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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 936x360 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np \n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"\n",
"N = 100\n",
"np.random.seed(123)\n",
"x1 = np.repeat([2, 5], N/2) + np.random.randn(N)\n",
"x2 = np.repeat([3, 0], N/2) + np.random.randn(N)\n",
"y = np.repeat([0, 1], N/2)\n",
"data = np.concatenate((x1.reshape(N, 1), x2.reshape(N, 1)), 1)\n",
"beta = np.array([[1],[-1]])\n",
"\n",
"\n",
"pal = ['cornflowerblue','darkblue']\n",
"fig, ax = plt.subplots(1, 2, figsize = (13,5))\n",
"\n",
"## first plot\n",
"sns.scatterplot(x1, x2, hue = y, palette = pal, ax = ax[0]);\n",
"\n",
"a = np.arange(-4, 10, step = 0.01)\n",
"b = a - 2\n",
"c = beta[1]/beta[0]*a\n",
"sns.lineplot(a, c, ax = ax[0], color = 'red')\n",
"sns.lineplot(a, b, ax = ax[0], color = 'purple')\n",
"ax[0].fill_between(a, b, 10, color = pal[0], alpha = 0.25)\n",
"ax[0].fill_between(a, b, -10, color = pal[1], alpha = 0.25)\n",
"\n",
"ax[0].get_legend().remove()\n",
"ax[0].spines['left'].set_position('zero')\n",
"ax[0].spines['bottom'].set_position('zero')\n",
"ax[0].set(xlim = (-2.5, 8.5), ylim = (-4.5, 6.5));\n",
"\n",
"ax[0].set_ylabel(ylabel = r'$x_2$', size = 14, labelpad = 55)\n",
"ax[0].set_xlabel(xlabel = r'$x_1$', size = 14, labelpad = 100)\n",
"ax[0].set_title(r'$x_2 \\hspace{.25} vs. x_1$', size = 16);\n",
"sns.despine()\n",
"\n",
"## second plot\n",
"projections = data @ beta\n",
"sns.distplot(projections[y == 0], bins = 10, color = pal[0], kde = False, ax = ax[1])\n",
"sns.distplot(projections[y == 1], bins = 10, color = pal[1], kde = False, ax = ax[1])\n",
"ax[1].axvline(2, color = 'purple')\n",
"ax[1].set_ylabel(ylabel = 'count', size = 14)\n",
"ax[1].set_xlabel(xlabel = r'$f\\hspace{.2}(\\mathbf{x}_n)$', size = 14)\n",
"ax[1].set_title('Histogram of 1-D Projections', size = 16);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 936x360 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X0 = data[y == 0]\n",
"X1 = data[y == 1]\n",
"\n",
"mu0 = X0.mean(0)\n",
"mu1 = X1.mean(0)\n",
"\n",
"demeaned0 = X0 - mu0\n",
"demeaned1 = X1 - mu1\n",
"\n",
"sigma_w0 = np.array([d.reshape(2, 1) @ d.reshape(1,2) for d in demeaned0]).sum(0)\n",
"sigma_w1 = np.array([d.reshape(2, 1) @ d.reshape(1,2) for d in demeaned1]).sum(0)\n",
"sigma_w = sigma_w0 + sigma_w1 \n",
"\n",
"beta = np.linalg.inv(sigma_w) @ (mu1 - mu0).reshape(2, 1)\n",
"\n",
"\n",
"fig, ax = plt.subplots(1, 2, figsize = (13,5))\n",
"\n",
"\n",
"\n",
"\n",
"sns.scatterplot(x1, x2, hue = y, palette = pal, ax = ax[0]);\n",
"\n",
"a = np.arange(-4, 10)\n",
"b = beta[1]/beta[0]*a\n",
"sns.lineplot(a, b, color = 'red', ax = ax[0])\n",
"\n",
"c = -beta[0]/beta[1]*a + 0.045/beta[1]\n",
"ax[0].fill_between(a, c, 9, color = pal[0], alpha = 0.25)\n",
"ax[0].fill_between(a, c, -5, color = pal[1], alpha = 0.25)\n",
"sns.lineplot(a, c, color = 'purple', ax = ax[0])\n",
"\n",
"ax[0].set(xlim = (-2.5, 8.5), ylim = (-4.5, 6.5));\n",
"ax[0].get_legend().remove()\n",
"ax[0].spines['left'].set_position('zero')\n",
"ax[0].spines['bottom'].set_position('zero')\n",
"sns.despine()\n",
"\n",
"## second plot\n",
"projections = data @ beta\n",
"sns.distplot(projections[y == 0], bins = 10, color = pal[0], kde = False, ax = ax[1])\n",
"sns.distplot(projections[y == 1], bins = 10, color = pal[1], kde = False, ax = ax[1])\n",
"ax[1].axvline(0.045, color = 'purple')\n",
"ax[1].set_ylabel(ylabel = 'count', size = 14)\n",
"ax[1].set_xlabel(xlabel = r'$f\\hspace{.2}(\\mathbf{x}_n)$', size = 14)\n",
"ax[1].set_title('Histogram of 1-D Projections', size = 16);\n",
"\n",
"ax[0].set_ylabel(ylabel = r'$x_2$', size = 14, labelpad = 55)\n",
"ax[0].set_xlabel(xlabel = r'$x_1$', size = 14, labelpad = 100)\n",
"ax[0].set_title(r'$x_2 \\hspace{.25} vs. x_1$', size = 16);"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Dendrogram"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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"display_name": "Python 3",
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"name": "python3"
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"name": "ipython",
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