CONVERGENCE OF THE MAJORIZATION METHOD FOR MULTIDIMENSIONAL-SCALING
CONVERGENCE OF THE MAJORIZATION METHOD FOR MULTIDIMENSIONAL-SCALING
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DOI：
10.1007/bf01897162
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发表时间：
1988-01-01
影响因子：
2
通讯作者：
DELEEUW, J
中科院分区：
文献类型：
--
作者：
DELEEUW, J
本文研究了一类重要的多维尺度算法的收敛性。我们统一和扩展以前的定性结果的收敛性，这告诉我们，当算法收敛。为了证明全局收敛结果，我们使用优化方法。我们还推导出，第一次，一些定量的收敛定理，这给信息的收敛速度。事实证明，在几乎所有情况下，收敛都是线性的，收敛速度接近1。这具有收敛通常将非常缓慢的实际后果，并且这使得加速收敛的技术非常重要。有人指出，步长技术一般不会成功地在这方面产生显着的改善。
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.