Clarify the mini-batch K-Means performance comparison diagram
Aurélien Geron
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71c40c7aec
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"scrolled": true
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"scrolled": false
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"inertia_ratios = []\n",
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"time_ratios = []\n",
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"for k in range(1, 100):\n",
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"times = np.empty((100, 2))\n",
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"inertias = np.empty((100, 2))\n",
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"for k in range(1, 101):\n",
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" kmeans = KMeans(n_clusters=k, random_state=42)\n",
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" minibatch_kmeans = MiniBatchKMeans(n_clusters=k, random_state=42)\n",
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" print(\"\\r{}/{}\".format(k + 1, 100), end=\"\")\n",
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" time_kmeans = timeit(\"kmeans.fit(X)\", number=10, globals=globals())\n",
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" time_minibatch_kmeans = timeit(\"minibatch_kmeans.fit(X)\", number=10, globals=globals())\n",
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" inertia_ratios.append(minibatch_kmeans.inertia_ / kmeans.inertia_)\n",
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" time_ratios.append(time_minibatch_kmeans / time_kmeans)"
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" print(\"\\r{}/{}\".format(k, 100), end=\"\")\n",
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" times[k-1, 0] = timeit(\"kmeans.fit(X)\", number=10, globals=globals())\n",
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" times[k-1, 1] = timeit(\"minibatch_kmeans.fit(X)\", number=10, globals=globals())\n",
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" inertias[k-1, 0] = kmeans.inertia_\n",
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" inertias[k-1, 1] = minibatch_kmeans.inertia_"
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]
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},
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{
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"execution_count": 103,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sklearn.linear_model import LinearRegression"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"scrolled": true
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"outputs": [],
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"source": [
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"plt.figure(figsize=(10,4))\n",
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"\n",
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"lin_reg_inertia = LinearRegression()\n",
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"lin_reg_time = LinearRegression()\n",
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"lin_reg_inertia.fit(np.arange(1, 100).reshape(-1, 1), inertia_ratios)\n",
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"lin_reg_time.fit(np.arange(1, 100).reshape(-1, 1), time_ratios)\n",
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"\n",
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"plt.subplot(121)\n",
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"plt.plot(range(1, 100), inertia_ratios, \"bo\")\n",
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"plt.plot([0, 100], [1.0, 1.0], \"r--\")\n",
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"plt.plot([0, 100], lin_reg_inertia.predict([[0], [100]]), \"k-\")\n",
|
||||
"plt.plot(range(1, 101), inertias[:, 0], \"r--\", label=\"K-Means\")\n",
|
||||
"plt.plot(range(1, 101), inertias[:, 1], \"b.-\", label=\"Mini-batch K-Means\")\n",
|
||||
"plt.xlabel(\"$k$\", fontsize=16)\n",
|
||||
"plt.ylabel(\"Minibatch / K-Means Ratio\", fontsize=14)\n",
|
||||
"plt.title(\"Inertia Ratio\", fontsize=14)\n",
|
||||
"plt.axis([1, 99, np.min(inertia_ratios) * 0.98, np.max(inertia_ratios) * 1.02])\n",
|
||||
"#plt.ylabel(\"Inertia\", fontsize=14)\n",
|
||||
"plt.title(\"Inertia\", fontsize=14)\n",
|
||||
"plt.legend(fontsize=14)\n",
|
||||
"plt.axis([1, 100, 0, 100])\n",
|
||||
"\n",
|
||||
"plt.subplot(122)\n",
|
||||
"plt.plot(range(1, 100), time_ratios, \"bo\")\n",
|
||||
"plt.plot([0, 100], [1.0, 1.0], \"r--\")\n",
|
||||
"plt.plot([0, 100], lin_reg_time.predict([[0], [100]]), \"k-\")\n",
|
||||
"plt.plot(range(1, 101), times[:, 0], \"r--\", label=\"K-Means\")\n",
|
||||
"plt.plot(range(1, 101), times[:, 1], \"b.-\", label=\"Mini-batch K-Means\")\n",
|
||||
"plt.xlabel(\"$k$\", fontsize=16)\n",
|
||||
"plt.title(\"Training Time Ratio\", fontsize=14)\n",
|
||||
"plt.axis([2, 99, np.min(time_ratios) * 0.98, np.max(time_ratios) * 1.02])\n",
|
||||
"#plt.ylabel(\"Training time (seconds)\", fontsize=14)\n",
|
||||
"plt.title(\"Training time (seconds)\", fontsize=14)\n",
|
||||
"plt.axis([1, 100, 0, 6])\n",
|
||||
"#plt.legend(fontsize=14)\n",
|
||||
"\n",
|
||||
"save_fig(\"minibatch_kmeans_vs_kmeans\")\n",
|
||||
"plt.show()"
|
||||
|
|
@ -2747,7 +2732,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 138,
|
||||
"execution_count": 118,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -2761,7 +2746,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 139,
|
||||
"execution_count": 119,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3324,7 +3309,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 176,
|
||||
"execution_count": 106,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3333,7 +3318,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 177,
|
||||
"execution_count": 107,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3342,7 +3327,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 178,
|
||||
"execution_count": 108,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3351,17 +3336,17 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 179,
|
||||
"execution_count": 112,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"dbscan = DBSCAN(eps=0.05)\n",
|
||||
"dbscan = DBSCAN(eps=0.05, min_samples=5)\n",
|
||||
"dbscan.fit(X)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 180,
|
||||
"execution_count": 113,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3370,7 +3355,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 181,
|
||||
"execution_count": 114,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3379,7 +3364,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 182,
|
||||
"execution_count": 115,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3388,7 +3373,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 183,
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3397,7 +3382,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 184,
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3406,7 +3391,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 185,
