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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solution Exercise 1: k-Means Clustering\n",
"Unsupervised Learning\n",
"CAS Practical Machine Learning, SS-HS23\n",
"Prof. Dr. Matthias Dehmer"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load and Prepare Dataset"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load data from tab-separated file using Pandas and show first rows."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Driver_ID</th>\n",
" <th>Distance_Feature</th>\n",
" <th>Speeding_Feature</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>3423311935</td>\n",
" <td>71.24</td>\n",
" <td>28.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>3423313212</td>\n",
" <td>52.53</td>\n",
" <td>25.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>3423313724</td>\n",
" <td>64.54</td>\n",
" <td>27.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>3423311373</td>\n",
" <td>55.69</td>\n",
" <td>22.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>3423310999</td>\n",
" <td>54.58</td>\n",
" <td>25.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Driver_ID Distance_Feature Speeding_Feature\n",
"0 3423311935 71.24 28.0\n",
"1 3423313212 52.53 25.0\n",
"2 3423313724 64.54 27.0\n",
"3 3423311373 55.69 22.0\n",
"4 3423310999 54.58 25.0"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv('data/data_delivery_fleet.tsv', sep='\\t', header=0)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Column 1: `Driver_ID` is the identification of the delivery driver.<br>\n",
"Column 2: `Distance_Feature` is the average number of miles driven per day.<br>\n",
"Column 3: `Speeding_Feature` is the % of time the driver exceeded the speed limit by more >5 mph."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create NumPy array `data` from the 2nd (`Distance_Feature`) and the 3rd (`Speeding_Feature`) column."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(4000, 2)\n",
"<class 'numpy.ndarray'>\n"
]
},
{
"data": {
"text/plain": [
"array([[ 71.24, 28. ],\n",
" [ 52.53, 25. ],\n",
" [ 64.54, 27. ],\n",
" ..., \n",
" [ 170.91, 12. ],\n",
" [ 176.14, 5. ],\n",
