摘要
本文将Okada ＆ Imaizumi等的模型加以推广,提出了一种用于处理非对称相异性矩阵的非度量多维尺度变换新方法.在模型中,我们假定每个研究对象可以表示为Minkowski度量空间中的一个点和一个超球面,超球面的半径揭示了相应研究对象的非对称性.文中我们给出了一种计算点坐标及球半径的算法.该算法使用了代数方法,比原来的方法收敛速度快,节省计算时间.最后给出了一个数值例子.
In this paper, a multidimensional scaling method which can be applied to an asymmetric interstimulus dissimilarity matrix is presented. In the model, each stimulus is represented as a point and a hypersphere whose center is at that point in a Minkowski-metric space. The radius of a hypersphere tells the skew-symmetry of the corresponding stimulus. In a sense, the model is a generalization of the models of Weeks (1982) and Okada (1987). An algorithm is given to derive the coordinates of points and radii of hyperspheres which minimize the discrepancy of the coordinates and radii from the monotone relationship with given interstimulus dissimilarities. An algebraic method is used in the algorithm, by which the CPU time is shorter than that of Okada and Imaizumi's algorithm. At last, a calculated example is given.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1992年第2期228-239,共12页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
关键词
矩阵
非对称
相异性
单调回归
Multidimensional Scaling, Nonmetric, Asymmetric, Dissimilarity, Monotonic Regression.
