Pushing the docs to dev/ for branch: main, commit bc44ea7ae849f533c3df6811b410f46d61998dff

Author: sklearn-ci

dev/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

@@ -26,7 +26,162 @@
       },
       "outputs": [],
       "source": [
-        "# Author: Jake Vanderplas -- <[email protected]>\n\nfrom collections import OrderedDict\nfrom functools import partial\nfrom time import time\n\nimport matplotlib.pyplot as plt\nfrom mpl_toolkits.mplot3d import Axes3D\nfrom matplotlib.ticker import NullFormatter\n\nfrom sklearn import manifold, datasets\n\n# Next line to silence pyflakes. This import is needed.\nAxes3D\n\nn_points = 1000\nX, color = datasets.make_s_curve(n_points, random_state=0)\nn_neighbors = 10\nn_components = 2\n\n# Create figure\nfig = plt.figure(figsize=(15, 8))\nfig.suptitle(\n    \"Manifold Learning with %i points, %i neighbors\" % (n_points, n_neighbors),\n    fontsize=14,\n)\n\n# Add 3d scatter plot\nax = fig.add_subplot(251, projection=\"3d\")\nax.scatter(X[:, 0], X[:, 1], X[:, 2], c=color, cmap=plt.cm.Spectral)\nax.view_init(4, -72)\n\n# Set-up manifold methods\nLLE = partial(\n    manifold.LocallyLinearEmbedding,\n    n_neighbors=n_neighbors,\n    n_components=n_components,\n    eigen_solver=\"auto\",\n    random_state=0,\n)\n\nmethods = OrderedDict()\nmethods[\"LLE\"] = LLE(method=\"standard\")\nmethods[\"LTSA\"] = LLE(method=\"ltsa\")\nmethods[\"Hessian LLE\"] = LLE(method=\"hessian\")\nmethods[\"Modified LLE\"] = LLE(method=\"modified\")\nmethods[\"Isomap\"] = manifold.Isomap(n_neighbors=n_neighbors, n_components=n_components)\nmethods[\"MDS\"] = manifold.MDS(n_components, max_iter=50, n_init=1, random_state=0)\nmethods[\"SE\"] = manifold.SpectralEmbedding(\n    n_components=n_components, n_neighbors=n_neighbors, random_state=0\n)\nmethods[\"t-SNE\"] = manifold.TSNE(\n    n_components=n_components, perplexity=30, n_iter=250, init=\"pca\", random_state=0\n)\n\n# Plot results\nfor i, (label, method) in enumerate(methods.items()):\n    t0 = time()\n    Y = method.fit_transform(X)\n    t1 = time()\n    print(\"%s: %.2g sec\" % (label, t1 - t0))\n    ax = fig.add_subplot(2, 5, 2 + i + (i > 3))\n    ax.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)\n    ax.set_title(\"%s (%.2g sec)\" % (label, t1 - t0))\n    ax.xaxis.set_major_formatter(NullFormatter())\n    ax.yaxis.set_major_formatter(NullFormatter())\n    ax.axis(\"tight\")\n\nplt.show()"
+        "# Author: Jake Vanderplas -- <[email protected]>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Dataset preparation\n\nWe start by generating the S-curve dataset.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from numpy.random import RandomState\nimport matplotlib.pyplot as plt\nfrom matplotlib import ticker\n\nfrom sklearn import manifold, datasets\n\nrng = RandomState(0)\n\nn_samples = 1500\nS_points, S_color = datasets.make_s_curve(n_samples, random_state=rng)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Let's look at the original data. Also define some helping\nfunctions, which we will use further on.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "def plot_3d(points, points_color, title):\n    x, y, z = points.T\n\n    fig, ax = plt.subplots(\n        figsize=(6, 6),\n        facecolor=\"white\",\n        tight_layout=True,\n        subplot_kw={\"projection\": \"3d\"},\n    )\n    fig.suptitle(title, size=16)\n    col = ax.scatter(x, y, z, c=points_color, s=50, alpha=0.8)\n    ax.view_init(azim=-60, elev=9)\n    ax.xaxis.set_major_locator(ticker.MultipleLocator(1))\n    ax.yaxis.set_major_locator(ticker.MultipleLocator(1))\n    ax.zaxis.set_major_locator(ticker.MultipleLocator(1))\n\n    fig.colorbar(col, ax=ax, orientation=\"horizontal\", shrink=0.6, aspect=60, pad=0.01)\n    plt.show()\n\n\ndef plot_2d(points, points_color, title):\n    fig, ax = plt.subplots(figsize=(3, 3), facecolor=\"white\", constrained_layout=True)\n    fig.suptitle(title, size=16)\n    add_2d_scatter(ax, points, points_color)\n    plt.show()\n\n\ndef add_2d_scatter(ax, points, points_color, title=None):\n    x, y = points.T\n    ax.scatter(x, y, c=points_color, s=50, alpha=0.8)\n    ax.set_title(title)\n    ax.xaxis.set_major_formatter(ticker.NullFormatter())\n    ax.yaxis.set_major_formatter(ticker.NullFormatter())\n\n\nplot_3d(S_points, S_color, \"Original S-curve samples\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Define algorithms for the manifold learning\n\nManifold learning is an approach to non-linear dimensionality reduction.