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      "source": [
        "\n# OT for domain adaptation on empirical distributions\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.1.9.</p></div>\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": {
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      "source": [
        "# Authors: Remi Flamary <remi.flamary@unice.fr>\n#          Stanislas Chambon <stan.chambon@gmail.com>\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()"
      ]
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