Note

Go to the end to download the full example code.

Note

Example added in release: 0.7.0.

This example introduces a domain adaptation in a 2D setting and OTDA approach with Laplacian regularization.

# Authors: Ievgen Redko <ievgen.redko@univ-st-etienne.fr>

# License: MIT License

import matplotlib.pylab as pl
import ot

Generate data

Instantiate the different transport algorithms and fit them

/home/circleci/project/ot/bregman/_sinkhorn.py:902: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
  warnings.warn(
/home/circleci/project/ot/backend.py:1203: RuntimeWarning: overflow encountered in exp
  return np.exp(a)

Fig 1 : plots source and target samples

pl.figure(1, figsize=(10, 5))
pl.subplot(1, 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(1, 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.tight_layout()
Source samples, Target samples

Fig 2 : plot optimal couplings and transported samples

param_img = {"interpolation": "nearest", "cmap": "gray_r"}

pl.figure(2, figsize=(15, 8))
pl.subplot(2, 3, 1)
pl.imshow(ot_emd.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nEMDTransport")

pl.figure(2, figsize=(15, 8))
pl.subplot(2, 3, 2)
pl.imshow(ot_sinkhorn.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nSinkhornTransport")

pl.subplot(2, 3, 3)
pl.imshow(ot_emd_laplace.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nEMDLaplaceTransport")

pl.subplot(2, 3, 4)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.3)
pl.scatter(
    transp_Xs_emd[:, 0],
    transp_Xs_emd[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.xticks([])
pl.yticks([])
pl.title("Transported samples\nEmdTransport")
pl.legend(loc="lower left")

pl.subplot(2, 3, 5)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.3)
pl.scatter(
    transp_Xs_sinkhorn[:, 0],
    transp_Xs_sinkhorn[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.xticks([])
pl.yticks([])
pl.title("Transported samples\nSinkhornTransport")

pl.subplot(2, 3, 6)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.3)
pl.scatter(
    transp_Xs_emd_laplace[:, 0],
    transp_Xs_emd_laplace[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.xticks([])
pl.yticks([])
pl.title("Transported samples\nEMDLaplaceTransport")
pl.tight_layout()

pl.show()
Optimal coupling EMDTransport, Optimal coupling SinkhornTransport, Optimal coupling EMDLaplaceTransport, Transported samples EmdTransport, Transported samples SinkhornTransport, Transported samples EMDLaplaceTransport
/home/circleci/project/examples/domain-adaptation/plot_otda_laplacian.py:88: UserWarning: Ignoring specified arguments in this call because figure with num: 2 already exists
  pl.figure(2, figsize=(15, 8))

Total running time of the script: (0 minutes 2.619 seconds)

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