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Go to the end to download the full example code.

Note

Example added in release: 0.1.9.

This example introduces a semi supervised domain adaptation in a 2D setting. It explicit the problem of semi supervised domain adaptation and introduces some optimal transport approaches to solve it.

Quantities such as optimal couplings, greater coupling coefficients and transported samples are represented in order to give a visual understanding of what the transport methods are doing.

# Authors: Remi Flamary <remi.flamary@unice.fr>
#          Stanislas Chambon <stan.chambon@gmail.com>
#
# License: MIT License

# sphinx_gallery_thumbnail_number = 3

import matplotlib.pylab as pl
import ot

Generate data

Transport source samples onto target samples

Fig 1 : plots source and target samples + matrix of pairwise distance

pl.figure(1, figsize=(10, 10))
pl.subplot(2, 2, 1)
pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker="+", label="Source samples")
pl.xticks([])
pl.yticks([])
pl.legend(loc=0)
pl.title("Source  samples")

pl.subplot(2, 2, 2)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples")
pl.xticks([])
pl.yticks([])
pl.legend(loc=0)
pl.title("Target samples")

pl.subplot(2, 2, 3)
pl.imshow(ot_sinkhorn_un.cost_, interpolation="nearest")
pl.xticks([])
pl.yticks([])
pl.title("Cost matrix - unsupervised DA")

pl.subplot(2, 2, 4)
pl.imshow(ot_sinkhorn_semi.cost_, interpolation="nearest")
pl.xticks([])
pl.yticks([])
pl.title("Cost matrix - semi-supervised DA")

pl.tight_layout()

# the optimal coupling in the semi-supervised DA case will exhibit " shape
# similar" to the cost matrix, (block diagonal matrix)
Source samples, Target samples, Cost matrix - unsupervised DA, Cost matrix - semi-supervised DA

Fig 2 : plots optimal couplings for the different methods

pl.figure(2, figsize=(8, 4))

pl.subplot(1, 2, 1)
pl.imshow(ot_sinkhorn_un.coupling_, interpolation="nearest", cmap="gray_r")
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nUnsupervised DA")

pl.subplot(1, 2, 2)
pl.imshow(ot_sinkhorn_semi.coupling_, interpolation="nearest", cmap="gray_r")
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nSemi-supervised DA")

pl.tight_layout()
Optimal coupling Unsupervised DA, Optimal coupling Semi-supervised DA

Fig 3 : plot transported samples

# display transported samples
pl.figure(4, figsize=(8, 4))
pl.subplot(1, 2, 1)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.5)
pl.scatter(
    transp_Xs_sinkhorn_un[:, 0],
    transp_Xs_sinkhorn_un[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.title("Transported samples\nEmdTransport")
pl.legend(loc=0)
pl.xticks([])
pl.yticks([])

pl.subplot(1, 2, 2)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.5)
pl.scatter(
    transp_Xs_sinkhorn_semi[:, 0],
    transp_Xs_sinkhorn_semi[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.title("Transported samples\nSinkhornTransport")
pl.xticks([])
pl.yticks([])

pl.tight_layout()
pl.show()
Transported samples EmdTransport, Transported samples SinkhornTransport

Total running time of the script: (0 minutes 1.510 seconds)

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