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‎master/_downloads/006964755fe89c4eeb7c8b8016e96890/plot_otda_semi_supervised.py‎

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pl.figure(2, figsize=(8, 4))
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pl.subplot(1, 2, 1)
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pl.imshow(ot_sinkhorn_un.coupling_, interpolation="nearest")
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pl.imshow(ot_sinkhorn_un.coupling_, interpolation="nearest", cmap="gray_r")
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pl.xticks([])
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pl.yticks([])
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pl.title("Optimal coupling\nUnsupervised DA")
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pl.subplot(1, 2, 2)
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pl.imshow(ot_sinkhorn_semi.coupling_, interpolation="nearest")
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pl.imshow(ot_sinkhorn_semi.coupling_, interpolation="nearest", cmap="gray_r")
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pl.xticks([])
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pl.yticks([])
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pl.title("Optimal coupling\nSemi-supervised DA")

‎master/_downloads/00efe738b664431523810a0d0baf5949/plot_lowrank_GW.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# Low rank Gromov-Wasterstein between samples\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.9.4.</p></div>\n\nComparison between entropic Gromov-Wasserstein and Low Rank Gromov Wasserstein [67]\non two curves in 2D and 3D, both sampled with 200 points.\n\nThe squared Euclidean distance is considered as the ground cost for both samples.\n\n[67] Scetbon, M., Peyr\u00e9, G. & Cuturi, M. (2022).\n\"Linear-Time GromovWasserstein Distances using Low Rank Couplings and Costs\".\nIn International Conference on Machine Learning (ICML), 2022.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Author: Laur\u00e8ne David <[email protected]>\n#\n# License: MIT License\n#\n# sphinx_gallery_thumbnail_number = 3"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import numpy as np\nimport matplotlib.pylab as pl\nimport ot.plot\nimport time"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Generate data\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"n_samples = 200\n\n# Generate 2D and 3D curves\ntheta = np.linspace(-4 * np.pi, 4 * np.pi, n_samples)\nz = np.linspace(1, 2, n_samples)\nr = z**2 + 1\nx = r * np.sin(theta)\ny = r * np.cos(theta)\n\n# Source and target distribution\nX = np.concatenate([x.reshape(-1, 1), z.reshape(-1, 1)], axis=1)\nY = np.concatenate([x.reshape(-1, 1), y.reshape(-1, 1), z.reshape(-1, 1)], axis=1)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Plot data\n\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Plot the source and target samples\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"fig = pl.figure(1, figsize=(10, 4))\n\nax = fig.add_subplot(121)\nax.plot(X[:, 0], X[:, 1], color=\"blue\", linewidth=6)\nax.tick_params(\n left=False, right=False, labelleft=False, labelbottom=False, bottom=False\n)\nax.set_title(\"2D curve (source)\")\n\nax2 = fig.add_subplot(122, projection=\"3d\")\nax2.plot(Y[:, 0], Y[:, 1], Y[:, 2], c=\"red\", linewidth=6)\nax2.tick_params(\n left=False, right=False, labelleft=False, labelbottom=False, bottom=False\n)\nax2.view_init(15, -50)\nax2.set_title(\"3D curve (target)\")\n\npl.tight_layout()\npl.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Entropic Gromov-Wasserstein\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Compute cost matrices\nC1 = ot.dist(X, X, metric=\"sqeuclidean\")\nC2 = ot.dist(Y, Y, metric=\"sqeuclidean\")\n\n# Scale cost matrices\nr1 = C1.max()\nr2 = C2.max()\n\nC1 = C1 / r1\nC2 = C2 / r2\n\n\n# Solve entropic gw\nreg = 5 * 1e-3\n\nstart = time.time()\ngw, log = ot.gromov.entropic_gromov_wasserstein(\n C1, C2, tol=1e-3, epsilon=reg, log=True, verbose=False\n)\n\nend = time.time()\ntime_entropic = end - start\n\nentropic_gw_loss = np.round(log[\"gw_dist\"], 3)\n\n# Plot entropic gw\npl.figure(2)\npl.imshow(gw, interpolation=\"nearest\", aspect=\"auto\", cmap=\"gray_r\")\npl.title(\"Entropic Gromov-Wasserstein (loss={})\".format(entropic_gw_loss))\npl.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Low rank squared euclidean cost matrices\n%%\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Compute the low rank sqeuclidean cost decompositions\nA1, A2 = ot.lowrank.compute_lr_sqeuclidean_matrix(X, X, rescale_cost=False)\nB1, B2 = ot.lowrank.compute_lr_sqeuclidean_matrix(Y, Y, rescale_cost=False)\n\n# Scale the low rank cost matrices\nA1, A2 = A1 / np.sqrt(r1), A2 / np.sqrt(r1)\nB1, B2 = B1 / np.sqrt(r2), B2 / np.sqrt(r2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Low rank Gromov-Wasserstein\n%%\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Solve low rank gromov-wasserstein with different ranks\nlist_rank = [10, 50]\nlist_P_GW = []\nlist_loss_GW = []\nlist_time_GW = []\n\nfor rank in list_rank:\n start = time.time()\n\n Q, R, g, log = ot.lowrank_gromov_wasserstein_samples(\n X,\n Y,\n reg=0,\n rank=rank,\n rescale_cost=False,\n cost_factorized_Xs=(A1, A2),\n cost_factorized_Xt=(B1, B2),\n seed_init=49,\n numItermax=1000,\n log=True,\n stopThr=1e-6,\n )\n end = time.time()\n\n P = log[\"lazy_plan\"][:]\n loss = log[\"value\"]\n\n list_P_GW.append(P)\n list_loss_GW.append(np.round(loss, 3))\n list_time_GW.append(end - start)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Plot low rank GW with different ranks\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"pl.figure(3, figsize=(10, 4))\n\npl.subplot(1, 2, 1)\npl.imshow(list_P_GW[0], interpolation=\"nearest\", aspect=\"auto\", cmap=\"gray_r\")\npl.title(\"Low rank GW (rank=10, loss={})\".format(list_loss_GW[0]))\n\npl.subplot(1, 2, 2)\npl.imshow(list_P_GW[1], interpolation=\"nearest\", aspect=\"auto\", cmap=\"gray_r\")\npl.title(\"Low rank GW (rank=50, loss={})\".format(list_loss_GW[1]))\n\npl.tight_layout()\npl.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Compare computation time between entropic GW and low rank GW\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"print(\"Entropic GW: {:.2f}s\".format(time_entropic))\nprint(\"Low rank GW (rank=10): {:.2f}s\".format(list_time_GW[0]))\nprint(\"Low rank GW (rank=50): {:.2f}s\".format(list_time_GW[1]))"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.18"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}

