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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n# Partial Wasserstein and Gromov-Wasserstein example\n\n\nThis example is designed to show how to use the Partial (Gromov-)Wassertsein\ndistance computation in POT.\n\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Author: Laetitia Chapel <laetitia.chapel@irisa.fr>\n# License: MIT License\n\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nimport scipy as sp\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sample two 2D Gaussian distributions and plot them\n--------------------------------------------------\n\nFor demonstration purpose, we sample two Gaussian distributions in 2-d\nspaces and add some random noise.\n\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_samples = 20 # nb samples (gaussian)\nn_noise = 20 # nb of samples (noise)\n\nmu = np.array([0, 0])\ncov = np.array([[1, 0], [0, 2]])\n\nxs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)\nxs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))\nxt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)\nxt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))\n\nM = sp.spatial.distance.cdist(xs, xt)\n\nfig = pl.figure()\nax1 = fig.add_subplot(131)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(132)\nax2.scatter(xt[:, 0], xt[:, 1], color='r')\nax3 = fig.add_subplot(133)\nax3.imshow(M)\npl.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compute partial Wasserstein plans and distance\n----------------------------------------------\n\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"p = ot.unif(n_samples + n_noise)\nq = ot.unif(n_samples + n_noise)\n\nw0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True)\nw, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5,\n log=True)\n\nprint('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist']))\nprint('Entropic partial Wasserstein distance (m = 0.5): ' +\n str(log['partial_w_dist']))\n\npl.figure(1, (10, 5))\npl.subplot(1, 2, 1)\npl.imshow(w0, cmap='jet')\npl.title('Partial Wasserstein')\npl.subplot(1, 2, 2)\npl.imshow(w, cmap='jet')\npl.title('Entropic partial Wasserstein')\npl.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sample one 2D and 3D Gaussian distributions and plot them\n---------------------------------------------------------\n\nThe Gromov-Wasserstein distance allows to compute distances with samples that\ndo not belong to the same metric space. For demonstration purpose, we sample\ntwo Gaussian distributions in 2- and 3-dimensional spaces.\n\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n_samples = 20 # nb samples\nn_noise = 10 # nb of samples (noise)\n\np = ot.unif(n_samples + n_noise)\nq = ot.unif(n_samples + n_noise)\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([0, 0, 0])\ncov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n\n\nxs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)\nxs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0)\nP = sp.linalg.sqrtm(cov_t)\nxt = np.random.randn(n_samples, 3).dot(P) + mu_t\nxt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0)\n\nfig = pl.figure()\nax1 = fig.add_subplot(121)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(122, projection='3d')\nax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')\npl.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compute partial Gromov-Wasserstein plans and distance\n-----------------------------------------------------\n\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"C1 = sp.spatial.distance.cdist(xs, xs)\nC2 = sp.spatial.distance.cdist(xt, xt)\n\n# transport 100% of the mass\nprint('-----m = 1')\nm = 1\nres0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)\nres, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,\n m=m, log=True)\n\nprint('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist']))\nprint('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist']))\n\npl.figure(1, (10, 5))\npl.title(\"mass to be transported m = 1\")\npl.subplot(1, 2, 1)\npl.imshow(res0, cmap='jet')\npl.title('Wasserstein')\npl.subplot(1, 2, 2)\npl.imshow(res, cmap='jet')\npl.title('Entropic Wasserstein')\npl.show()\n\n# transport 2/3 of the mass\nprint('-----m = 2/3')\nm = 2 / 3\nres0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)\nres, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,\n m=m, log=True)\n\nprint('Partial Wasserstein distance (m = 2/3): ' +\n str(log0['partial_gw_dist']))\nprint('Entropic partial Wasserstein distance (m = 2/3): ' +\n str(log['partial_gw_dist']))\n\npl.figure(1, (10, 5))\npl.title(\"mass to be transported m = 2/3\")\npl.subplot(1, 2, 1)\npl.imshow(res0, cmap='jet')\npl.title('Partial Wasserstein')\npl.subplot(1, 2, 2)\npl.imshow(res, cmap='jet')\npl.title('Entropic partial Wasserstein')\npl.show()"
]
}
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