Note
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Wasserstein Discriminant Analysis
This example illustrate the use of WDA as proposed in [11].
[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). Wasserstein Discriminant Analysis.
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()
Compute Fisher Discriminant Analysis
Compute Wasserstein Discriminant Analysis
Optimizing...
Iteration Cost Gradient norm
--------- ----------------------- --------------
1 +8.3042776946697494e-01 5.65147154e-01
2 +4.4401037686381040e-01 2.16760501e-01
3 +4.2234351238819928e-01 1.30555049e-01
4 +4.2169879996364462e-01 1.39115407e-01
5 +4.1924746118060602e-01 1.25387848e-01
6 +4.1177409528990749e-01 6.70993539e-02
7 +4.0862213476139048e-01 3.52716830e-02
8 +4.0747229322240269e-01 3.34923131e-02
9 +4.0678766065261684e-01 2.74029183e-02
10 +4.0621337155459647e-01 2.03651803e-02
11 +4.0577080390746939e-01 2.59605592e-02
12 +4.0543140912472148e-01 3.28883715e-02
13 +4.0470236926310577e-01 1.47528039e-02
14 +4.0445628467498224e-01 5.03183254e-02
15 +4.0364189455866245e-01 3.31006504e-02
16 +4.0303977563823823e-01 1.39885352e-02
17 +4.0301476238242911e-01 2.17467624e-02
18 +4.0292344306414324e-01 1.79959907e-02
19 +4.0271888325518124e-01 6.94408237e-03
20 +4.0183214741002155e-01 1.98322994e-02
21 +3.9762636217090053e-01 1.03196875e-01
22 +3.8225627240876070e-01 1.36012863e-01
23 +3.0855506616050116e-01 1.92702943e-01
24 +2.8001027160864295e-01 2.01920255e-01
25 +2.3687486090807947e-01 9.01780640e-02
26 +2.3431203993360381e-01 7.23716793e-02
27 +2.3118645266923005e-01 2.90753137e-02
28 +2.3067593392325469e-01 1.02767925e-02
29 +2.3064856262240019e-01 8.07925279e-03
30 +2.3060699763593800e-01 1.95215754e-03
31 +2.3060442760754873e-01 2.77368118e-05
32 +2.3060442709529139e-01 5.34108449e-06
33 +2.3060442708435561e-01 3.52599061e-06
34 +2.3060442707674844e-01 1.07742368e-06
35 +2.3060442707600512e-01 2.36125504e-07
Terminated - min grad norm reached after 35 iterations, 11.45 seconds.
Plot 2D projections
xsp = projfda(xs)
xtp = projfda(xt)
xspw = projwda(xs)
xtpw = projwda(xt)
pl.figure(2)
pl.subplot(2, 2, 1)
pl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker='+', label='Projected samples')
pl.legend(loc=0)
pl.title('Projected training samples FDA')
pl.subplot(2, 2, 2)
pl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker='+', label='Projected samples')
pl.legend(loc=0)
pl.title('Projected test samples FDA')
pl.subplot(2, 2, 3)
pl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker='+', label='Projected samples')
pl.legend(loc=0)
pl.title('Projected training samples WDA')
pl.subplot(2, 2, 4)
pl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker='+', label='Projected samples')
pl.legend(loc=0)
pl.title('Projected test samples WDA')
pl.tight_layout()
pl.show()
/home/circleci/.local/lib/python3.10/site-packages/matplotlib/cbook.py:1762: ComplexWarning: Casting complex values to real discards the imaginary part
return math.isfinite(val)
/home/circleci/.local/lib/python3.10/site-packages/matplotlib/collections.py:197: ComplexWarning: Casting complex values to real discards the imaginary part
offsets = np.asanyarray(offsets, float)
Total running time of the script: (0 minutes 12.414 seconds)