 Graphical Representation of Asymmetric MatricesA. G. Constantine and J. C. Gower Journal of the Royal Statistical Society Series C, 1978, vol. 27, issue 3, 297-304 Abstract: When sample units are plotted against orthogonal principal axes in a components analysis, the concept of (Euclidean) distance plays a central point in interpretation. Variants of such diagrams are common throughout multivariate analysis. Because distance between a pair of points is independent of the order in which they are taken, displays of this kind are especially associated with symmetric matrices, but methods are also required for displaying asymmetric matrices. In this paper two methods for displaying asymmetric square matrices are presented and illustrated by examples. In the first method (multidimensional unfolding) the square matrix is regarded as part of an otherwise unknown symmetric matrix and the resulting diagram is interpreted using distances, much as with classical methods. In the second method the matrix is partitioned into its symmetric and skew‐symmetric components. While the symmetric part is represented by some established distance‐based method, the skew‐symmetric part is represented by points whose relationships are interpreted in terms of areas of triangles and co‐linearities. Date: 1978 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssc:v:27:y:1978:i:3:p:297-304 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of the Royal Statistical Society Series C is currently edited by R. Chandler and P. W. F. Smith More articles in Journal of the Royal Statistical Society Series C from Royal Statistical Society Contact information at EDIRC. |
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