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# -*- coding: utf-8 -*-
"""
===========================================
OT mapping estimation for domain adaptation
===========================================
This example presents how to use MappingTransport to estimate at the same
time both the coupling transport and approximate the transport map with either
a linear or a kernelized mapping as introduced in [8].
[8] M. Perrot, N. Courty, R. Flamary, A. Habrard,
"Mapping estimation for discrete optimal transport",
Neural Information Processing Systems (NIPS), 2016.
"""
# Authors: Remi Flamary <remi.flamary@unice.fr>
# Stanislas Chambon <stan.chambon@gmail.com>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 2
import numpy as np
import matplotlib.pylab as pl
import ot
##############################################################################
# Generate data
# -------------
n_source_samples = 100
n_target_samples = 100
theta = 2 * np.pi / 20
noise_level = 0.1
Xs, ys = ot.datasets.make_data_classif("gaussrot", n_source_samples, nz=noise_level)
Xs_new, _ = ot.datasets.make_data_classif("gaussrot", n_source_samples, nz=noise_level)
Xt, yt = ot.datasets.make_data_classif(
"gaussrot", n_target_samples, theta=theta, nz=noise_level
)
# one of the target mode changes its variance (no linear mapping)
Xt[yt == 2] *= 3
Xt = Xt + 4
##############################################################################
# Plot data
# ---------
pl.figure(1, (10, 5))
pl.clf()
pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker="+", label="Source samples")
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples")
pl.legend(loc=0)
pl.title("Source and target distributions")
##############################################################################
# Instantiate the different transport algorithms and fit them
# -----------------------------------------------------------
# MappingTransport with linear kernel
ot_mapping_linear = ot.da.MappingTransport(
kernel="linear", mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True
)
ot_mapping_linear.fit(Xs=Xs, Xt=Xt)
# for original source samples, transform applies barycentric mapping
transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs)
# for out of source samples, transform applies the linear mapping
transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new)
# MappingTransport with gaussian kernel
ot_mapping_gaussian = ot.da.MappingTransport(
kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1, max_iter=10, verbose=True
)
ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt)
# for original source samples, transform applies barycentric mapping
transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs)
# for out of source samples, transform applies the gaussian mapping
transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new)
##############################################################################
# Plot transported samples
# ------------------------
pl.figure(2)
pl.clf()
pl.subplot(2, 2, 1)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.2)
pl.scatter(
transp_Xs_linear[:, 0],
transp_Xs_linear[:, 1],
c=ys,
marker="+",
label="Mapped source samples",
)
pl.title("Bary. mapping (linear)")
pl.legend(loc=0)
pl.subplot(2, 2, 2)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.2)
pl.scatter(
transp_Xs_linear_new[:, 0],
transp_Xs_linear_new[:, 1],
c=ys,
marker="+",
label="Learned mapping",
)
pl.title("Estim. mapping (linear)")
pl.subplot(2, 2, 3)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.2)
pl.scatter(
transp_Xs_gaussian[:, 0],
transp_Xs_gaussian[:, 1],
c=ys,
marker="+",
label="barycentric mapping",
)
pl.title("Bary. mapping (kernel)")
pl.subplot(2, 2, 4)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.2)
pl.scatter(
transp_Xs_gaussian_new[:, 0],
transp_Xs_gaussian_new[:, 1],
c=ys,
marker="+",
label="Learned mapping",
)
pl.title("Estim. mapping (kernel)")
pl.tight_layout()
pl.show()
|
