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Clarify the 'not in the book' comments

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Aurélien Geron 2021-11-21 18:04:07 +13:00
parent 7f0c64b0f4
commit 6465bc9907
1 changed files with 18 additions and 73 deletions
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91
07_dimensionality_reduction.ipynb
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@ -145,7 +145,7 @@
"metadata": {},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – we've generated plenty of datasets before with similar code\n",
"\n",
"import numpy as np\n",
"\n",
@ -160,13 +160,6 @@
"X += [0.2, 0, 0.2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–2. A 3D dataset lying close to a 2D subspace:**"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -182,7 +175,7 @@
},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – this code generates and saves Figure 7–2\n",
"\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
@ -244,20 +237,13 @@
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–3. The new 2D dataset after projection:**"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – this code generates and saves Figure 7–3\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(1, 1, 1, aspect='equal')\n",
@ -276,13 +262,6 @@
"save_fig(\"dataset_2d_plot\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–4. Swiss roll dataset:**"
]
},
{
"cell_type": "code",
"execution_count": 8,
@ -300,7 +279,7 @@
"metadata": {},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – this code generates and saves Figure 7–4\n",
"\n",
"from matplotlib.colors import ListedColormap\n",
"\n",
@ -318,19 +297,14 @@
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–5. Squashing by projecting onto a plane (left) versus unrolling the Swiss roll (right):**"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# not in the book – this code generates and saves plots for Figure 7–5\n",
"\n",
"plt.figure(figsize=(10, 4))\n",
"\n",
"plt.subplot(121)\n",
@ -350,19 +324,14 @@
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–6. The decision boundary may not always be simpler with lower dimensions:**"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# not in the book – this code generates and saves plots for Figure 7–6\n",
" \n",
"axes = [-11.5, 14, -2, 23, -12, 15]\n",
"x2s = np.linspace(axes[2], axes[3], 10)\n",
"x3s = np.linspace(axes[4], axes[5], 10)\n",
@ -427,20 +396,13 @@
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–7. Selecting the subspace to project on:**"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – this code generates and saves Figure 7–7\n",
"\n",
"angle = np.pi / 5\n",
"stretch = 5\n",
@ -545,7 +507,7 @@
"metadata": {},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – this code shows how to construct Σ from s\n",
"m, n = X.shape\n",
"Σ = np.zeros_like(X_centered)\n",
"Σ[:n, :n] = np.diag(s)\n",
@ -827,20 +789,13 @@
"X_recovered = pca.inverse_transform(X_reduced)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–9. MNIST compression that preserves 95% of the variance:**"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – this cell generates and saves Figure 7–9\n",
"\n",
"plt.figure(figsize=(7, 4))\n",
"for idx, X in enumerate((X_train[::2100], X_recovered[::2100])):\n",
@ -974,7 +929,7 @@
"metadata": {},
"outputs": [],
"source": [
"# not in the book\n",
"# not in the book – show the equation computed by johnson_lindenstrauss_min_dim\n",
"d = int(4 * np.log(m) / (ε ** 2 / 2 - ε ** 3 / 3))\n",
"d"
]
@ -1028,7 +983,7 @@
"metadata": {},
"outputs": [],
"source": [
"# not in the book, performance comparison between Gaussian and Sparse RP\n",
"# not in the book – performance comparison between Gaussian and Sparse RP\n",
"\n",
"from sklearn.random_projection import SparseRandomProjection\n",
"\n",
@ -1066,19 +1021,14 @@
"X_unrolled = lle.fit_transform(X_swiss)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–12. Unrolled Swiss roll using LLE:**"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"# not in the book – this cell generates and saves Figure 7–10\n",
"\n",
"plt.title(\"Unrolled swiss roll using LLE\")\n",
"plt.scatter(X_unrolled[:, 0], X_unrolled[:, 1],\n",
" c=t, cmap=darker_hot)\n",
@ -1097,7 +1047,7 @@
"metadata": {},
"outputs": [],
"source": [
"# not in the book: shows how well correlated z1 is to t: LLE worked fine\n",
"# not in the book – shows how well correlated z1 is to t: LLE worked fine\n",
"plt.title(\"$z_1$ vs $t$\")\n",
"plt.scatter(X_unrolled[:, 0], t, c=t, cmap=darker_hot)\n",
"plt.xlabel(\"$z_1$\")\n",
@ -1143,19 +1093,14 @@
"X_reduced_tsne = tsne.fit_transform(X_swiss)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Code to generate Figure 8–13. Using various techniques to reduce the Swill roll to 2D:**"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"# not in the book – this cell generates and saves Figure 7–11\n",
"\n",
"titles = [\"MDS\", \"Isomap\", \"t-SNE\"]\n",
"\n",
"plt.figure(figsize=(11,4))\n",