Pushing the docs to dev/ for branch: main, commit 31439d22f12703c90d8809d08dd35629d5ae3cbf

Author: sklearn-ci

dev/_downloads/02192f99342d6d1323161978b6c80bfc/plot_ols_ridge.zip

@@ -87,7 +87,7 @@
       },
       "outputs": [],
       "source": [
-        "from sklearn.decomposition import TruncatedSVD\nfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysis\nfrom sklearn.ensemble import RandomTreesEmbedding\nfrom sklearn.manifold import (\n    MDS,\n    TSNE,\n    Isomap,\n    LocallyLinearEmbedding,\n    SpectralEmbedding,\n)\nfrom sklearn.neighbors import NeighborhoodComponentsAnalysis\nfrom sklearn.pipeline import make_pipeline\nfrom sklearn.random_projection import SparseRandomProjection\n\nembeddings = {\n    \"Random projection embedding\": SparseRandomProjection(\n        n_components=2, random_state=42\n    ),\n    \"Truncated SVD embedding\": TruncatedSVD(n_components=2),\n    \"Linear Discriminant Analysis embedding\": LinearDiscriminantAnalysis(\n        n_components=2\n    ),\n    \"Isomap embedding\": Isomap(n_neighbors=n_neighbors, n_components=2),\n    \"Standard LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"standard\"\n    ),\n    \"Modified LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"modified\"\n    ),\n    \"Hessian LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"hessian\"\n    ),\n    \"LTSA LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"ltsa\"\n    ),\n    \"MDS embedding\": MDS(n_components=2, n_init=1, max_iter=120, n_jobs=2),\n    \"Random Trees embedding\": make_pipeline(\n        RandomTreesEmbedding(n_estimators=200, max_depth=5, random_state=0),\n        TruncatedSVD(n_components=2),\n    ),\n    \"Spectral embedding\": SpectralEmbedding(\n        n_components=2, random_state=0, eigen_solver=\"arpack\"\n    ),\n    \"t-SNE embedding\": TSNE(\n        n_components=2,\n        max_iter=500,\n        n_iter_without_progress=150,\n        n_jobs=2,\n        random_state=0,\n    ),\n    \"NCA embedding\": NeighborhoodComponentsAnalysis(\n        n_components=2, init=\"pca\", random_state=0\n    ),\n}"
+        "from sklearn.decomposition import TruncatedSVD\nfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysis\nfrom sklearn.ensemble import RandomTreesEmbedding\nfrom sklearn.manifold import (\n    MDS,\n    TSNE,\n    Isomap,\n    LocallyLinearEmbedding,\n    SpectralEmbedding,\n)\nfrom sklearn.neighbors import NeighborhoodComponentsAnalysis\nfrom sklearn.pipeline import make_pipeline\nfrom sklearn.random_projection import SparseRandomProjection\n\nembeddings = {\n    \"Random projection embedding\": SparseRandomProjection(\n        n_components=2, random_state=42\n    ),\n    \"Truncated SVD embedding\": TruncatedSVD(n_components=2),\n    \"Linear Discriminant Analysis embedding\": LinearDiscriminantAnalysis(\n        n_components=2\n    ),\n    \"Isomap embedding\": Isomap(n_neighbors=n_neighbors, n_components=2),\n    \"Standard LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"standard\"\n    ),\n    \"Modified LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"modified\"\n    ),\n    \"Hessian LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"hessian\"\n    ),\n    \"LTSA LLE embedding\": LocallyLinearEmbedding(\n        n_neighbors=n_neighbors, n_components=2, method=\"ltsa\"\n    ),\n    \"MDS embedding\": MDS(n_components=2, n_init=1, max_iter=120, eps=1e-6),\n    \"Random Trees embedding\": make_pipeline(\n        RandomTreesEmbedding(n_estimators=200, max_depth=5, random_state=0),\n        TruncatedSVD(n_components=2),\n    ),\n    \"Spectral embedding\": SpectralEmbedding(\n        n_components=2, random_state=0, eigen_solver=\"arpack\"\n    ),\n    \"t-SNE embedding\": TSNE(\n        n_components=2,\n        max_iter=500,\n        n_iter_without_progress=150,\n        n_jobs=2,\n        random_state=0,\n    ),\n    \"NCA embedding\": NeighborhoodComponentsAnalysis(\n        n_components=2, init=\"pca\", random_state=0\n    ),\n}"
       ]
     },
     {

