Title: Asymmetric MDS with sparse regularization term
Authors: Kensuke Tanioka - Doshisha University (Japan) [presenting]
Hiroshi Yadohisa - Doshisha University (Japan)
Abstract: Asymmetric (dis)similarity data are (dis)similarity data in which the relationship between the proximity from subject $i$ to subject $j$ and the proximity from subject $j$ to subject $i$ is not necessarily equivalent and can be observed in various fields. Asymmetric multidimensional scaling (Asymmetric MDS) is one of the methods to visualize asymmetric relationships among objects from such asymmetric (dis)similarity data. Although various asymmetric MDS methods have been proposed, we assume a situation in which covariate data are given as external information for the same subject as the asymmetric (dis)similarity data. In concretely, we propose an asymmetric multidimensional scaling method that can draw asymmetric relationships between asymmetric results and objects that can be visually interpreted, and identify covariates of external information that are related to the asymmetry. In the proposed method, coordinates and parameters in a low-dimensional space are represented by a linear combination of covariate data and a loading matrix, and by introducing a regularization term, such as lasso, it is possible to simultaneously implement variable selection to interpret asymmetric relationships.