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    {
      "cell_type": "markdown",
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      "source": [
        "\n# OT mapping estimation for domain adaptation\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.1.9.</p></div>\n\nThis example presents how to use MappingTransport to estimate at the same\ntime both the coupling transport and approximate the transport map with either\na linear or a kernelized mapping as introduced in [8].\n\n[8] M. Perrot, N. Courty, R. Flamary, A. Habrard,\n\"Mapping estimation for discrete optimal transport\",\nNeural Information Processing Systems (NIPS), 2016.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "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 numpy as np\nimport matplotlib.pylab as pl\nimport ot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Generate data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "n_source_samples = 100\nn_target_samples = 100\ntheta = 2 * np.pi / 20\nnoise_level = 0.1\n\nXs, ys = ot.datasets.make_data_classif(\"gaussrot\", n_source_samples, nz=noise_level)\nXs_new, _ = ot.datasets.make_data_classif(\"gaussrot\", n_source_samples, nz=noise_level)\nXt, yt = ot.datasets.make_data_classif(\n    \"gaussrot\", n_target_samples, theta=theta, nz=noise_level\n)\n\n# one of the target mode changes its variance (no linear mapping)\nXt[yt == 2] *= 3\nXt = Xt + 4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(1, (10, 5))\npl.clf()\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.legend(loc=0)\npl.title(\"Source and target distributions\")"
      ]
    },
    {
      "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": [
        "# MappingTransport with linear kernel\not_mapping_linear = ot.da.MappingTransport(\n    kernel=\"linear\", mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True\n)\n\not_mapping_linear.fit(Xs=Xs, Xt=Xt)\n\n# for original source samples, transform applies barycentric mapping\ntransp_Xs_linear = ot_mapping_linear.transform(Xs=Xs)\n\n# for out of source samples, transform applies the linear mapping\ntransp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new)\n\n\n# MappingTransport with gaussian kernel\not_mapping_gaussian = ot.da.MappingTransport(\n    kernel=\"gaussian\", eta=1e-5, mu=1e-1, bias=True, sigma=1, max_iter=10, verbose=True\n)\not_mapping_gaussian.fit(Xs=Xs, Xt=Xt)\n\n# for original source samples, transform applies barycentric mapping\ntransp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs)\n\n# for out of source samples, transform applies the gaussian mapping\ntransp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot transported samples\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(2)\npl.clf()\npl.subplot(2, 2, 1)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\", alpha=0.2)\npl.scatter(\n    transp_Xs_linear[:, 0],\n    transp_Xs_linear[:, 1],\n    c=ys,\n    marker=\"+\",\n    label=\"Mapped source samples\",\n)\npl.title(\"Bary. mapping (linear)\")\npl.legend(loc=0)\n\npl.subplot(2, 2, 2)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\", alpha=0.2)\npl.scatter(\n    transp_Xs_linear_new[:, 0],\n    transp_Xs_linear_new[:, 1],\n    c=ys,\n    marker=\"+\",\n    label=\"Learned mapping\",\n)\npl.title(\"Estim. mapping (linear)\")\n\npl.subplot(2, 2, 3)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\", alpha=0.2)\npl.scatter(\n    transp_Xs_gaussian[:, 0],\n    transp_Xs_gaussian[:, 1],\n    c=ys,\n    marker=\"+\",\n    label=\"barycentric mapping\",\n)\npl.title(\"Bary. mapping (kernel)\")\n\npl.subplot(2, 2, 4)\npl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker=\"o\", label=\"Target samples\", alpha=0.2)\npl.scatter(\n    transp_Xs_gaussian_new[:, 0],\n    transp_Xs_gaussian_new[:, 1],\n    c=ys,\n    marker=\"+\",\n    label=\"Learned mapping\",\n)\npl.title(\"Estim. mapping (kernel)\")\npl.tight_layout()\n\npl.show()"
      ]
    }
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