{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n# OT for domain adaptation on empirical distributions\n\n

Note

Example added in release: 0.1.9.

\n\nThis example introduces a domain adaptation in a 2D setting. It explicit\nthe problem of domain adaptation and introduces some optimal transport\napproaches to solve it.\n\nQuantities such as optimal couplings, greater coupling coefficients and\ntransported samples are represented in order to give a visual understanding\nof what the transport methods are doing.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Authors: Remi Flamary \n# Stanislas Chambon \n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 2\n\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate data\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n_samples_source = 150\nn_samples_target = 150\n\nXs, ys = ot.datasets.make_data_classif(\"3gauss\", n_samples_source)\nXt, yt = ot.datasets.make_data_classif(\"3gauss2\", n_samples_target)\n\n# Cost matrix\nM = ot.dist(Xs, Xt, metric=\"sqeuclidean\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Instantiate the different transport algorithms and fit them\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# EMD Transport\not_emd = ot.da.EMDTransport()\not_emd.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport\not_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)\not_sinkhorn.fit(Xs=Xs, Xt=Xt)\n\n# Sinkhorn Transport with Group lasso regularization\not_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)\not_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)\n\n# transport source samples onto target samples\ntransp_Xs_emd = ot_emd.transform(Xs=Xs)\ntransp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)\ntransp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fig 1 : plots source and target samples + matrix of pairwise distance\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pl.figure(1, figsize=(10, 10))\npl.subplot(2, 2, 1)\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker=\"+\", label=\"Source samples\")\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title(\"Source samples\")\n\npl.subplot(2, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\")\npl.xticks([])\npl.yticks([])\npl.legend(loc=0)\npl.title(\"Target samples\")\n\npl.subplot(2, 2, 3)\npl.imshow(M, interpolation=\"nearest\")\npl.xticks([])\npl.yticks([])\npl.title(\"Matrix of pairwise distances\")\npl.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fig 2 : plots optimal couplings for the different methods\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pl.figure(2, figsize=(10, 6))\n\npl.subplot(2, 3, 1)\npl.imshow(ot_emd.coupling_, interpolation=\"nearest\", cmap=\"gray_r\")\npl.xticks([])\npl.yticks([])\npl.title(\"Optimal coupling\\nEMDTransport\")\n\npl.subplot(2, 3, 2)\npl.imshow(ot_sinkhorn.coupling_, interpolation=\"nearest\", cmap=\"gray_r\")\npl.xticks([])\npl.yticks([])\npl.title(\"Optimal coupling\\nSinkhornTransport\")\n\npl.subplot(2, 3, 3)\npl.imshow(ot_lpl1.coupling_, interpolation=\"nearest\", cmap=\"gray_r\")\npl.xticks([])\npl.yticks([])\npl.title(\"Optimal coupling\\nSinkhornLpl1Transport\")\n\npl.subplot(2, 3, 4)\not.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[0.5, 0.5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker=\"+\", label=\"Source samples\")\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\")\npl.xticks([])\npl.yticks([])\npl.title(\"Main coupling coefficients\\nEMDTransport\")\n\npl.subplot(2, 3, 5)\not.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[0.5, 0.5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker=\"+\", label=\"Source samples\")\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\")\npl.xticks([])\npl.yticks([])\npl.title(\"Main coupling coefficients\\nSinkhornTransport\")\n\npl.subplot(2, 3, 6)\not.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[0.5, 0.5, 1])\npl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker=\"+\", label=\"Source samples\")\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\")\npl.xticks([])\npl.yticks([])\npl.title(\"Main coupling coefficients\\nSinkhornLpl1Transport\")\npl.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fig 3 : plot transported samples\n\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# display transported samples\npl.figure(4, figsize=(10, 4))\npl.subplot(1, 3, 1)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\", alpha=0.5)\npl.scatter(\n transp_Xs_emd[:, 0],\n transp_Xs_emd[:, 1],\n c=ys,\n marker=\"+\",\n label=\"Transp samples\",\n s=30,\n)\npl.title(\"Transported samples\\nEmdTransport\")\npl.legend(loc=0)\npl.xticks([])\npl.yticks([])\n\npl.subplot(1, 3, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\", alpha=0.5)\npl.scatter(\n transp_Xs_sinkhorn[:, 0],\n transp_Xs_sinkhorn[:, 1],\n c=ys,\n marker=\"+\",\n label=\"Transp samples\",\n s=30,\n)\npl.title(\"Transported samples\\nSinkhornTransport\")\npl.xticks([])\npl.yticks([])\n\npl.subplot(1, 3, 3)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\", alpha=0.5)\npl.scatter(\n transp_Xs_lpl1[:, 0],\n transp_Xs_lpl1[:, 1],\n c=ys,\n marker=\"+\",\n label=\"Transp samples\",\n s=30,\n)\npl.title(\"Transported samples\\nSinkhornLpl1Transport\")\npl.xticks([])\npl.yticks([])\n\npl.tight_layout()\npl.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.18" } }, "nbformat": 4, "nbformat_minor": 0 }