A1293
Title: Unfolding of asymmetric dissimilarity data based on clustered lasso
Authors: Ryohei Moriya - Doshisha University (Japan) [presenting]
Kensuke Tanioka - Doshisha University (Japan)
Hiroshi Yadohisa - Doshisha University (Japan)
Abstract: Asymmetric multidimensional scaling (AMDS) is a representative method for mapping asymmetric dissimilarity data into a low-dimensional space for understanding and visualizing asymmetric relationships among objects. The unfolding model within AMDS and the slide-vector model, which is a parsimonious version of that method, are considered. The unfolding method represents asymmetric relationships by introducing two position coordinates for each object; however, interpretation can become difficult as the number of objects increases. In contrast, the slide-vector model represents asymmetric relationships using object coordinates and a single slide vector. Because asymmetry is represented by a single slide vector, the number of parameters can be reduced; however, the model may fail to accurately reproduce the original asymmetric structure. A new AMDS method is proposed that provides a unified framework for both the unfolding method and the slide-vector model. Specifically, the unfolding method is reformulated and a clustered lasso penalty is introduced to construct an intermediate model between the unfolding method and the slide-vector model within a common framework. Through numerical simulations and applications to real data, the proposed method demonstrates superior reconstruction accuracy of asymmetric structures compared to the unfolding method and the slide-vector model, confirming its effectiveness.
