Brusco Michael J, Stahl Stephanie
Department of Marketing, College of Business, Florida State University, Tallahassee 32306-1110, USA.
Br J Math Stat Psychol. 2005 Nov;58(Pt 2):333-43. doi: 10.1348/000711005X63908.
The decomposition of an asymmetric proximity matrix into its symmetric and skew-symmetric components is a well-known principle in combinatorial data analysis. The seriation of the skew-symmetric component can emphasize information corresponding to the sign or absolute magnitude of the matrix elements, and the choice of objective criterion can have a profound impact on the ordering. In this research note, we propose a bicriterion approach for seriation of a skew-symmetric matrix incorporating both sign and magnitude information. Two numerical demonstrations reveal that the bicriterion procedure is an effective alternative to direct seriation of the skew-symmetric matrix, facilitating favourable trade-offs among sign and magnitude information.
在组合数据分析中，将非对称邻近矩阵分解为其对称和反对称分量是一个众所周知的原理。反对称分量的序列化可以强调与矩阵元素的符号或绝对值大小相对应的信息，而客观标准的选择可能会对排序产生深远影响。在本研究报告中，我们提出了一种用于反对称矩阵序列化的双标准方法，该方法同时纳入了符号和大小信息。两个数值示例表明，双标准程序是反对称矩阵直接序列化的有效替代方法，有助于在符号和大小信息之间进行有利的权衡。
