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Multidimensional Scaling in the Poincaré disk |
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PP: 125-133 |
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doi:10.18576/amis/100112
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Author(s) |
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Andrej Cvetkovski,
Mark Crovella,
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Abstract |
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| 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. |
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