Package {otTensor}

Type: Package
Title: Optimal Tensor Transport
Version: 0.99.0
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 <k.t.the-answer@hotmail.co.jp>
Repository: CRAN
Date/Publication: 2026-05-13 07:30:17 UTC

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 = "k.t.the-answer@hotmail.co.jp"))
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
Author: Koki Tsuyuzaki [aut, cre]
Maintainer: Koki Tsuyuzaki <k.t.the-answer@hotmail.co.jp>

Index of help topics: 

OTT                     Optimal Tensor Transport
otTensor-package        Optimal Tensor Transport

Author(s)

NA

Maintainer: NA

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)