Multidimensional Scaling in the Poincaré disk

Authors

Andrej Cvetkovski, School of Informatics, European University, Skopje, MacedoniaFollow
Mark Crovella, Department of Computer Science, Boston University, Boston MA, USAFollow

Author Country (or Countries)

Macedonia

Abstract

Multidimensional scaling (MDS) is a class of projective algorithms traditionally used in Euclidean space to produce twoor three-dimensional visualizations of datasets of multidimensional points or point distances. More recently however, several authors have pointed out that for certain datasets, hyperbolic target space may provide a better fit than Euclidean space. In this paper we develop PD-MDS, a metric MDS algorithm designed specifically for the Poincar´e disk (PD) model of the hyperbolic plane. Emphasizing the importance of proceeding from first principles in spite of the availability of various black box optimizers, our construction is based on an elementary hyperbolic line search and reveals numerous particulars that need to be carefully addressed when implementing this as well as more sophisticated iterative optimization methods in a hyperbolic space model.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100112

Recommended Citation

Cvetkovski, Andrej and Crovella, Mark (2016) "Multidimensional Scaling in the Poincaré disk," Applied Mathematics & Information Sciences: Vol. 10: Iss. 1, Article 12.
DOI: http://dx.doi.org/10.18576/amis/100112
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/12