‎master/_downloads/059a63fc6cb655dcd2f1c9a61bb9d7ec/plot_OT_2D_samples.ipynb‎

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# Optimal Transport between 2D empirical distributions\n\nIllustration of 2D optimal transport between distributions that are weighted\nsum of Diracs. The OT matrix is plotted with the samples.\n"
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"\n# Optimal Transport between empirical distributions\n\nIllustration of optimal transport between distributions in 2D that are weighted\nsum of Diracs. The OT matrix is plotted with the samples.\n"
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]
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{
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},
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"outputs": [],
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"source": [
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"pl.figure(1)\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"Source and target distributions\")\n\npl.figure(2)\npl.imshow(M, interpolation=\"nearest\")\npl.title(\"Cost matrix M\")"
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"pl.figure(1)\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"Source and target distributions\")\n\npl.figure(2)\npl.imshow(M, interpolation=\"nearest\", cmap=\"gray_r\")\npl.title(\"Cost matrix M\")"
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]
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},
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{
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},
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"outputs": [],
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"source": [
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"G0 = ot.solve(M, a, b).plan\n\npl.figure(3)\npl.imshow(G0, interpolation=\"nearest\")\npl.title(\"OT matrix G0\")\n\npl.figure(4)\not.plot.plot2D_samples_mat(xs, xt, G0, c=[0.5, 0.5, 1])\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"OT matrix with samples\")"
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"G0 = ot.solve(M, a, b).plan\n\npl.figure(3)\npl.imshow(G0, interpolation=\"nearest\", cmap=\"gray_r\")\npl.title(\"OT matrix G0\")\n\npl.figure(4)\not.plot.plot2D_samples_mat(xs, xt, G0, c=[0.5, 0.5, 1])\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"OT matrix with samples\")"
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{
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},
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"outputs": [],
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"source": [
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"# reg term\nlambd = 1e-1\n\nGs = ot.sinkhorn(a, b, M, lambd)\n\npl.figure(5)\npl.imshow(Gs, interpolation=\"nearest\")\npl.title(\"OT matrix sinkhorn\")\n\npl.figure(6)\not.plot.plot2D_samples_mat(xs, xt, Gs, color=[0.5, 0.5, 1])\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"OT matrix Sinkhorn with samples\")\n\npl.show()"
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"# reg term\nlambd = 1e-1\n\nGs = ot.sinkhorn(a, b, M, lambd)\n\npl.figure(5)\npl.imshow(Gs, interpolation=\"nearest\", cmap=\"gray_r\")\npl.title(\"OT matrix sinkhorn\")\n\npl.figure(6)\not.plot.plot2D_samples_mat(xs, xt, Gs, color=[0.5, 0.5, 1])\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"OT matrix Sinkhorn with samples\")\n\npl.show()"
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{
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},
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"outputs": [],
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"source": [
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"# reg term\nlambd = 1e-1\n\nGes = ot.bregman.empirical_sinkhorn(xs, xt, lambd)\n\npl.figure(7)\npl.imshow(Ges, interpolation=\"nearest\")\npl.title(\"OT matrix empirical sinkhorn\")\n\npl.figure(8)\not.plot.plot2D_samples_mat(xs, xt, Ges, color=[0.5, 0.5, 1])\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"OT matrix Sinkhorn from samples\")\n\npl.show()"
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"# reg term\nlambd = 1e-1\n\nGes = ot.bregman.empirical_sinkhorn(xs, xt, lambd)\n\npl.figure(7)\npl.imshow(Ges, interpolation=\"nearest\", cmap=\"gray_r\")\npl.title(\"OT matrix empirical sinkhorn\")\n\npl.figure(8)\not.plot.plot2D_samples_mat(xs, xt, Ges, color=[0.5, 0.5, 1])\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"OT matrix Sinkhorn from samples\")\n\npl.show()"
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]
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}
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],

