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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
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"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n# OT for domain adaptation on empirical distributions\n\n\nThis example introduces a domain adaptation in a 2D setting. It explicits\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\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\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"generate data\n-------------\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\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\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\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')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nEMDTransport')\n\npl.subplot(2, 3, 2)\npl.imshow(ot_sinkhorn.coupling_, interpolation='nearest')\npl.xticks([])\npl.yticks([])\npl.title('Optimal coupling\\nSinkhornTransport')\n\npl.subplot(2, 3, 3)\npl.imshow(ot_lpl1.coupling_, interpolation='nearest')\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=[.5, .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=[.5, .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=[.5, .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\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',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\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',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\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',\n label='Target samples', alpha=0.5)\npl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,\n marker='+', label='Transp samples', s=30)\npl.title('Transported samples\\nSinkhornLpl1Transport')\npl.xticks([])\npl.yticks([])\n\npl.tight_layout()\npl.show()"
]
}
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