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{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def estimate_mu(points):\n",
" return (np.array(points).T.sum(axis=1) / len(points)).reshape(2, 1)\n",
"\n",
"def estimate_cov(points, mu):\n",
" sigma = np.zeros((2, 2))\n",
" for i in range(len(points)):\n",
" sigma = np.add(np.multiply((np.array(points[i]) - mu), (np.array(points[i]) - mu).reshape(2, 1)), sigma)\n",
" return sigma / len(points)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def likelihood(x, mu, cov):\n",
" return (1 / np.sqrt(np.linalg.det(cov))) * (np.exp((-1/2) * np.dot(np.dot((x - mu).T, np.linalg.inv(cov)), (x - mu))))\n",
"\n",
"def decision_boundary(x, mu1, cov1, mu2, cov2, priors=[0.5, 0.5], landa=np.array([[0,1],[1,0]])):\n",
" risk_coeff = ((landa[0, 1] - landa[1, 1]) / (landa[1, 0] - landa[0, 0])) * (priors[1] / priors[0])\n",
" return likelihood(x, mu1, cov1) - risk_coeff * likelihood(x, mu2, cov2)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def plot_points(points, marker='o', color='black'):\n",
" for point in points:\n",
" plt.scatter(point[0], point[1],marker=marker, color=color)\n",
"\n",
"def plot_decision_boundary(x1, x2, mu1, mu2, cov1, cov2, priors=[0.5, 0.5], landa=np.array([[0,1],[1,0]])):\n",
" x = np.linspace(-6, 4, 100)\n",
" y = np.linspace(-6, 4, 100)\n",
" X, Y = np.meshgrid(x, y)\n",
" Z = np.zeros_like(X)\n",
"\n",
" for i in range(len(x)):\n",
" for j in range(len(y)):\n",
" Z[j, i] = decision_boundary(np.array([[X[j, i]], [Y[j, i]]]), mu1, cov1, mu2, cov2, priors, landa)\n",
"\n",
" plt.contourf(X, Y, Z, levels=[0,np.max(Z)], colors='green', alpha=0.3)\n",
" plt.contour(X, Y, Z, levels=[0], colors='green')\n",
"\n",
" plot_points(x1, color='green')\n",
" plot_points(x2, marker='X')\n",
"\n",
" plt.xlabel('x1')\n",
" plt.ylabel('x2')\n",
" plt.grid()\n",
" plt.title('Decision boundary')\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"x1 = [[0.5,0.5], [0.5,-0.5], [1.5,0.5], [1.5,-0.5], [1,-1], [-0.5,0.5], [-1,-1], [-2,0], [-2,1], [-2.5,-1]]\n",
"x2 = [[0,0.5], [1.5,0], [1,1], [0.5,2], [1.5,2], [2,1], [2.5,2], [1,3], [2,3]]\n",
"\n",
"mu1 = estimate_mu(x1)\n",
"mu2 = estimate_mu(x2)\n",
"\n",
"cov1 = estimate_cov(x1, mu1.T)\n",
"cov2 = estimate_cov(x2, mu2.T)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_decision_boundary(x1, x2, mu1, mu2, cov1, cov2)\n",
"plt.savefig('../assets/Q5_a.png')"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_decision_boundary(x1, x2, mu1, mu2, cov1, cov2, landa=np.array([[0, 2],[1, 0]]))\n",
"plt.savefig('../assets/Q5_b.png')"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_decision_boundary(x1, x2, mu1, mu2, cov1, cov2, priors=[1/3, 2/3], landa=np.array([[0, 2],[1, 0]]))\n",
"plt.savefig('../assets/Q5_c.png')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "base",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

Xet Storage Details

Size:
102 kB
·
Xet hash:
6e6fbf2e9fe47597cd2824a6c5944f8c7c93a3784fe383c47ae809e0bdf451a0

Xet efficiently stores files, intelligently splitting them into unique chunks and accelerating uploads and downloads. More info.