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‎master/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

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‎master/_downloads/2d8c2602150613db60963995928178a5/plot_lowrank_GW.py

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# -*- coding: utf-8 -*-
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"""
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========================================
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Low rank Gromov-Wasterstein between samples
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========================================
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Comparaison between entropic Gromov-Wasserstein and Low Rank Gromov Wasserstein [67]
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on two curves in 2D and 3D, both sampled with 200 points.
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The squared Euclidean distance is considered as the ground cost for both samples.
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[67] Scetbon, M., Peyré, G. & Cuturi, M. (2022).
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"Linear-Time GromovWasserstein Distances using Low Rank Couplings and Costs".
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In International Conference on Machine Learning (ICML), 2022.
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"""
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# Author: Laurène David <[email protected]>
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#
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# License: MIT License
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#
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# sphinx_gallery_thumbnail_number = 3
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#%%
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import numpy as np
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import matplotlib.pylab as pl
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import ot.plot
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import time
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##############################################################################
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# Generate data
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# -------------
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#%% parameters
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n_samples = 200
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# Generate 2D and 3D curves
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theta = np.linspace(-4 * np.pi, 4 * np.pi, n_samples)
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z = np.linspace(1, 2, n_samples)
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r = z**2 + 1
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x = r * np.sin(theta)
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y = r * np.cos(theta)
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# Source and target distribution
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X = np.concatenate([x.reshape(-1, 1), z.reshape(-1, 1)], axis=1)
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Y = np.concatenate([x.reshape(-1, 1), y.reshape(-1, 1), z.reshape(-1, 1)], axis=1)
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##############################################################################
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# Plot data
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# ------------
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#%%
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# Plot the source and target samples
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fig = pl.figure(1, figsize=(10, 4))
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ax = fig.add_subplot(121)
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ax.plot(X[:, 0], X[:, 1], color="blue", linewidth=6)
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ax.tick_params(left=False, right=False, labelleft=False,
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labelbottom=False, bottom=False)
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ax.set_title("2D curve (source)")
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ax2 = fig.add_subplot(122, projection="3d")
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ax2.plot(Y[:, 0], Y[:, 1], Y[:, 2], c='red', linewidth=6)
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ax2.tick_params(left=False, right=False, labelleft=False,
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labelbottom=False, bottom=False)
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ax2.view_init(15, -50)
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ax2.set_title("3D curve (target)")
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pl.tight_layout()
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pl.show()
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##############################################################################
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# Entropic Gromov-Wasserstein
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# ------------
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#%%
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# Compute cost matrices
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C1 = ot.dist(X, X, metric="sqeuclidean")
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C2 = ot.dist(Y, Y, metric="sqeuclidean")
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# Scale cost matrices
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r1 = C1.max()
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r2 = C2.max()
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C1 = C1 / r1
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C2 = C2 / r2
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# Solve entropic gw
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reg = 5 * 1e-3
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start = time.time()
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gw, log = ot.gromov.entropic_gromov_wasserstein(
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C1, C2, tol=1e-3, epsilon=reg,
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log=True, verbose=False)
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end = time.time()
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time_entropic = end - start
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entropic_gw_loss = np.round(log['gw_dist'], 3)
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# Plot entropic gw
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pl.figure(2)
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pl.imshow(gw, interpolation="nearest", aspect="auto")
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pl.title("Entropic Gromov-Wasserstein (loss={})".format(entropic_gw_loss))
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pl.show()
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##############################################################################
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# Low rank squared euclidean cost matrices
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# ------------
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# %%
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# Compute the low rank sqeuclidean cost decompositions
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A1, A2 = ot.lowrank.compute_lr_sqeuclidean_matrix(X, X, rescale_cost=False)
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B1, B2 = ot.lowrank.compute_lr_sqeuclidean_matrix(Y, Y, rescale_cost=False)
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# Scale the low rank cost matrices
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A1, A2 = A1 / np.sqrt(r1), A2 / np.sqrt(r1)
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B1, B2 = B1 / np.sqrt(r2), B2 / np.sqrt(r2)
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##############################################################################
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# Low rank Gromov-Wasserstein
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# ------------
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# %%
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# Solve low rank gromov-wasserstein with different ranks
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list_rank = [10, 50]
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list_P_GW = []
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list_loss_GW = []
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list_time_GW = []
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for rank in list_rank:
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start = time.time()
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Q, R, g, log = ot.lowrank_gromov_wasserstein_samples(
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X, Y, reg=0, rank=rank, rescale_cost=False, cost_factorized_Xs=(A1, A2),
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cost_factorized_Xt=(B1, B2), seed_init=49, numItermax=1000, log=True, stopThr=1e-6,
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)
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end = time.time()
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P = log["lazy_plan"][:]
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loss = log["value"]
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list_P_GW.append(P)
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list_loss_GW.append(np.round(loss, 3))
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list_time_GW.append(end - start)
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# %%
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# Plot low rank GW with different ranks
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pl.figure(3, figsize=(10, 4))
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pl.subplot(1, 2, 1)
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pl.imshow(list_P_GW[0], interpolation="nearest", aspect="auto")
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pl.title('Low rank GW (rank=10, loss={})'.format(list_loss_GW[0]))
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pl.subplot(1, 2, 2)
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pl.imshow(list_P_GW[1], interpolation="nearest", aspect="auto")
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pl.title('Low rank GW (rank=50, loss={})'.format(list_loss_GW[1]))
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pl.tight_layout()
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pl.show()
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# %%
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# Compare computation time between entropic GW and low rank GW
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print("Entropic GW: {:.2f}s".format(time_entropic))
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print("Low rank GW (rank=10): {:.2f}s".format(list_time_GW[0]))
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print("Low rank GW (rank=50): {:.2f}s".format(list_time_GW[1]))

‎master/_downloads/6f1e7a639e0699d6164445b55e6c116d/auto_examples_jupyter.zip

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‎master/_downloads/f57ac3920f640711f894fc67edcc0ae6/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\nComparaison 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(left=False, right=False, labelleft=False,\n labelbottom=False, bottom=False)\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(left=False, right=False, labelleft=False,\n labelbottom=False, bottom=False)\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,\n log=True, verbose=False)\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\")\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, Y, reg=0, rank=rank, rescale_cost=False, cost_factorized_Xs=(A1, A2),\n cost_factorized_Xt=(B1, B2), seed_init=49, numItermax=1000, log=True, 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\")\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\")\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": "3.10.14"
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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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}

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‎master/_modules/index.html

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@@ -104,6 +104,7 @@ <h1>All modules for which code is available</h1>
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<li><a href="ot/gromov/_dictionary.html">ot.gromov._dictionary</a></li>
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<li><a href="ot/gromov/_estimators.html">ot.gromov._estimators</a></li>
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<li><a href="ot/gromov/_gw.html">ot.gromov._gw</a></li>
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<li><a href="ot/gromov/_lowrank.html">ot.gromov._lowrank</a></li>
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<li><a href="ot/gromov/_semirelaxed.html">ot.gromov._semirelaxed</a></li>
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<li><a href="ot/gromov/_utils.html">ot.gromov._utils</a></li>
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<li><a href="ot/lowrank.html">ot.lowrank</a></li>

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