised stress function and its features are theoretically analysed. Common rank-based visualisation quality measures are reviewed. Finally the version of CCA together with other MMDS methods are tested on three standard data sets.

M3 - Article

JO - Computing and Information Systems Technical Reports

JF - Computing and Information Systems Technical Reports

SN - 1461-6122

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