dev/_downloads/02fe21a1f5d14bd1ebbe34aa905d9bf6/plot_multilabel.zip

@@ -130,7 +130,7 @@ def plot_embedding(X, title):
     "LTSA LLE embedding": LocallyLinearEmbedding(
         n_neighbors=n_neighbors, n_components=2, method="ltsa"
     ),
-    "MDS embedding": MDS(n_components=2, n_init=1, max_iter=120, n_jobs=2),
+    "MDS embedding": MDS(n_components=2, n_init=1, max_iter=120, eps=1e-6),
     "Random Trees embedding": make_pipeline(
         RandomTreesEmbedding(n_estimators=200, max_depth=5, random_state=0),
         TruncatedSVD(n_components=2),

dev/_downloads/0358b1921962fd7c6f5a94c5abc91476/plot_hashing_vs_dict_vectorizer.zip

@@ -4,7 +4,7 @@
       "cell_type": "markdown",
       "metadata": {},
       "source": [
-        "\n# Multi-dimensional scaling\n\nAn illustration of the metric and non-metric MDS on generated noisy data.\n\nThe reconstructed points using the metric MDS and non metric MDS are slightly\nshifted to avoid overlapping.\n"
+        "\n# Multi-dimensional scaling\n\nAn illustration of the metric and non-metric MDS on generated noisy data.\n"
       ]
     },
     {
@@ -15,7 +15,115 @@
       },
       "outputs": [],
       "source": [
-        "# Authors: The scikit-learn developers\n# SPDX-License-Identifier: BSD-3-Clause\n\nimport numpy as np\nfrom matplotlib import pyplot as plt\nfrom matplotlib.collections import LineCollection\n\nfrom sklearn import manifold\nfrom sklearn.decomposition import PCA\nfrom sklearn.metrics import euclidean_distances\n\n# Generate the data\nEPSILON = np.finfo(np.float32).eps\nn_samples = 20\nrng = np.random.RandomState(seed=3)\nX_true = rng.randint(0, 20, 2 * n_samples).astype(float)\nX_true = X_true.reshape((n_samples, 2))\n\n# Center the data\nX_true -= X_true.mean()\n\n# Compute pairwise Euclidean distances\ndistances = euclidean_distances(X_true)\n\n# Add noise to the distances\nnoise = rng.rand(n_samples, n_samples)\nnoise = noise + noise.T\nnp.fill_diagonal(noise, 0)\ndistances += noise\n\nmds = manifold.MDS(\n    n_components=2,\n    max_iter=3000,\n    eps=1e-9,\n    random_state=42,\n    dissimilarity=\"precomputed\",\n    n_jobs=1,\n)\nX_mds = mds.fit(distances).embedding_\n\nnmds = manifold.MDS(\n    n_components=2,\n    metric=False,\n    max_iter=3000,\n    eps=1e-12,\n    dissimilarity=\"precomputed\",\n    random_state=42,\n    n_jobs=1,\n    n_init=1,\n)\nX_nmds = nmds.fit_transform(distances)\n\n# Rescale the data\nX_mds *= np.sqrt((X_true**2).sum()) / np.sqrt((X_mds**2).sum())\nX_nmds *= np.sqrt((X_true**2).sum()) / np.sqrt((X_nmds**2).sum())\n\n# Rotate the data\npca = PCA(n_components=2)\nX_true = pca.fit_transform(X_true)\nX_mds = pca.fit_transform(X_mds)\nX_nmds = pca.fit_transform(X_nmds)\n\n# Align the sign of PCs\nfor i in [0, 1]:\n    if np.corrcoef(X_mds[:, i], X_true[:, i])[0, 1] < 0:\n        X_mds[:, i] *= -1\n    if np.corrcoef(X_nmds[:, i], X_true[:, i])[0, 1] < 0:\n        X_nmds[:, i] *= -1\n\nfig = plt.figure(1)\nax = plt.axes([0.0, 0.0, 1.0, 1.0])\n\ns = 100\nplt.scatter(X_true[:, 0], X_true[:, 1], color=\"navy\", s=s, lw=0, label=\"True Position\")\nplt.scatter(X_mds[:, 0], X_mds[:, 1], color=\"turquoise\", s=s, lw=0, label=\"MDS\")\nplt.scatter(X_nmds[:, 0], X_nmds[:, 1], color=\"darkorange\", s=s, lw=0, label=\"NMDS\")\nplt.legend(scatterpoints=1, loc=\"best\", shadow=False)\n\n# Plot the edges\nstart_idx, end_idx = X_mds.nonzero()\n# a sequence of (*line0*, *line1*, *line2*), where::\n#            linen = (x0, y0), (x1, y1), ... (xm, ym)\nsegments = [\n    [X_true[i, :], X_true[j, :]] for i in range(len(X_true)) for j in range(len(X_true))\n]\nedges = distances.max() / (distances + EPSILON) * 100\nnp.fill_diagonal(edges, 0)\nedges = np.abs(edges)\nlc = LineCollection(\n    segments, zorder=0, cmap=plt.cm.Blues, norm=plt.Normalize(0, edges.max())\n)\nlc.set_array(edges.flatten())\nlc.set_linewidths(np.full(len(segments), 0.5))\nax.add_collection(lc)\n\nplt.show()"
