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authorRémi Flamary <remi.flamary@gmail.com>2017-09-01 18:42:52 +0200
committerRémi Flamary <remi.flamary@gmail.com>2017-09-01 18:42:52 +0200
commite70313cb2eef5d889532eb004de0eb7361d616e6 (patch)
tree671e891ab385f028fdc9ac445f9a2fbc341a7097 /notebooks/plot_OT_2D_samples.ipynb
parent98ae0808417d0f82e761f85265e8dcfa9ebe7e5f (diff)
add converted notebooks
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+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "# 2D Optimal transport between empirical distributions\n",
+ "\n",
+ "\n",
+ "Illustration of 2D optimal transport between discributions that are weighted\n",
+ "sum of diracs. The OT matrix is plotted with the samples.\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# Author: Remi Flamary <remi.flamary@unice.fr>\n",
+ "#\n",
+ "# License: MIT License\n",
+ "\n",
+ "import numpy as np\n",
+ "import matplotlib.pylab as pl\n",
+ "import ot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Generate data\n",
+ "-------------\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "#%% parameters and data generation\n",
+ "\n",
+ "n = 50 # nb samples\n",
+ "\n",
+ "mu_s = np.array([0, 0])\n",
+ "cov_s = np.array([[1, 0], [0, 1]])\n",
+ "\n",
+ "mu_t = np.array([4, 4])\n",
+ "cov_t = np.array([[1, -.8], [-.8, 1]])\n",
+ "\n",
+ "xs = ot.datasets.get_2D_samples_gauss(n, mu_s, cov_s)\n",
+ "xt = ot.datasets.get_2D_samples_gauss(n, mu_t, cov_t)\n",
+ "\n",
+ "a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples\n",
+ "\n",
+ "# loss matrix\n",
+ "M = ot.dist(xs, xt)\n",
+ "M /= M.max()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot data\n",
+ "---------\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.text.Text at 0x7ff7483c3be0>"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7ff74a486438>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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rp67z2kM0XOJrJ1Ooxxe1crW4W0Qf7uLl3KS2NJPpvXyGTfJYPMPnmxPXdLXf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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7ff748402c88>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#%% plot samples\n",
+ "\n",
+ "pl.figure(1)\n",
+ "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n",
+ "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n",
+ "pl.legend(loc=0)\n",
+ "pl.title('Source and target distributions')\n",
+ "\n",
+ "pl.figure(2)\n",
+ "pl.imshow(M, interpolation='nearest')\n",
+ "pl.title('Cost matrix M')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute EMD\n",
+ "-----------\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.text.Text at 0x7ff7482661d0>"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7ff74a486128>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
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meOR7L8bq1bwXHh6cmbTbHY/NvzRicijg9YJt0fL//o+hSo1tygGgdPo8iHkG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7t5E0KLjUUrP38eQvrkJ32X6Hl5eLslJby+c2f7TTdaE/yjj0xNFM1mmTePcWVkQC4BAbx/yRK8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\nAKOf94eua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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7ff7482bb320>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#%% EMD\n",
+ "\n",
+ "G0 = ot.emd(a, b, M)\n",
+ "\n",
+ "pl.figure(3)\n",
+ "pl.imshow(G0, interpolation='nearest')\n",
+ "pl.title('OT matrix G0')\n",
+ "\n",
+ "pl.figure(4)\n",
+ "ot.plot.plot2D_samples_mat(xs, xt, G0, c=[.5, .5, 1])\n",
+ "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n",
+ "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n",
+ "pl.legend(loc=0)\n",
+ "pl.title('OT matrix with samples')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute Sinkhorn\n",
+ "----------------\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7ff778595748>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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GhtNx2Qt01tEBusaXX1LHkZVFjtjiYrLSMzKog+uuHbg81tEB0v6//546ypEj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\ngL25GVlePI4xgpdfb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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7ff7483e20b8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#%% sinkhorn\n",
+ "\n",
+ "# reg term\n",
+ "lambd = 1e-3\n",
+ "\n",
+ "Gs = ot.sinkhorn(a, b, M, lambd)\n",
+ "\n",
+ "pl.figure(5)\n",
+ "pl.imshow(Gs, interpolation='nearest')\n",
+ "pl.title('OT matrix sinkhorn')\n",
+ "\n",
+ "pl.figure(6)\n",
+ "ot.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])\n",
+ "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n",
+ "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n",
+ "pl.legend(loc=0)\n",
+ "pl.title('OT matrix Sinkhorn with samples')\n",
+ "\n",
+ "pl.show()"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}