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

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:

It.  |Loss        |Relative loss|Absolute loss
------------------------------------------------
    0|9.472352e+00|0.000000e+00|0.000000e+00
    1|2.220770e+00|3.265346e+00|7.251582e+00
    2|1.972600e+00|1.258087e-01|2.481702e-01
    3|1.910353e+00|3.258364e-02|6.224626e-02
    4|1.889941e+00|1.080050e-02|2.041232e-02
    5|1.877882e+00|6.421892e-03|1.205955e-02
    6|1.870451e+00|3.972430e-03|7.430237e-03
    7|1.868019e+00|1.302179e-03|2.432494e-03
    8|1.866747e+00|6.812295e-04|1.271683e-03
    9|1.864417e+00|1.249760e-03|2.330073e-03
   10|1.862101e+00|1.243770e-03|2.316025e-03
   11|1.859600e+00|1.344766e-03|2.500727e-03
   12|1.857986e+00|8.690383e-04|1.614661e-03
   13|1.857326e+00|3.553437e-04|6.599890e-04
   14|1.856924e+00|2.164263e-04|4.018872e-04
   15|1.856207e+00|3.863508e-04|7.171468e-04
   16|1.855639e+00|3.059559e-04|5.677436e-04
   17|1.855032e+00|3.273474e-04|6.072398e-04
   18|1.854653e+00|2.039525e-04|3.782612e-04
   19|1.853839e+00|4.391075e-04|8.140347e-04
It.  |Loss        |Relative loss|Absolute loss
------------------------------------------------
   20|1.853304e+00|2.886334e-04|5.349256e-04

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'}

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()
Optimal coupling EMDTransport, Optimal coupling SinkhornTransport, Optimal coupling SinkhornLpl1Transport, Optimal coupling SinkhornL1l2Transport, Transported samples EmdTransport, Transported samples SinkhornTransport, Transported samples SinkhornLpl1Transport, Transported samples SinkhornL1l2Transport

Total running time of the script: ( 0 minutes 2.069 seconds)

Gallery generated by Sphinx-Gallery