+        "# Authors: The scikit-learn developers\n# SPDX-License-Identifier: BSD-3-Clause"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Dataset preparation\n\nWe start by uniformly generating 20 points in a 2D space.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\nfrom matplotlib import pyplot as plt\nfrom matplotlib.collections import LineCollection\n\nfrom sklearn import manifold\nfrom sklearn.decomposition import PCA\nfrom sklearn.metrics import euclidean_distances\n\n# Generate the data\nEPSILON = np.finfo(np.float32).eps\nn_samples = 20\nrng = np.random.RandomState(seed=3)\nX_true = rng.randint(0, 20, 2 * n_samples).astype(float)\nX_true = X_true.reshape((n_samples, 2))\n\n# Center the data\nX_true -= X_true.mean()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Now we compute pairwise distances between all points and add\na small amount of noise to the distance matrix. We make sure\nto keep the noisy distance matrix symmetric.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "# Compute pairwise Euclidean distances\ndistances = euclidean_distances(X_true)\n\n# Add noise to the distances\nnoise = rng.rand(n_samples, n_samples)\nnoise = noise + noise.T\nnp.fill_diagonal(noise, 0)\ndistances += noise"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Here we compute metric and non-metric MDS of the noisy distance matrix.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "mds = manifold.MDS(\n    n_components=2,\n    max_iter=3000,\n    eps=1e-9,\n    n_init=1,\n    random_state=42,\n    dissimilarity=\"precomputed\",\n    n_jobs=1,\n)\nX_mds = mds.fit(distances).embedding_\n\nnmds = manifold.MDS(\n    n_components=2,\n    metric=False,\n    max_iter=3000,\n    eps=1e-12,\n    dissimilarity=\"precomputed\",\n    random_state=42,\n    n_jobs=1,\n    n_init=1,\n)\nX_nmds = nmds.fit_transform(distances)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Rescaling the non-metric MDS solution to match the spread of the original data.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "X_nmds *= np.sqrt((X_true**2).sum()) / np.sqrt((X_nmds**2).sum())"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "To make the visual comparisons easier, we rotate the original data and both MDS\nsolutions to their PCA axes. And flip horizontal and vertical MDS axes, if needed,\nto match the original data orientation.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "# Rotate the data\npca = PCA(n_components=2)\nX_true = pca.fit_transform(X_true)\nX_mds = pca.fit_transform(X_mds)\nX_nmds = pca.fit_transform(X_nmds)\n\n# Align the sign of PCs\nfor i in [0, 1]:\n    if np.corrcoef(X_mds[:, i], X_true[:, i])[0, 1] < 0:\n        X_mds[:, i] *= -1\n    if np.corrcoef(X_nmds[:, i], X_true[:, i])[0, 1] < 0:\n        X_nmds[:, i] *= -1"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Finally, we plot the original data and both MDS reconstructions.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "fig = plt.figure(1)\nax = plt.axes([0.0, 0.0, 1.0, 1.0])\n\ns = 100\nplt.scatter(X_true[:, 0], X_true[:, 1], color=\"navy\", s=s, lw=0, label=\"True Position\")\nplt.scatter(X_mds[:, 0], X_mds[:, 1], color=\"turquoise\", s=s, lw=0, label=\"MDS\")\nplt.scatter(X_nmds[:, 0], X_nmds[:, 1], color=\"darkorange\", s=s, lw=0, label=\"NMDS\")\nplt.legend(scatterpoints=1, loc=\"best\", shadow=False)\n\n# Plot the edges\nstart_idx, end_idx = X_mds.nonzero()\n# a sequence of (*line0*, *line1*, *line2*), where::\n#            linen = (x0, y0), (x1, y1), ... (xm, ym)\nsegments = [\n    [X_true[i, :], X_true[j, :]] for i in range(len(X_true)) for j in range(len(X_true))\n]\nedges = distances.max() / (distances + EPSILON) * 100\nnp.fill_diagonal(edges, 0)\nedges = np.abs(edges)\nlc = LineCollection(\n    segments, zorder=0, cmap=plt.cm.Blues, norm=plt.Normalize(0, edges.max())\n)\nlc.set_array(edges.flatten())\nlc.set_linewidths(np.full(len(segments), 0.5))\nax.add_collection(lc)\n\nplt.show()"
       ]
     }
   ],

