Note
Click here to download the full example code
OT for domain adaptation
This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently supported in POT.
# Authors: Remi Flamary <remi.flamary@unice.fr>
# Stanislas Chambon <stan.chambon@gmail.com>
#
# License: MIT License
import matplotlib.pylab as pl
import ot
Generate data
n_source_samples = 150
n_target_samples = 150
Xs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples)
Xt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples)
Instantiate the different transport algorithms and fit them
# EMD Transport
ot_emd = ot.da.EMDTransport()
ot_emd.fit(Xs=Xs, Xt=Xt)
# Sinkhorn Transport
ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
# Sinkhorn Transport with Group lasso regularization
ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)
ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)
# Sinkhorn Transport with Group lasso regularization l1l2
ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20,
verbose=True)
ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt)
# transport source samples onto target samples
transp_Xs_emd = ot_emd.transform(Xs=Xs)
transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)
transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)
transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs)
Out:
/home/circleci/project/ot/bregman.py:517: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
warnings.warn("Sinkhorn did not converge. You might want to "
It. |Loss |Relative loss|Absolute loss
------------------------------------------------
0|9.681742e+00|0.000000e+00|0.000000e+00
1|2.076665e+00|3.662159e+00|7.605077e+00
2|1.842318e+00|1.272021e-01|2.343467e-01
3|1.786018e+00|3.152297e-02|5.630059e-02
4|1.765588e+00|1.157116e-02|2.042990e-02
5|1.757048e+00|4.860230e-03|8.539659e-03
6|1.751069e+00|3.414435e-03|5.978912e-03
7|1.747136e+00|2.251270e-03|3.933275e-03
8|1.746081e+00|6.039405e-04|1.054529e-03
9|1.744198e+00|1.079987e-03|1.883711e-03
10|1.742512e+00|9.676721e-04|1.686180e-03
11|1.741263e+00|7.173058e-04|1.249018e-03
12|1.739394e+00|1.074269e-03|1.868577e-03
13|1.738035e+00|7.819079e-04|1.358983e-03
14|1.737329e+00|4.063527e-04|7.059683e-04
15|1.736111e+00|7.013263e-04|1.217581e-03
16|1.735657e+00|2.617568e-04|4.543200e-04
17|1.735205e+00|2.605834e-04|4.521656e-04
18|1.734610e+00|3.430567e-04|5.950696e-04
19|1.734112e+00|2.872413e-04|4.981086e-04
It. |Loss |Relative loss|Absolute loss
------------------------------------------------
20|1.734026e+00|4.947858e-05|8.579715e-05
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()

Fig 2 : plot optimal couplings and transported samples
param_img = {'interpolation': 'nearest'}
pl.figure(2, figsize=(15, 8))
pl.subplot(2, 4, 1)
pl.imshow(ot_emd.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title('Optimal coupling\nEMDTransport')
pl.subplot(2, 4, 2)
pl.imshow(ot_sinkhorn.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title('Optimal coupling\nSinkhornTransport')
pl.subplot(2, 4, 3)
pl.imshow(ot_lpl1.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title('Optimal coupling\nSinkhornLpl1Transport')
pl.subplot(2, 4, 4)
pl.imshow(ot_l1l2.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title('Optimal coupling\nSinkhornL1l2Transport')
pl.subplot(2, 4, 5)
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, 4, 6)
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, 4, 7)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=0.3)
pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,
marker='+', label='Transp samples', s=30)
pl.xticks([])
pl.yticks([])
pl.title('Transported samples\nSinkhornLpl1Transport')
pl.subplot(2, 4, 8)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
label='Target samples', alpha=0.3)
pl.scatter(transp_Xs_l1l2[:, 0], transp_Xs_l1l2[:, 1], c=ys,
marker='+', label='Transp samples', s=30)
pl.xticks([])
pl.yticks([])
pl.title('Transported samples\nSinkhornL1l2Transport')
pl.tight_layout()
pl.show()

Total running time of the script: ( 0 minutes 2.045 seconds)