Scaling of Asymmetric Similarity Matrix with Diagonal Elements

We find many asymmetric relations from an object to another object of n objects, for example, journal citation data etc. Okada and Imaizumi (1987) proposed a non-metric scaling model and method for analyzing asymmetric similarity matrices. As Okada and Imaizumi’s model do not utilize any information of diagonal elements of similarity matrix, some important information will be ignored. A redefined and extended model of Okada and Imaizumi will be proposed to account the diagonal elements and off-diagonal elements of asymmetric similarity matrix. An application to real data set will be shown.