@article{Zheng:2019:10.1109/TVCG.2018.2859997,
author = {Zheng, JX and Pawar, S and Goodman, DFM},
doi = {10.1109/TVCG.2018.2859997},
journal = {IEEE Transactions on Visualization and Computer Graphics},
pages = {2738--2748},
title = {Graph drawing by stochastic gradient descent},
url = {http://dx.doi.org/10.1109/TVCG.2018.2859997},
volume = {25},
year = {2019}
}

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TY  - JOUR
AB  - A popular method of force-directed graph drawing is multidimensional scaling using graph-theoretic distances as input. We present an algorithm to minimize its energy function, known as stress, by using stochastic gradient descent (SGD) to move a single pair of vertices at a time. Our results show that SGD can reach lower stress levels faster and more consistently than majorization, without needing help from a good initialization. We then show how the unique properties of SGD make it easier to produce constrained layouts than previous approaches. We also show how SGD can be directly applied within the sparse stress approximation of Ortmann et al. [1], making the algorithm scalable up to large graphs.
AU  - Zheng,JX
AU  - Pawar,S
AU  - Goodman,DFM
DO  - 10.1109/TVCG.2018.2859997
EP  - 2748
PY  - 2019///
SN  - 1077-2626
SP  - 2738
TI  - Graph drawing by stochastic gradient descent
T2  - IEEE Transactions on Visualization and Computer Graphics
UR  - http://dx.doi.org/10.1109/TVCG.2018.2859997
UR  - http://arxiv.org/abs/1710.04626v3
UR  - https://ieeexplore.ieee.org/document/8419285
VL  - 25
ER  - 

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