Package 'otTensor'

Optimal Tensor Transport

Description

An optimal transport (OT) method, which can handle tensors of any order by learning possibly multiple transport plans. For the details of the methods, see Kerdoncuff et al. (2022) <doi:10.1609/aaai.v36i7.20695>.

Details

The DESCRIPTION file:

Package:	otTensor
Type:	Package
Title:	Optimal Tensor Transport
Version:	0.99.0
Authors@R:	c(person("Koki", "Tsuyuzaki", role = c("aut", "cre"), email = "[email protected]"))
Depends:	R (>= 3.4.0)
Imports:	methods,
Suggests:	rTensor, knitr, rmarkdown, testthat
Description:	An optimal transport (OT) method, which can handle tensors of any order by learning possibly multiple transport plans. For the details of the methods, see Kerdoncuff et al. (2022) <doi:10.1609/aaai.v36i7.20695>.
License:	MIT + file LICENSE
URL:	https://github.com/rikenbit/otTensor
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2026-05-08 11:45:49 UTC; koki
Author:	Koki Tsuyuzaki [aut, cre]
Maintainer:	Koki Tsuyuzaki <[email protected]>
Repository:	https://cran.r-universe.dev
Date/Publication:	2026-05-13 10:47:50 UTC
RemoteUrl:	https://github.com/cran/otTensor
RemoteRef:	HEAD
RemoteSha:	262c64ef94762da49f1dc990edbcd4c469f4f169

Index of help topics:

OTT                     Optimal Tensor Transport
otTensor-package        Optimal Tensor Transport

Further information is available in the following vignettes:

otTensor-1	Introduction to otTensor (source, pdf)
otTensor-2	Optimal Tensor Transport (source, pdf)

Author(s)

Koki Tsuyuzaki [aut, cre]

Maintainer: Koki Tsuyuzaki <[email protected]>

References

Kerdoncuff, T. et al., (2022). Optimal Tensor Transport. Proceedings of the AAAI Conference on Artificial Intelligence, 36(7), 7124-7132.

See Also

OTT

Examples

ls("package:otTensor")

---

Optimal Tensor Transport

Description

Transport plans to align two tensors X and Y are estimated.

Usage

OTT(X, Y, f, ps=NULL, qs=NULL,
    loss=.absolute_error, num.sample=1000,
    num.iter=200, epsilon=1e-10, verbose=FALSE)

Arguments

X	The first tensor data ('rTensor' object). The order must be the same as that of Y.
Y	The second tensor data ('rTensor' object). The order must be the same as that of X.
f	Affectation function to assign transport plan to each pair of mode of X and Y.
ps	Row-wise weight vectors for transport plans (Default: NULL, which means uniform distribution).
qs	Column-wise weight vectors for transport plans (Default: NULL, which means uniform distribution).
loss	Loss function (Default: .absolute_error).
num.sample	Number of samples to calculate the gradient (Default: 1000).
num.iter	Number of iterations (Default: 200).
epsilon	Regularization parameter (Default: 1e-10).
verbose	Verbose option (Default: FALSE).

Value

Ts : A list contains transport plans.

Author(s)

Koki Tsuyuzaki

Examples

library("rTensor")
D <- 3
A <- 2
Is <- c(4, 4, 5)
Ks <- c(6, 6, 7)
f <- c(1, 1, 2)
arrX <- array(rep(0, prod(Is)), Is)
arrY <- array(rep(0, prod(Ks)), Ks)

for (i1 in 1:Is[1]) {
    for (i2 in 1:Is[2]) {
        for (i3 in 1:Is[3]) {
            arrX[i1, i2, i3] <- i1 + i2 + i3
        }
    }
}
for (k1 in 1:Ks[1]) {
    for (k2 in 1:Ks[2]) {
        for (k3 in 1:Ks[3]) {
            arrY[k1, k2, k3] <- k1 + k2 + k3
        }
    }
}

ps <- list()
for (a in 1:A) {
    ds <- which(f == a)
    d <- ds[1]
    length_of_p_a <- dim(arrX)[d]
    ps[[a]] <- rep(0.01, length_of_p_a); ps[[a]][c(1, 3)] <- 1
    ps[[a]] <- ps[[a]] / sum(ps[[a]])
}
qs <- list()
for (a in 1:A) {
    ds <- which(f == a)
    d <- ds[1]
    length_of_q_a <- dim(arrY)[d]
    qs[[a]] <- rep(1, length_of_q_a); qs[[a]][c(2, 3)] <- 0
    qs[[a]] <- qs[[a]] / sum(qs[[a]])
}

# Test Dataset
X <- as.tensor(arrX)
Y <- as.tensor(arrY)

# This is just for an example.
# In real data analysis,
# please specify larger num.sample and num.iter such as 1000 and 200, respectively.
OTT(X = X, Y = Y, f = f,
    ps=ps, qs=qs, num.sample=10,
    loss = function (x, y) {abs(x - y)},
    num.iter=2, epsilon=1e-10)

---