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Computational Statistics & Data Analysis
Volume 52, Issue 1, 15 September 2007, Pages 201-210
 
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doi:10.1016/j.csda.2006.11.012    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2006 Elsevier B.V. All rights reserved.

Constrained unidimensional scaling with application to genomicsstar, open

S.I. Aoa, Michael K. Ngb, Corresponding Author Contact Information, E-mail The Corresponding Author and Pak C. Shamc

aDepartment of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong bDepartment of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong cGenome Research Centre, The University of Hong Kong, Pokfulam Road, Hong Kong

Available online 1 December 2006.

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Abstract

A constrained unidimensional scaling model where the objects are required to be placed in a given order on the real line, is studied. A procedure formulated as a least squares problem with nonnegativity is considered to solve this problem. An application to linkage disequilibrium (LD) maps for human genome is presented to demonstrate the proposed model. The LD maps are also constructed for four populations from Hapmap data sets, and analyze some of their similarities.

Keywords: Unidimensional scaling; Constraints; Least squares problem; Nonnegativity; Genomics; Linkage disequilibrium

Article Outline

1. Introduction
2. Mathematical formulation
3. Application to genomics
3.1. Examples
3.2. Hapmap data analysis
4. Concluding remarks
References











 
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