‎master/_downloads/06f3dd7c3258690ab730be0a658b5e36/plot_ssw_unif_torch.zip‎

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‎master/_downloads/0dbd57c6090215001a0a712021c577e5/plot_GMMOT_plan.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# OT between GMM : plan and maps in 1D\n\nIllustration of the GMM plan for\nthe Mixture Wasserstein between two GMM in 1D,\nas well as the two maps T_mean and T_rand.\nT_mean is the barycentric projection of the GMM coupling,\nand T_rand takes a random gaussian image between two components,\naccording to the coupling and the GMMs.\nSee [69] for details.\n.. [69] Delon, J., & Desolneux, A. (2020). A Wasserstein-type distance in the space of Gaussian mixture models. SIAM Journal on Imaging Sciences, 13(2), 936-970.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Author: Eloi Tanguy <eloi.tanguy@u-paris>\n# Remi Flamary <[email protected]>\n# Julie Delon <[email protected]>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 1\n\nimport numpy as np\nfrom ot.plot import plot1D_mat, rescale_for_imshow_plot\nfrom ot.gmm import gmm_ot_plan_density, gmm_pdf, gmm_ot_apply_map\nimport matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Generate GMMOT plan plot it\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"ks = 2\nkt = 3\nd = 1\neps = 0.1\nm_s = np.array([[1], [2]])\nm_t = np.array([[3], [4.2], [5]])\nC_s = np.array([[[0.05]], [[0.06]]])\nC_t = np.array([[[0.03]], [[0.07]], [[0.04]]])\nw_s = np.array([0.4, 0.6])\nw_t = np.array([0.4, 0.2, 0.4])\n\nn = 500\na_x, b_x = 0, 3\nx = np.linspace(a_x, b_x, n)\na_y, b_y = 2, 6\ny = np.linspace(a_y, b_y, n)\nplan_density = gmm_ot_plan_density(\n x[:, None], y[:, None], m_s, m_t, C_s, C_t, w_s, w_t, plan=None, atol=2e-2\n)\n\na = gmm_pdf(x[:, None], m_s, C_s, w_s)\nb = gmm_pdf(y[:, None], m_t, C_t, w_t)\nplt.figure(figsize=(8, 8))\nplot1D_mat(\n a,\n b,\n plan_density,\n title=\"GMM OT plan\",\n plot_style=\"xy\",\n a_label=\"Source distribution\",\n b_label=\"Target distribution\",\n)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Generate GMMOT maps and plot them over plan\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"plt.figure(figsize=(8, 8))\nax_s, ax_t, ax_M = plot1D_mat(\n a,\n b,\n plan_density,\n plot_style=\"xy\",\n title=\"GMM OT plan with T_mean and T_rand maps\",\n a_label=\"Source distribution\",\n b_label=\"Target distribution\",\n)\nT_mean = gmm_ot_apply_map(x[:, None], m_s, m_t, C_s, C_t, w_s, w_t, method=\"bary\")[:, 0]\nx_rescaled, T_mean_rescaled = rescale_for_imshow_plot(x, T_mean, n, a_y=a_y, b_y=b_y)\n\nax_M.plot(\n x_rescaled, T_mean_rescaled, label=\"T_mean\", alpha=0.5, linewidth=5, color=\"aqua\"\n)\n\nT_rand = gmm_ot_apply_map(\n x[:, None], m_s, m_t, C_s, C_t, w_s, w_t, method=\"rand\", seed=0\n)[:, 0]\nx_rescaled, T_rand_rescaled = rescale_for_imshow_plot(x, T_rand, n, a_y=a_y, b_y=b_y)\n\nax_M.scatter(\n x_rescaled, T_rand_rescaled, label=\"T_rand\", alpha=0.5, s=20, color=\"orange\"\n)\n\nax_M.legend(loc=\"upper left\", fontsize=13)"
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]
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}
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],
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.18"
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}
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},
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"nbformat_minor": 0
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}

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