Users without a subscription are not able to see the full content.

## John C Gower and Garmt B Dijksterhuis

Print publication date: 2004

Print ISBN-13: 9780198510581

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198510581.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 25 March 2019

# Weighting, scaling, and missing values

Chapter:
(p.91) 8 Weighting, scaling, and missing values
Source:
Procrustes Problems
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198510581.003.0008

This chapter introduces the different forms of weighting. One form of weighting is when the rows of X1 are weighted. It is also possible to weight the columns. In these cases the weighting is expressed in terms of diagonal matrices. The most general form of weighting is when every cell of X1 gets separate weighting. Missing values may be specified by giving rows, columns, or cells zero weights. The important case of isotropic scaling is considered, where a scaling factor can be applied to the whole of the matrix X1 . This allows for the common situation where the relative sizes of X1 and X2 are unknown. Anisotropic scaling is introduced, represented by diagonal matrices S and T. Unlike weighting-matrices, which are given, scaling matrices need to be estimated. However, in iterative algorithms, the current estimates of scaling matrices may be treated as given weights while estimating updates of transformation matrices or further scaling matrices.

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.