Vector Representation of Asymmetry in Multidimensional Scaling

Abstract

A vector model for representing asymmetry in multidimensional scaling is proposed. Given an asymmetric square matrix of (dis)similarity measures for all pairs of objects in the analysis, and assuming that the locations of objects have already been determined from the symmetric component of the data through some suitable multidimensional scaling model, a set of vectors which represents the latent structure of asymmetry in the data matrix is then determined from the remaining skew-symmetric part of the matrix by the model here in proposed. The discussion is extended to the asymmetric structure of the data, giving indices of several types of asymmetry. A real-data application of the vector model is also described.

Vector field representation of asymmetric proximity data

“…To overco me th ese inconveni ences , Niki ( 1990) propose a simple and natural model for repr esent ing the two-way as ym metric da ta . Yadohi sa and Niki (1994) and Yadohisa (1996) extend th e mod el for th e three-way dat a.…”