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Suppose we have a matrix A of size \(M \times S\), the cost matrix C of size \(M \times N\), and we are aiming to compute the barycenter vector of size \(N\). For example,
A <- rbind(
c(.3, .2),
c(.2, .1),
c(.1, .2),
c(.1, .1),
c(.3, .4)
)
C <- rbind(
c(.1, .2, .3, .4, .5),
c(.2, .3, .4, .3, .2),
c(.4, .3, .2, .1, .2),
c(.3, .2, .1, .2, .5),
c(.5, .5, .4, .0, .2)
)
w <- c(.4, .6)
reg <- .1
sol <- barycenter(A, C, w, barycenter_control = list(reg = reg))
#> `method` is automatically switched to "log"
#> Forward pass:
#> iter: 1, err: 0.3207, last speed: 0.012, avg speed: 0.012
#> iter: 11, err: 0.0020, last speed: 0.000, avg speed: 0.001
#> iter: 21, err: 0.0000, last speed: 0.000, avg speed: 0.001sinkhorn()The interface for barycenter() is almost identical to
sinkhorn() (see vignette("sinkhorn")), except
for the name of the algorithm. sinkhorn() accepts three
parameters for the method argument: vanilla,
log, and auto; whereas
barycenter() accepts parallel,
log, and auto.
You can still set the gradient, threading (only for
log), and all other parameters to control the computation
as in sinkhorn(), but you will also need to supply an
external vector for b_ext to compute the quadratic loss
between the output barycenter and b_ext.
See also vignette("sinkhorn").
Peyré, G., & Cuturi, M. (2019). Computational Optimal Transport: With Applications to Data Science. Foundations and Trends® in Machine Learning, 11(5–6), 355–607. https://doi.org/10.1561/2200000073
Xie, F. (2025). Deriving the Gradients of Some Popular Optimal Transport Algorithms (No. arXiv:2504.08722). arXiv. https://doi.org/10.48550/arXiv.2504.08722
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