摘要
在非计量多维尺度分析中,对变量进行单调顺序转换所用的最小二乘单调回归算法是非计量多维尺度分析的核心技术。它是Kruskal(1964)提出来的,其作用就是找到一个能够和数据尽可能匹配的具有最小压力值的结构空间。用迭代法求解压力函数S(Q,A),找到压力值最小结构空间,从而完成顺序尺度的转换。残差的平方和Q是来自于Yi对Xi的单调回归,将Q看成是Yi的函数,用一个简单的公式证明梯度▽Q存在且在每个点上都连续。S具有连续性和可微性是成功求解压力函数的关键。
The technique of Least-squares monotone regression has played a central role in non-metric multidimensional scaling,and it was prosposed by Kruskal in 1964. The technique could be used to find a configuration of points which match the dissimilaritues （ data ） as well as possible. And a numerical method could be used to solve the stress function S （Q, A）, and find the best-fitting configuration at which S has a minimum value, thus finished the monotone ordinral conversion of dissimilarities. Consid- er residual sum of squares Q obtained from the least-squares monotone regression of Yi on xi. Treating Q as a function of the Yi, we use a simple formula to prove that the gradient V Q exists and is continuous in every point. The continuity and differentiablity properties of S are important to solve the stress function successfully.
出处
《贵州师范大学学报（自然科学版）》
CAS
2011年第4期73-75,共3页
Journal of Guizhou Normal University：Natural Sciences
基金
贵州省高层次科研人才特助项目成果
关键词
最小二乘单调回归
梯度
可微性
连续性
least-squares monotone regression
gradient
differentiability
continuity
