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1.
Robert B. Schneider 《Journal of Classification》1992,9(2):257-273
We present a method and an algorithm that puts interval and ordinal multidimensional scaling at two ends of a continuum. Theory
and simulation show that the method compares favorably with classical scaling methods. A parameter is identified that produces
scaling that combines benefits of interval, and ordinal scaling. 相似文献
2.
We present an approach, independent of the common gradient-based necessary conditions for obtaining a (locally) optimal solution,
to multidimensional scaling using the city-block distance function, and implementable in either a metric or nonmetric context.
The difficulties encountered in relying on a gradient-based strategy are first reviewed: the general weakness in indicating
a good solution that is implied by the satisfaction of the necessary condition of a zero gradient, and the possibility of
actual nonconvergence of the associated optimization strategy. To avoid the dependence on gradients for guiding the optimization
technique, an alternative iterative procedure is proposed that incorporates (a) combinatorial optimization to construct good
object orders along the chosen number of dimensions and (b) nonnegative least-squares to re-estimate the coordinates for the
objects based on the object orders. The re-estimated coordinates are used to improve upon the given object orders, which may
in turn lead to better coordinates, and so on until convergence of the entire process occurs to a (locally) optimal solution.
The approach is illustrated through several data sets on the perception of similarity of rectangles and compared to the results
obtained with a gradient-based method. 相似文献