Wasserstein Discriminant Analysis

Note

Example added in release: 0.3.0.

This example illustrate the use of WDA as proposed in [11].

[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). Wasserstein Discriminant Analysis.

# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License

# sphinx_gallery_thumbnail_number = 2

import numpy as np
import matplotlib.pylab as pl

from ot.dr import wda, fda

Generate data

n = 1000  # nb samples in source and target datasets
nz = 0.2

np.random.seed(1)

# generate circle dataset
t = np.random.rand(n) * 2 * np.pi
ys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1
xs = np.concatenate((np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)
xs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2)

t = np.random.rand(n) * 2 * np.pi
yt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1
xt = np.concatenate((np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)
xt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2)

nbnoise = 8

xs = np.hstack((xs, np.random.randn(n, nbnoise)))
xt = np.hstack((xt, np.random.randn(n, nbnoise)))

Plot data

pl.figure(1, figsize=(6.4, 3.5))

pl.subplot(1, 2, 1)
pl.scatter(xt[:, 0], xt[:, 1], c=ys, marker="+", label="Source samples")
pl.legend(loc=0)
pl.title("Discriminant dimensions")

pl.subplot(1, 2, 2)
pl.scatter(xt[:, 2], xt[:, 3], c=ys, marker="+", label="Source samples")
pl.legend(loc=0)
pl.title("Other dimensions")
pl.tight_layout()