共查询到3条相似文献,搜索用时 0 毫秒
1.
Jan de Leeuw 《Journal of Classification》1988,5(2):163-180
In this paper we study the convergence properties of an important class of multidimensional scaling algorithms. We unify and extend earlier qualitative results on convergence, which tell us when the algorithms are convergent. In order to prove global convergence results we use the majorization method. We also derive, for the first time, some quantitative convergence theorems, which give information about the speed of convergence. It turns out that in almost all cases convergence is linear, with a convergence rate close to unity. This has the practical consequence that convergence will usually be very slow, and this makes techniques to speed up convergence very important. It is pointed out that step-size techniques will generally not succeed in producing marked improvements in this respect. 相似文献
2.
3.
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