dev/_downloads/038d1885eb5f5ea53aca42da3031fe38/plot_document_clustering.zip

@@ -134,7 +134,7 @@
       },
       "outputs": [],
       "source": [
-        "md_scaling = manifold.MDS(\n    n_components=n_components,\n    max_iter=50,\n    n_init=4,\n    random_state=0,\n    normalized_stress=False,\n)\nS_scaling = md_scaling.fit_transform(S_points)\n\nplot_2d(S_scaling, S_color, \"Multidimensional scaling\")"
+        "md_scaling = manifold.MDS(\n    n_components=n_components,\n    max_iter=50,\n    n_init=1,\n    random_state=0,\n    normalized_stress=False,\n)\nS_scaling = md_scaling.fit_transform(S_points)\n\nplot_2d(S_scaling, S_color, \"Multidimensional scaling\")"
       ]
     },
     {

dev/_downloads/03c018a16384c69f3a89e473650d57ee/plot_svm_margin.zip

@@ -166,7 +166,7 @@ def add_2d_scatter(ax, points, points_color, title=None):
 md_scaling = manifold.MDS(
     n_components=n_components,
     max_iter=50,
-    n_init=4,
+    n_init=1,
     random_state=0,
     normalized_stress=False,
 )

dev/_downloads/04b9a7769df5b331f4d94e1d065b4311/plot_voting_decision_regions.zip

@@ -5,14 +5,17 @@
 
 An illustration of the metric and non-metric MDS on generated noisy data.
 
-The reconstructed points using the metric MDS and non metric MDS are slightly
-shifted to avoid overlapping.
-
 """
 
 # Authors: The scikit-learn developers
 # SPDX-License-Identifier: BSD-3-Clause
 
+# %%
+# Dataset preparation
+# -------------------
+#
+# We start by uniformly generating 20 points in a 2D space.
+
 import numpy as np
 from matplotlib import pyplot as plt
 from matplotlib.collections import LineCollection
@@ -31,6 +34,11 @@
 # Center the data
 X_true -= X_true.mean()
 
+# %%
+# Now we compute pairwise distances between all points and add
+# a small amount of noise to the distance matrix. We make sure
+# to keep the noisy distance matrix symmetric.
+
 # Compute pairwise Euclidean distances
 distances = euclidean_distances(X_true)
 
@@ -40,10 +48,14 @@
 np.fill_diagonal(noise, 0)
 distances += noise
 
+# %%
+# Here we compute metric and non-metric MDS of the noisy distance matrix.
+
 mds = manifold.MDS(
     n_components=2,
     max_iter=3000,
     eps=1e-9,
+    n_init=1,
     random_state=42,
     dissimilarity="precomputed",
     n_jobs=1,
@@ -62,10 +74,16 @@
 )
 X_nmds = nmds.fit_transform(distances)
 
-# Rescale the data
-X_mds *= np.sqrt((X_true**2).sum()) / np.sqrt((X_mds**2).sum())
+# %%
+# Rescaling the non-metric MDS solution to match the spread of the original data.
+
 X_nmds *= np.sqrt((X_true**2).sum()) / np.sqrt((X_nmds**2).sum())
 
+# %%
+# To make the visual comparisons easier, we rotate the original data and both MDS
+# solutions to their PCA axes. And flip horizontal and vertical MDS axes, if needed,
+# to match the original data orientation.
+
 # Rotate the data
 pca = PCA(n_components=2)
 X_true = pca.fit_transform(X_true)
@@ -79,6 +97,9 @@
     if np.corrcoef(X_nmds[:, i], X_true[:, i])[0, 1] < 0:
         X_nmds[:, i] *= -1
 
+# %%
+# Finally, we plot the original data and both MDS reconstructions.
+
 fig = plt.figure(1)
 ax = plt.axes([0.0, 0.0, 1.0, 1.0])