ISSN:
1432-1343
Keywords:
Dimensionality reduction
;
Distances
;
Graphics
;
Multidimensional scaling
;
Symmetric matrices
;
Unfolding
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Graphical displays which show inter-sample distances are important for the interpretation and presentation of multivariate data. Except when the displays are two-dimensional, however, they are often difficult to visualize as a whole. A device, based on multidimensional unfolding, is described for presenting some intrinsically high-dimensional displays in fewer, usually two, dimensions. This goal is achieved by representing each sample by a pair of points, sayR i andr i, so that a theoretical distance between thei-th andj-th samples is represented twice, once by the distance betweenR i andr j and once by the distance betweenR j andr i. Selfdistances betweenR i andr i need not be zero. The mathematical conditions for unfolding to exhibit symmetry are established. Algorithms for finding approximate fits, not constrained to be symmetric, are discussed and some examples are given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01202583
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