On the stochastic geometrical foundations of metric multidimensional scaling. (English) Zbl 0567.62094
This paper deals with the topological and measure theoretic probability foundations of metric multidimensional scaling. The first four sections develop minimal separation properties for a set of points or space to model a stimulus. The next three sections give measure theoretic probabilistic structure to random stimulus points and their random connecting paths.
MSC:
| 62P15 | Applications of statistics to psychology |
| 62H99 | Multivariate analysis |
| 60D05 | Geometric probability and stochastic geometry |
| 62A01 | Foundations and philosophical topics in statistics |
Keywords:
topological spaces; monotonic metric transforms; Riemannian metric; metric multidimensional scaling; minimal separation properties; random stimulus points; random connecting pathsReferences:
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