\nAlgorithms for this task are based on the idea that the dimensionality of\nmany data sets is only artificially high.\n\nRead more in the `User Guide <manifold>`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "n_neighbors = 12  # neighborhood which is used to recover the locally linear structure\nn_components = 2  # number of coordinates for the manifold"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "### Locally Linear Embeddings\n\nLocally linear embedding (LLE) can be thought of as a series of local\nPrincipal Component Analyses which are globally compared to find the\nbest non-linear embedding.\nRead more in the `User Guide <locally_linear_embedding>`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "params = {\n    \"n_neighbors\": n_neighbors,\n    \"n_components\": n_components,\n    \"eigen_solver\": \"auto\",\n    \"random_state\": rng,\n}\n\nlle_standart = manifold.LocallyLinearEmbedding(method=\"standard\", **params)\nS_standart = lle_standart.fit_transform(S_points)\n\nlle_ltsa = manifold.LocallyLinearEmbedding(method=\"ltsa\", **params)\nS_ltsa = lle_ltsa.fit_transform(S_points)\n\nlle_hessian = manifold.LocallyLinearEmbedding(method=\"hessian\", **params)\nS_hessian = lle_hessian.fit_transform(S_points)\n\nlle_mod = manifold.LocallyLinearEmbedding(method=\"modified\", modified_tol=0.8, **params)\nS_mod = lle_mod.fit_transform(S_points)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "fig, axs = plt.subplots(\n    nrows=2, ncols=2, figsize=(7, 7), facecolor=\"white\", constrained_layout=True\n)\nfig.suptitle(\"Locally Linear Embeddings\", size=16)\n\nlle_methods = [\n    (\"Standart locally linear embedding\", S_standart),\n    (\"Local tangent space alignment\", S_ltsa),\n    (\"Hessian eigenmap\", S_hessian),\n    (\"Modified locally linear embedding\", S_mod),\n]\nfor ax, method in zip(axs.flat, lle_methods):\n    name, points = method\n    add_2d_scatter(ax, points, S_color, name)\n\nplt.show()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "### Isomap Embedding\n\nNon-linear dimensionality reduction through Isometric Mapping.\nIsomap seeks a lower-dimensional embedding which maintains geodesic\ndistances between all points. Read more in the `User Guide <isomap>`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "isomap = manifold.Isomap(n_neighbors=n_neighbors, n_components=n_components, p=1)\nS_isomap = isomap.fit_transform(S_points)\n\nplot_2d(S_isomap, S_color, \"Isomap Embedding\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "### Multidimensional scaling\n\nMultidimensional scaling (MDS) seeks a low-dimensional representation\nof the data in which the distances respect well the distances in the\noriginal high-dimensional space.\nRead more in the `User Guide <multidimensional_scaling>`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "md_scaling = manifold.MDS(\n    n_components=n_components, max_iter=50, n_init=4, random_state=rng\n)\nS_scaling = md_scaling.fit_transform(S_points)\n\nplot_2d(S_scaling, S_color, \"Multidimensional scaling\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "### Spectral embedding for non-linear dimensionality reduction\n\nThis implementation uses Laplacian Eigenmaps, which finds a low dimensional\nrepresentation of the data using a spectral decomposition of the graph Laplacian.\nRead more in the `User Guide <spectral_embedding>`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "spectral = manifold.SpectralEmbedding(\n    n_components=n_components, n_neighbors=n_neighbors\n)\nS_spectral = spectral.fit_transform(S_points)\n\nplot_2d(S_spectral, S_color, \"Spectral Embedding\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "### T-distributed Stochastic Neighbor Embedding\n\nIt converts similarities between data points to joint probabilities and\ntries to minimize the Kullback-Leibler divergence between the joint probabilities\nof the low-dimensional embedding and the high-dimensional data. t-SNE has a cost\nfunction that is not convex, i.e. with different initializations we can get\ndifferent results. Read more in the `User Guide <t_sne>`.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "t_sne = manifold.TSNE(\n    n_components=n_components,\n    learning_rate=\"auto\",\n    perplexity=30,\n    n_iter=250,\n    init=\"random\",\n    random_state=rng,\n)\nS_t_sne = t_sne.fit_transform(S_points)\n\nplot_2d(S_t_sne, S_color, \"T-distributed Stochastic  \\n Neighbor Embedding\")"
       ]
     }
   ],