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3416,7 +3401,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 186,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3444,22 +3429,22 @@
|
|||
" plt.ylabel(\"$x_2$\", fontsize=14, rotation=0)\n",
|
||||
" else:\n",
|
||||
" plt.tick_params(labelleft='off')\n",
|
||||
" plt.title(\"eps={:.2f}\".format(dbscan.eps), fontsize=14)"
|
||||
" plt.title(\"eps={:.2f}, min_samples={}\".format(dbscan.eps, dbscan.min_samples), fontsize=14)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 187,
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"plt.figure(figsize=(9, 3.2))\n",
|
||||
"\n",
|
||||
"plt.subplot(121)\n",
|
||||
"plot_dbscan(dbscan, X, size=600)\n",
|
||||
"plot_dbscan(dbscan, X, size=100)\n",
|
||||
"\n",
|
||||
"plt.subplot(122)\n",
|
||||
"plot_dbscan(dbscan2, X, size=100, show_ylabels=False)\n",
|
||||
"plot_dbscan(dbscan2, X, size=600, show_ylabels=False)\n",
|
||||
"\n",
|
||||
"save_fig(\"dbscan_diagram\")\n",
|
||||
"plt.show()\n"
|
||||
|
|
@ -3683,7 +3668,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 205,
|
||||
"execution_count": 18,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3704,7 +3689,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 206,
|
||||
"execution_count": 19,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3713,7 +3698,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 207,
|
||||
"execution_count": 20,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3730,7 +3715,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 208,
|
||||
"execution_count": 21,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3739,7 +3724,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 209,
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3748,7 +3733,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 210,
|
||||
"execution_count": 23,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3764,7 +3749,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 211,
|
||||
"execution_count": 24,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3780,7 +3765,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 212,
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3796,7 +3781,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 213,
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3805,7 +3790,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 214,
|
||||
"execution_count": 27,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3821,7 +3806,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 215,
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3831,7 +3816,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 216,
|
||||
"execution_count": 29,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3854,7 +3839,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 217,
|
||||
"execution_count": 30,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3870,7 +3855,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 218,
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3893,7 +3878,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 219,
|
||||
"execution_count": 178,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -3932,7 +3917,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 220,
|
||||
"execution_count": 155,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4028,7 +4013,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 225,
|
||||
"execution_count": 94,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4039,7 +4024,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 226,
|
||||
"execution_count": 100,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4047,8 +4032,9 @@
|
|||
"\n",
|
||||
"plot_gaussian_mixture(gm, X)\n",
|
||||
"plt.scatter(anomalies[:, 0], anomalies[:, 1], color='r', marker='*')\n",
|
||||
"plt.ylim(ymax=5.1)\n",
|
||||
"\n",
|
||||
"save_fig(\"anomaly_detection_diagram\")\n",
|
||||
"save_fig(\"mixture_anomaly_detection_diagram\")\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
|
|
@ -4254,7 +4240,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 238,
|
||||
"execution_count": 157,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4263,7 +4249,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 239,
|
||||
"execution_count": 158,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4280,7 +4266,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 240,
|
||||
"execution_count": 159,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4289,7 +4275,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 241,
|
||||
"execution_count": 160,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4300,7 +4286,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 242,
|
||||
"execution_count": 161,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4315,7 +4301,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 243,
|
||||
"execution_count": 162,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4324,7 +4310,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 244,
|
||||
"execution_count": 163,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4333,7 +4319,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 245,
|
||||
"execution_count": 179,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -4351,33 +4337,49 @@
|
|||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Note: the fact that you see only 3 regions in the right plot although there are 4 centroids is not a bug: the weight of the top-right cluster is much larger than the weight of the lower-right cluster, so the probability that any given point in this region belongs to the top right cluster is greater than the probability that it belongs to the lower-right cluster."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 246,
|
||||
"execution_count": 167,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"X_moons, y_moons = make_moons(n_samples=1000, noise=0.05, random_state=42)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 168,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"bgm = BayesianGaussianMixture(n_components=10, n_init=10, random_state=42)\n",
|
||||
"bgm.fit(X)"
|
||||
"bgm.fit(X_moons)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 247,
|
||||
"execution_count": 169,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"plt.figure(figsize=(9, 3.2))\n",
|
||||
"\n",
|
||||
"plt.subplot(121)\n",
|
||||
"plot_data(X)\n",
|
||||
"plot_data(X_moons)\n",
|
||||
"plt.xlabel(\"$x_1$\", fontsize=14)\n",
|
||||
"plt.ylabel(\"$x_2$\", fontsize=14, rotation=0)\n",
|
||||
"\n",
|
||||
"plt.subplot(122)\n",
|
||||
"plot_gaussian_mixture(bgm, X, show_ylabels=False)\n",
|
||||
"plot_gaussian_mixture(bgm, X_moons, show_ylabels=False)\n",
|
||||
"\n",
|
||||
"save_fig(\"moons_vs_bgm_diagram\")\n",
|
||||
"plt.show()"
|
||||
|
|
@ -5284,7 +5286,7 @@
|
|||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.6.4"
|
||||
"version": "3.6.5"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
Loading…
Reference in New Issue