Abstract
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 present various
real-world applications to 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.
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