We present an extension of multidimensional scaling (MDS) to uncertain data, facilitating uncertainty visualization of multidimensional data. Our approach uses local projection operators that map high-dimensional random vectors to low-dimensional space to formulate a generalized stress. In this way, our generic model supports arbitrary distributions and various stress types. We use our uncertainty-aware multidimensional scaling (UAMDS) concept to derive a formulation for the case of normally distributed random vectors and a squared stress. The resulting minimization problem is numerically solved via gradient descent. We complement UAMDS by additional visualization techniques that address the sensitivity and trustworthiness of dimensionality reduction under uncertainty. With several examples, we demonstrate the usefulness of our approach and the importance of uncertainty-aware techniques.
Description
Article was accepted at IEEE VIS 2022 and is published as early access in TVCG.
%0 Journal Article
%1 haegele2023uamds
%A Hägele, David
%A Krake, Tim
%A Weiskopf, Daniel
%D 2023
%J IEEE Transactions on Visualization and Computer Graphics
%K 2023 a01 from:christinawarren sfbtrr161 visus visus:haegeldd visus:kraketm visus:weiskopf
%N 1
%P 23--32
%R 10.1109/TVCG.2022.3209420
%T Uncertainty-Aware Multidimensional Scaling
%U https://doi.org/10.1109/TVCG.2022.3209420
%V 29
%X We present an extension of multidimensional scaling (MDS) to uncertain data, facilitating uncertainty visualization of multidimensional data. Our approach uses local projection operators that map high-dimensional random vectors to low-dimensional space to formulate a generalized stress. In this way, our generic model supports arbitrary distributions and various stress types. We use our uncertainty-aware multidimensional scaling (UAMDS) concept to derive a formulation for the case of normally distributed random vectors and a squared stress. The resulting minimization problem is numerically solved via gradient descent. We complement UAMDS by additional visualization techniques that address the sensitivity and trustworthiness of dimensionality reduction under uncertainty. With several examples, we demonstrate the usefulness of our approach and the importance of uncertainty-aware techniques.
@article{haegele2023uamds,
abstract = {We present an extension of multidimensional scaling (MDS) to uncertain data, facilitating uncertainty visualization of multidimensional data. Our approach uses local projection operators that map high-dimensional random vectors to low-dimensional space to formulate a generalized stress. In this way, our generic model supports arbitrary distributions and various stress types. We use our uncertainty-aware multidimensional scaling (UAMDS) concept to derive a formulation for the case of normally distributed random vectors and a squared stress. The resulting minimization problem is numerically solved via gradient descent. We complement UAMDS by additional visualization techniques that address the sensitivity and trustworthiness of dimensionality reduction under uncertainty. With several examples, we demonstrate the usefulness of our approach and the importance of uncertainty-aware techniques.},
added-at = {2022-11-25T10:55:34.000+0100},
author = {Hägele, David and Krake, Tim and Weiskopf, Daniel},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2c8088d8ee78f71b9840a6cbce25deda5/sfbtrr161},
description = {Article was accepted at IEEE VIS 2022 and is published as early access in TVCG.},
doi = {10.1109/TVCG.2022.3209420},
interhash = {206809bfa2dd1b0b91dbce1bee79c89a},
intrahash = {c8088d8ee78f71b9840a6cbce25deda5},
journal = {IEEE Transactions on Visualization and Computer Graphics},
keywords = {2023 a01 from:christinawarren sfbtrr161 visus visus:haegeldd visus:kraketm visus:weiskopf},
number = 1,
pages = {23--32},
timestamp = {2023-02-16T08:53:25.000+0100},
title = {Uncertainty-Aware Multidimensional Scaling},
url = {https://doi.org/10.1109/TVCG.2022.3209420},
volume = 29,
year = 2023
}
