The effects of incorrect specification of the Minkowski metric: Some analytical results
Journal of the Academy of Marketing Science · 1974 · Volume 2 · Issue 3
Abstract
This article investigates the consequences of incorrectly specifying the Minkowski metric. Five theorems are developed which hold if the true and assumed spaces have the same axis orientations. If is further shown that four of these theorems hold only for the special Euclidean case when the axis orientations of the true and assumed spaces are different. A second part of this study, scheduled to be published in the Fall issue of this journal, investigates the sensitivity of the TORSCA nonmetric multidimensional scaling algorithm to incorrect specification of the Minkowski metric and the ability of Kruskal's “stress” measure to detect such incorrect specification.
Keywords
Distance Function, Solution Space, Axis Orientation, Nonmetric Multidimensional Scaling, City Block
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