{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# 1D Wasserstein barycenter demo\n", "\n", "\n", "This example illustrates the computation of regularized Wassersyein Barycenter\n", "as proposed in [3].\n", "\n", "\n", "[3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015).\n", "Iterative Bregman projections for regularized transportation problems\n", "SIAM Journal on Scientific Computing, 37(2), A1111-A1138.\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Author: Remi Flamary \n", "#\n", "# License: MIT License\n", "\n", "import numpy as np\n", "import matplotlib.pylab as pl\n", "import ot\n", "# necessary for 3d plot even if not used\n", "from mpl_toolkits.mplot3d import Axes3D # noqa\n", "from matplotlib.collections import PolyCollection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate data\n", "-------------\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#%% parameters\n", "\n", "n = 100 # nb bins\n", "\n", "# bin positions\n", "x = np.arange(n, dtype=np.float64)\n", "\n", "# Gaussian distributions\n", "a1 = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std\n", "a2 = ot.datasets.get_1D_gauss(n, m=60, s=8)\n", "\n", "# creating matrix A containing all distributions\n", "A = np.vstack((a1, a2)).T\n", "n_distributions = A.shape[1]\n", "\n", "# loss matrix + normalization\n", "M = ot.utils.dist0(n)\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": { "image/png": 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F3UBWq+eD7W3tHiMiHiAZOGg/Hwz8E/iOMWZbexcwxjxpjMk3xuRnZmZ27S8I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\nf17bI7LGndgbl1FhyON24XG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#%% plot the distributions\n", "\n", "pl.figure(1, figsize=(6.4, 3))\n", "for i in range(n_distributions):\n", " pl.plot(x, A[:, i])\n", "pl.title('Distributions')\n", "pl.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Barycenter computation\n", "----------------------\n", "\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0uQlqNS+5No3vSTvl/EGycTokzIX0UxBcCRpdDI27OY960c6SH6bISjRBiUgf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\n7lO97DJTnkA1LU11+nTVlStVS0vdsa0x+P2q2dm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#%% barycenter computation\n", "\n", "alpha = 0.2 # 0<=alpha<=1\n", "weights = np.array([1 - alpha, alpha])\n", "\n", "# l2bary\n", "bary_l2 = A.dot(weights)\n", "\n", "# wasserstein\n", "reg = 1e-3\n", "bary_wass = ot.bregman.barycenter(A, M, reg, weights)\n", "\n", "pl.figure(2)\n", "pl.clf()\n", "pl.subplot(2, 1, 1)\n", "for i in range(n_distributions):\n", " pl.plot(x, A[:, i])\n", "pl.title('Distributions')\n", "\n", "pl.subplot(2, 1, 2)\n", "pl.plot(x, bary_l2, 'r', label='l2')\n", "pl.plot(x, bary_wass, 'g', label='Wasserstein')\n", "pl.legend()\n", "pl.title('Barycenters')\n", "pl.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Barycentric interpolation\n", "-------------------------\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fh8/nQzqdhslkyou47HZ7lmAZzkIDg/IwBMpgUcitYQKyhUmSJExOTmJychKrV6/G7t27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\nvr6ef/qnfwJS51mPPvoo7777bsp+lsVi4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g448/hlarTcuI9Oqrr+LOO++EIAi4/fbbce+990bcHwgEcNttt+Hjjz9GdXU1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\nmH6W0+ns46Zrs9n6yAtBdLGzsrKSjIwMs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TBk1q1bx0svvQREFQa2bdt2QgQniI41f/TR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\nsUcynvMIGwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#%% barycenter interpolation\n", "\n", "n_alpha = 11\n", "alpha_list = np.linspace(0, 1, n_alpha)\n", "\n", "\n", "B_l2 = np.zeros((n, n_alpha))\n", "\n", "B_wass = np.copy(B_l2)\n", "\n", "for i in range(0, n_alpha):\n", " alpha = alpha_list[i]\n", " weights = np.array([1 - alpha, alpha])\n", " B_l2[:, i] = A.dot(weights)\n", " B_wass[:, i] = ot.bregman.barycenter(A, M, reg, weights)\n", "\n", "#%% plot interpolation\n", "\n", "pl.figure(3)\n", "\n", "cmap = pl.cm.get_cmap('viridis')\n", "verts = []\n", "zs = alpha_list\n", "for i, z in enumerate(zs):\n", " ys = B_l2[:, i]\n", " verts.append(list(zip(x, ys)))\n", "\n", "ax = pl.gcf().gca(projection='3d')\n", "\n", "poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\n", "poly.set_alpha(0.7)\n", "ax.add_collection3d(poly, zs=zs, zdir='y')\n", "ax.set_xlabel('x')\n", "ax.set_xlim3d(0, n)\n", "ax.set_ylabel('$\\\\alpha$')\n", "ax.set_ylim3d(0, 1)\n", "ax.set_zlabel('')\n", "ax.set_zlim3d(0, B_l2.max() * 1.01)\n", "pl.title('Barycenter interpolation with l2')\n", "pl.tight_layout()\n", "\n", "pl.figure(4)\n", "cmap = pl.cm.get_cmap('viridis')\n", "verts = []\n", "zs = alpha_list\n", "for i, z in enumerate(zs):\n", " ys = B_wass[:, i]\n", " verts.append(list(zip(x, ys)))\n", "\n", "ax = pl.gcf().gca(projection='3d')\n", "\n", "poly = PolyCollection(verts, facecolors=[cmap(a) for a in alpha_list])\n", "poly.set_alpha(0.7)\n", "ax.add_collection3d(poly, zs=zs, zdir='y')\n", "ax.set_xlabel('x')\n", "ax.set_xlim3d(0, n)\n", "ax.set_ylabel('$\\\\alpha$')\n", "ax.set_ylim3d(0, 1)\n", "ax.set_zlabel('')\n", "ax.set_zlim3d(0, B_l2.max() * 1.01)\n", "pl.title('Barycenter interpolation with Wasserstein')\n", "pl.tight_layout()\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 }