Journal of Classification

, Volume 28, Issue 3, pp 315–326 | Cite as

Between-Group Metrics

  • John C. GowerEmail author
  • Casper J. Albers


In canonical analysis with more variables than samples, it is shown that, as well as the usual canonical means in the range-space of the within-groups dispersion matrix, canonical means may be defined in its null space. In the range space we have the usual Mahalanobis metric; in the null space explicit expressions are given and interpreted for a new metric.


Between-group distances Canonical analysis Mahalanobis distance 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUnited Kingdom
  2. 2.Department of Psychometrics and StatisticsUniversity of GroningenGroningenThe Netherlands

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