" [ 168.03, 9. ]])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = df[['Distance_Feature', 'Speeding_Feature']].as_matrix()\n",
"print(data.shape)\n",
"print(data.__class__)\n",
"data"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1130bac88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(df.Distance_Feature, df.Speeding_Feature, marker='.')\n",
"plt.xlabel('distance [mi]')\n",
"plt.ylabel('speeding fraction [%]')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Cluster the Data "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Initially, pick some cluster count k that you see fit."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.cluster import KMeans\n",
"\n",
"k_means = KMeans(n_clusters=4).fit(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Visualize the clusters."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e2a9780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def visualize_k_means(data, k_means):\n",
" plt.figure()\n",
" k = len(k_means.cluster_centers_)\n",
" for i in range(k):\n",
" colors = ['r', 'g', 'b', 'y', 'c', 'm']\n",
" points_in_cluster = np.array([data[j] for j in range(len(data)) if k_means.labels_[j] == i])\n",
" plt.scatter(points_in_cluster[:, 0], points_in_cluster[:, 1], \\\n",
" marker='.', color=colors[i % len(colors)])\n",
" plt.scatter(k_means.cluster_centers_[:,0], k_means.cluster_centers_[:, 1], marker='*', color='k')\n",
" plt.title('k-Means Clustering with k={} clusters'.format(k))\n",
" plt.show()\n",
" \n",
"visualize_k_means(data, k_means)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot cluster assignments for k=2 ... 8"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c4bc550>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114352a90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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ArF5dWY+9kVMqFJu8Db0x5hUR+T/ALuAQcD+wGThgjBmJHvYycLzf+SKyFFgKMGXKlHy7oSiKi0JK+zlhm0gERKC/v/A288G53q5dmlKhWORt6EVkHHAZcCJwAPgVMN/nUON3vjFmDbAGYO7cub7HKIqSPYV6wH4TreX2qt3XCwahKWqhdOK3MAoJ3VwI/NEY8zqAiNwOnAOMFZGmqFd/ArCn8G4qSv3S2wvd3fb3hQvzN6SFJhXzS2GwcmV5vWr3PQAsWQJTpmhKhUIpxNDvAs4WkdHY0M0FwCbgIeCTwC+ARcCdhXZSUeqV3l5rxIaG7PtbboGHHsrPqBVD+uhNYVBuOaX3eoV88SlxConRPy4i/w48BYwAW7ChmHuAX4jId6Lb1hajo4pSj4RCMDwcf1+I1+znkRcaXy93ojJNjFYaxJjKh8fnzp1rNm3aVOluKErZ8Xr0ra35e/R+batqpb4Rkc3GmLmZjtOVsYpSQdrbrfdajBi9l2xi9qVW1GTTfrlVPY2IGnpFqTClSu2bKb5eao8/m/Z11FEeNKmZotQJ3lWkmdIVuD3+wUHo7CzOClSnH93dmROgVSpJWqOtuFWPXlHqgFSecbrRguPxDw7aRVIPPggbNxbmVbv70dRktfCQWrFTiSRpjTiKUI9eUeqA7m4YGIh7xt3dmT1Wx+O/8EKb8iASyc2r9vOK3R76yAhcfXX6BGhOH5YsgUWLcrnj/GnIVMvGmIr/zJkzxyiKkh+PPmpMa6sxYH+am41paTEmGDTmsMPs/kznH3ZY9senO6eYbZWKcl+vlACbTBY2Vj16RalxQiHrPYPNUTNrlvVWs/VY80k9nMorLmZbhZIqDt+IqZY1Rq8oNY43zr14MWzbllvcO1flT7rYejHbypdMcfhGK2Kuhl5Rahy/1aQzZpROm+7o3levthkuC71GKVbDFpr3p97QlbGKomRNrShWaqWfhZLtyliN0StKDZJOB14sjfhbb73FiSd+gH/8x7dibdWKYqUR4/Dp0NCNotQY6bzVYnqyq1ffw86d27n++nv5/vc/y4YNtVUcvNHi8OlQQ68oNUa6+HMqj7u7G/btgwkTMufT+bM/u4JQ6C5GRgYBMGYhhw4t4dpr/5ytW/8tIZ4OdvSguWyqGzX0ilJjpPOqvfva2uD88+3qV4d161JPTvb2wiOPfJvh4T5gJzYDeTMi7+Mb37geiHvKmsumdtAYvaLUGOniz959/f3xFMgOw8OpY+tWk38K8G1gmKamwwkEhrn++m/xqU+dnHRsLrlsBgbiWTqV8qIevaLUIOniz959Tj4bh+bm1LF1Z0Rw6NBtwOFce+03+elPr+d3v/sVtnBc8rHp4vUdHTbnTThs1+2uW6dVoyqByisVpc5xatJmG6Pv7YWf/exJLrlkCh/72HG8+uqr7N69m7lzk1V82cTfv/AF6Oqyhj4QgO98B1asKMqtNTxaeERRFCB39Yk9/sOx98cddxzHHXdc3m3PmmWNPNjEaW1t2fdFKQ4ao1eUKqOUudJL0XamNvv7rScP9rW/v3jXVrJDPXpFqSJKqVIpRdvZtNnRYWvh1oL2vl5Rj15RKojXGy7lytNStJ1Nm7pKtfKoR68oFcLPGy7lytNStJ1tm7pKtbKooVeUCuHnDa9YUfxMjg6lyBIJtjKUo+hRqhM19IpSIVJ5w6X0fovZtjMicWrOBgKwfr2GZ6oRjdFXGb27e1m5cSW9uxukPH0DU+uxa2dEEonY97nWnC0WpVQp1Qvq0VcRvbt7uaD7AobCQ7QEW9iwcAPtk2vsv1/JiVqOXTsjErdHX25VjebSyQ419FVEaGeIofAQYRNmKDxEaGdIDb1Stbhj/m1t8WpTkDmjZbHQSlLZoYa+iuiY2kFLsCXm0XdM7ah0lxQlLd4RSbk97FrKj19J1NBXEe2T29mwcAOhnSE6pnaoN6/UHOX2sEulJKo31NBXGe2T29XAKzVLJTzsWp7nKBcFGXoRGQv8BPggYICrgR3AL4Gp2MoFnzbGvFlQL+uY3t296sErNYlf5sp69bBrvUpWoR79D4DfGGM+KSItwGjg74ANxpjvicjXga8DXyvwOnWJqmyUWiVdLL7ePOx6UPbkraMXkSOB84C1AMaYIWPMAeAyYH30sPXA5YV2sl7xU9koSi1Qypw81UY93GshC6ZOAl4HbhGRLSLyExE5HDjOGLMXIPp6bBH6WZc4KpugBFVlo9QUTiw+GKx/tUs93GveFaZEZC7wGDDPGPO4iPwAeBu4zhgz1nXcm8aYcT7nLwWWAkyZMmXOSy+9lFc/qoV8Y+1rNq+hZ3sPC6YvYOmcpSW7jlIfVFOsuJr6Umqq9V6zrTBViKGfADxmjJkafX8uNh5/CtBhjNkrIhOBkDHmtHRt1XopwXxj7bmepzH9xqYeYsVKccnW0OcdujHG7AN2i4hjxC8AtgN3AYui2xYBd+Z7jVoh31h7rudpTL+x6e6GgYF4rLi7u7w5XtasgYsusq9KbVGo6uY64Nao4uZF4Crsl8dtIrIY2AV8qsBrVD35rmjN9TxdOdu49PbCLbfEa6+K2PcjI+Xx7tesgWuusb/ff799XZo50qhUCQUZemNMH+A3bLigkHZrjXxXtOZ6nq6cLZxqjbVmIhSyRh2skZ89GzZvTr0Ctdj32dOT/L5Yhr5W/yY1hTGm4j9z5swxilJqHn3UmMMOMyYYtK+PPlrpHmWPt+9dXanvpRT32dVljB1P2J+ursLbNKa2/ybVALDJZGFjNQWC0jCUKw9LKTxUvxWnM2Ykvneuu2uX/30W0i/He+/pgQUL7PveXjtPALBwYX73qtkny0PeqptiUuuqm2xwZJFto9voP9ifVehFpZTFpRyqlUopY9zXDQZteMcdvwdr4IeHobm5cIPa22vbGxqy71tb4aGHcm9TlUSFka3qRj36MuDIIgdHBokQISABWoOtaeWRKqUsPuXIw1IpD9V9XYAlS2DKlPh9fuELcaPsKHYK6VcoZL80HPK913rNjVNtqKEvA44sMoKtuRYxEQZGBuje2p3SeGsRktJQ6jwslcqP7r1uvqGUXK7X3Bz/8ijkXustN041ojVjy4Ajiwy4HrfBcEvfLSlrw2p6hNqkUnVgM1134UIbXhGxrwsXFn69UAiuvdb+5BO2UcqHxuizpNB4uXP+E3ue4M4/3InBEJQg159/PSvOXeHbfrbX1Fi+4sVv4jWbyViVOtYWJU+BUEyq3dAXM17u1xaQd/say1e85DvBqROjtUfJUyA0EsVMPeAserr+/OtjRrmQ9jUtguIl37S6xU7H29tb3hQNxaJW+50OnYzNgmKnHvCWCyykfU2LoHjJd0K4mBPJtTo6qNV+Z0INfRaUKvWAO7a++uLVsXTFubSvaRHqm3xi5tlIFktdBrCSC6EKmWeo1wVcGqOvEO7YejAQRBBGIiMaZ1dilMq7bJSFY/lct9Y8eo3RV5De3b2s3LgypXQSEmPrw+Hh2O+Ovr7Q9pXap1Ql7NztDgzE0xgUk0JkpoXEyAt9ZpWSx5YaDd0UmWxVMO7YejAQxBjDcGQYg2Fd3zoWnrHQ9zxV2TQOpVp81dEBTU3WGBoD69aVZoFVPguhCvWoi/HM6nEBl3r0LorhKYd2hhgMDxI2YQbDgylVMG71TWhRiMWzFiMIAOFIOOV5+apsdBRQeXL1VEvpXZ5xhl08BdbgFzJaKKZKRT3y0qAefZRiecpto9uImHiqg7bRbSmP9apv1m9dn1E9k4/KRkcBlSdfT7XY3qXTj8FB680HAoWNFood01aPvDSoRx+lWHr0/oP9sVQHAQL0H+zP+txFZyxiyewlaQ2xnw4/E6q1rzylirfn249IxBr5Cy8szDgX+77UIy8N6tFHKZYevWNqB61NrQV53AvPSJ+IxDsSyKZPqrWvLJVKdpapH52dlffAvahHXnxUXumiWDljcm1n5caVfOOhbxAxNoXx0tlLmXLUlKzPz+Z6mg+n8lRLHpli96Na7stLtfarmGiumxpizeY1XHP3NbH3zYFmIiaSVTxd4++Kkkyt6eHzRQuPVAHpMlK6K005cX0nX/1IZASDYSg8RPfW7rSeuOatbxzcHirUv7daCPW6wjVf1NCXiHRZKr2VplZfvDoW13evkg0GgtzSd0vaFbMaf28MMpUKbGQj5ke1zIlUCw1n6HONVbuPB7I+18/TfmLPExwaORQ7JmIiDIWH6D/Yz+qLV7P2qbVMOmIS86fNp/9gP7ve2sWap9YQMZGYJt97Xc110xi4PdSIHfhhjL+32gixaYdU96olChNpKEOfazy7kHw0Xk/7wOAB7vjDHQnHBAjQEmyhbXQbX7rvSwyGBwG49/l7CS0Kse21bVlp8nNV4Si1h9tD9Xr0bm+1UWLTkPleVb0Tp6F09Lnqyb35aGIrXkdSr3h1aJ/czuqLV3PBiRew+uLV9O3tSzrmwpMuZMPCDfQf7GcoPBTbPhwepjPUyZa9W/LW5Cv1hVtfftNNcNVVtgC417hVi16/HDTSvRZKQ3n0ucaz3ceLWG8eIEL6Fa9gRwPLfrOMofAQG3dt5LqzruP+F++P7W8KNNHZ0Un75Ha2vbYNQ1z9ZDA8+McHaX6pmaZgE+FIWOPvSsygu71Yb+3XRopNN9K9FkpDGfpc49mOV96zvYfRzaO569m7Ylr3LXu3sHLjypSxe/doYDA8SN/ePpbPW07oj6FYHL57a3csU6VbdSMIERNhJDLCktlLctLUg2rm65lMapJqjk0Xe+6gmu+12lAdfRrcMfqmQBMGQzgSTvm7O3bvnDsYHrRfDgRobWqNqW/OX39+LCbfFGgiKMGY0qaQ3PSqq69vajUGX6v9rnZUR18EnEyUERPBRExsxequt3Zx81M3EzZhImHrhRtMLJe8Mzm6YeEGlv1mGU/ueZIIkdj+KUdNSYjJhyNhPj/n8zHP3bl22+g2QjvtpOyt227lxf0vcsWHruCGC29I22fV1dcvterFqq69sqihT4M3E+WsibNYOmcpvbt7Y5kmmwJNhE04tsjplr5bEnLJb311ayz+7uy/cf6NtARbYh59c7DZN/+8W3PvsOq3qwBSGnvV1dc/tagm0Xh6ZVFDnwb3ilWv6mXRGYsAWHjGQrq3dtO1uQuDYSQyEvOiQztDsQlch5HICFv2buGqmVex/Y3tDAwPsHj2Yra9to3OUCcLpi9g6ZyldG/tZmBkIGGS1uEnm3/CyeNO5r7n7uPZ/mc5te1Uls9bnjCS0Bi94qaU2vps2q7VkUi9UHCMXkSCwCbgFWPMpSJyIvAL4GjgKeBzxpihdG3UQozeu7o10zYnTu+OxYPNYyMijIRHYqtjgxJkODIcO2b5vOX84LEfJJyXieZAMw//5cNq2JUkShkf19h7ZSlnzdgvA8+43t8A/JMxZhrwJrC4CNeoCH6531Np8f1yybdPbmf+KfNj7QnCrAmzGA4Px8IxERNJMPJgPXbvNoCApP5zDUeGk7T9WlVKgdLqzVXLXhsUFLoRkROAjwHfBf5GRAT4U+CK6CHrgU7gR4Vcp5J4V516Y+Bto9tS5pLv3d3Lfc/fF3vfHGxmWts0ntjzRNpr7h/YDyRKLoHYfIEfQQkmxONVfaM4lDI+rrH32qBQj341sBxi1qgNOGCMcQLTLwPH+50oIktFZJOIbHr99dcL7Eb58Hr5zqrWsAkzMDLAst8si3nQ3Vu7E8IvV8+8muf6n8v6WmNHjWXmhJlJ21uDrUnbPn7qxwntDMWurVWlFIdSVm2q2YpQxSx0WwPk7dGLyKXAa8aYzSLS4Wz2OdR3EsAYswZYAzZGn28/KoHXyw8GgoTDYQyGJ/Y8Qcf6Dm6afxNrt6xNOO/IUUeyee/mrK+zf2A/+/ftJyhBwiYc2+6N3QclyH3P38evn/11zHtX9Y3ippRKnZpTATXgxEIhoZt5wJ+LyCXAKOBIrIc/VkSaol79CcCewrtZedJlsbx65tX8ePOPY8cOh4fp2d6TpLgJ/TGUNvySioljJhIMBHnprZcSto8fPZ55k+cxYcyEmK7f0er/6NIfqfpGqW1KlYC/AUX9RVkZG/XovxpV3fwK6DHG/EJEfgz8zhjzL+nOr1bVjUOapmzJAAAgAElEQVSmLJaQuNK1JdjCTfNv4rr7rktYGNUcaCYcCSfE3bNBEF+ZZWuwlYcWPeR7/dAiXSil1DClTMBfRx59OVU3Xr6GnZh9HhuzX5vh+KrAUais2bwm4dXx5N1ZLN05bDpDnQB8+ewvc8IRJzBt3DRmHmfj6qFFIc6cdCYSjWilSzUMcPSooxPej24aDeBr5MGGcFb9dhXtk9u5auZVsesMh4dZ9egqVdwotYvb6x4eLq60p2YnFvJHc91AUl4ax4N2V4ByMlE6Hv1wZDiWwyYQCCSFaQC6Lu1ixrEzEkYD4Ug4Id5eDJzreDX77vw66t0rNYWW1MqKhsp1U2i2Rsdjd+LnjgcdMTY/zZa9WxLi3QCdoU4efPFBIkSIRPxDMV+9/6tccJLNR79l7xae2vtURmmlH4Lw/mPezzNvPOPr3fds72HpnKXMP2U+d+yIFzeJENF8N0p2VFtZKu9SWqiu/tUYNe/RF0Mvnsqjd/CLebuv685V70dToImABBgOD6cMw6TC8cqvO+u6WJ4bL+rRKwVRRzHrRqNhPPpiZGt054dpG91G/8F+nnjlCe7ccScGY2Pev13FhDETAGIJyNzn3LrtVl7Y/wIfGP8BNu3ZFFv0BKT9EsjE3ElzmT1xNo/tfsx3/+WnX87SOUtZuXFl7DqCcNnpl3HmpDNVcaNkpgFVKI1GzRv6YunFvdp4Z1XrYHgQg0kIiazrW5fg4bs96dcPvs6ys5el9L7BGuKmQJNvmgM3TYEmtr66lSf3PJk0EnDmD5afsxxIfg7Lz1muBl7JDl3eWvfUvKEvZrZGJ9bvePXzT5kf8+rdDIeH6d7aTWhniCf2PJEQLhkOD/P2wNtcfvrl7HhjB8/vfz7JoI8fPZ7TjzmdXW/vYueBnb59aQ22cvK4k33j8u876n1cM+ea2P06/b7urOvo29vHgukL1Mgr2eOOh7e1xVUt6tXXDTUfoy8WfhWhmoJNVmHjSkIG8YpQ3u0Qz07pVJyaceyMjBOwfhks0+HOVBnrdzRvvePpa1xeyRmN1dccDROjLxZe5U2ECCPhEZbOsVWl2ka3sWXvFgD2vbePO/+Q7OmPHz2eY0Yfwx/e+AMGw6GRQ7wz9E7Ga08aM4krPnQFdz97N9tf357x+LAJx0cUrzyRkLfeUQo5la4UJWs0Vl+3qEcfxfGMvcU+ui7tYumcpQnHnfev5yVMsKZauZorubTTFGgiEomkXGWrq2OVnFGPvuao5MrYmsSJ9X/0pI/GVpgGJLGqFFjPPxxJXPB08riTi9IHx8iPHz0+47HeVAqCMPWoqQn7NWOlkhPVsGK0wbJKlgs19C7aJ7fT2dHJqKZRBCVIa7A1ScXTMbWD5mBz7H1rsJW/nfe3vqmD82X/of00B+LXCEow6ZimQBOB6J8vIAGag8288s4rCfs1Y6WSM+3tsGJF5Yz8BRfAN79pX9XYFw2N0XtwPPvurd1J+3p399K9tZtLTrkEgAljJnDkqCPp2d7DJ6d/kuf6n2PSEZPYf2g/j+x6JO8+hE2YJbOXJGxzZ8cEWDxrcWzuoP9gP7ve2sXNT90MWO/+qplXAbBy48q81UiFrjhWlJzQOYKS0fCG3i/9cNvoNtb1rWM4PBzTzAOce8u5sTw1TYEmzpl8Do+8lGjQW4It+M17NAeaY8XDHbx55t089spjnH382Sw8YyE/fPKHCftag62xRVvOPXRv7SYYCELE9mHWxFkp69hmY7y1QpVSdlTPXzIa2tC7jVlToAmDicXfHQM8FB6ie2s3+97dl2CURyIjSUbeOd6J8TsIwuJZizly1JEJC6nSJTfr29dH374+1mxekxSLv3H+jQlG3n0PS2YvYeEZC1NWmMrWeBdjxbGi5IQ3v41680WjoQ2925hFwvGEZl5DDbDnnezqp/iteg1IgFkTZ9GzvSfnPnpVNQaTMEEc2hmKKYVM2DDlqCkxg+xdMZyL8dYKVUrGRGelSIRWc+WqaoOGNvRuY+Z49CORkYQqUM2BZhaesZBZE2clLHxyT5C6PfMrZlzBbU/flnCdsAnzpfu+xJfP/jL3v3h/wf1257Q/MHggrqEnwoHBA0DqFcPZGu9irjhWapBMUkuVYtYUDW3ovcYMEtMPOyEXdx6cnu09LJi+gBnHzohN2B456kj69vYxc+JM+vb2+SYxGwwP8vbA20w9aio739oZ2/7+Y97PaW2n2TcCz77xLNvfSFw0NbZ1bMyACxIbGfQf7OfXO36dcGzf3r6E+3OHeEI7Q6y+eDX9B/uzMt7e/D9KHeP1zjNNjOrEaU2hC6Y8ZDsJ6T3OKU7ipCLwI0DAN2WCk87AadebbthZSJXq1c3yecu54cIb8ronpUHx885BPfoaQFMgZIlXhZJtyMIb7+7Z3hMz8k6hkOfffD6hZqzfF8BwZJiF/7GQT0z/BGNbx9I2uo35p8yn79U+3ht6jzcOvhGrdnXS2JN48cCLSQVS3PTt7aN3d29CvwuZWFWJZQPg552vWJF+YrSeJ06rrQhLEWhoQ5/K080mZOGdrJw5cWYs/m4w/OGNP2RdBPz5N59n1W9XpUyB4CQq+9t5f5tx1PDAiw+wcdfGBK8934lVHQk0CKlkjZkmRutx4rRORyp1Zehz9T7z9XT94t2hnSECEohVqMrWyLtJlefm9LbT+fLZX6b/YH/smk/secI3sZrBJN1LvhOrKrFsEGrZOy+2912ncw91Y+jz8T7z8XTTXac12BpT8IxERnIuAp7Ko9/+xna+eO8XiZhI7JodUzu459l7klIbByTgey/5TKyqxLKBqEXvvBTed50u2qobQ5+P95mPpxvaGYrlrB8MD8bSBbeNbmPRGYsAmDVxFlv2buG2p2+LlRQUhKNaj4qpZxxGNY1ibOtYhsPDhE2YY0YfQ3OwmZ1v7uRQ+FDsOMegOwu4phw1hVOOPoVn3ngmdsz08dP5ixl/UbR4ukoslaomlfddiJdfy6ObNNSN6qZc8eQ1m9dwzd3XxN670wUHJBBLdeBXCDxdyoNMNAeaiZhIyhW84K+4UZS6JR+1UJ3RcKqbUnmf3rh//8H+BJlkOBJOKPrhlkV6ydfIj2sdx0emfgQEdryxI8GLd/P2wNt5ta9UGXWo+igJft73ypV1GWMvlLrx6EuB3ygByKhzT0UhHn02bbYGW3lo0UMaYqll6lT1UTYa7Pk1ZOGR3t29rNy4kt7dxclj3b21m4GRgaS4v5MCGKyR/+hJH+XKGVcybtS4tO25c8wXizkT58Ry84xERpKKjRT7mSglxi/unC3FLNpRqwVAqqF4ShVSN6GbYsfoe3f3ckvfLTEPPRgIxlQnsybOih1nMIw/fDy3brs1Y5sD4YGc+uCX2tjLtLZpbHttm68yRnXwNUi+qo9ierK17hXXooKoxNSNoc9HdZNOdx/aGYoZWEG4eubVsWP6D/YnaOYf3vlw3v0e1TSKgZHkL4Dxo8czb/I8Tj3mVEJ/DPHu0Ls888YzSaGhx19+PGX+GtXB1yC5qD7csfxQCAYHIRKxr+li05nmAKpNS15PcxYVupe6MfS5ar4zebve9haesTBhX3OgmcHwIAbD3nf35t1vPyMP8PrB17ljxx2ww+bIaQ420xxsTlLzvPDmCyz7zTJfb1118DVKNh6p1+u+7jpr5MG+trVld56ft15NWvJaH124qeC91I2hz6S68XrvmbzdTO2dcdwZsbTFERPh8tMv5/ev/p4X3nwh7YRsPkSIMBweZumcpUw5agoHBg9w+/bbef7N5zEYDo0contrt6+37mj73RWplBrF68G7ve6+PggErJEPBKC/37+NbLz1VKOKXLxRv2PzyW+fas6iFj38Co6U8jb0IjIZ6AYmABFgjTHmByJyNPBLYCqwE/i0MebNwruamVSrP/2892y8Xb/2nLYOjcQXMxkMp7adyvJzlnNB9wVpc9HkS4QIsybOYumcpbFt7mpVP9nyk6Tygu57do9IlBrE6w2uXp3odS9YABs3ZvbCs/XWvaOKXLzRYmbD9Pa3ra12PfwKjpQKUd2MAF8xxrwfOBv4XyIyHfg6sMEYMw3YEH1fUVJ57xsWbuD686/PaZLSactL396+WJvf+dPvsHzeck4Zd0pMESMI5005j8ObD8/qOmNbxyYdu2XvloTrufEqblKVElSKRLlVKU4MPhy2r1u2wKJF8PGP29cZM7JTm+SrSunuhoEBfzWQ91m4PdfBQejstOenUxP5ndPbm9zf/v7cVEnVpB6qoCIob4/eGLMX2Bv9/R0ReQY4HrgM6Igeth4IAV8rqJcFksp7LyT/i1O+z2HB9AVJbV5+2uUxrzoYCNL7cm9SbppUeFMlQKLXvmD6goRqVc2B5oRRicbnS0glYq1tbYkx+LVrrbFzQjXr19t+rFiRua1cVSm9vXDLLeCsuQkG496o37NwPFdncvjBB6Gpyf6Avzfrd87GjfFn6+5vtl5xNcb3K6QIKkqMXkSmArOAx4Hjol8CGGP2isixKc5ZCiwFmDJlSjG6kZJirpptn9zO6otX07O9h/GHj+e5/ueYdOQkZhw7I+G4NZvX0LO9h+vOuo6xrWPZ9dYuujZ3JRwzunk0B4cPZn1tx2tvn9weC+GsfWotk46cxPJzluc0x6AUQDljrWvWQE8PjB4dj8GLwMhI3PBmo7RxcOLgbW3WO3YMpV/M2zl21y57PbDXvvrqeE6Zzs64cR4YgGXLbFhpwwb7+5NP2n3hMCxZAlOmpM9v39lpjbzTXnd34rG5qJKqTT1UQQpeGSsiY4CHge8aY24XkQPGmLGu/W8aY9KuJKrWlbF+uGPfwUAQQRiJjCQod7z5cLou7WLGsTMSVtS2BFtYdvayhDh7NnRd2pUQp1cqQLk8xTVr4Jr454jmZmsAm5qskR8ejht7gK4uWJrms+H02zHMgYBt0xhrDN334r5H53ruYyCxLTetrXDjjVYJNDQU3/bQQ9l9EXV05H5euvutJo++yJQl142INAM9wK3GmNujm18VkYlRb34i8Foh16g23LHvSDhe6ckd+3dqujr0bO9h6Zyl3Dj/RuuBHzGJ5fOW5xw3D0iA/oMp1BQ+9O7ujdW1VdVNESlGhsNsFCxr1ya+nzULZs+O/97TAw88YI2wn9ImVR1YdwjIMajG2N+7u+3PU08lGnHHG29ri3v57rbcDA7aENJwNEwpAlddld1zam+HSy6BO+6w70dG/D1x98hkS3TuauHC/L3/OqcQ1Y0Aa4FnjDH/z7XrLmAR8L3o650F9bDKcMe+vR69Ewf3xs8XTF9A7+5elv1mGUPhIba9to3l85YntOWQKh+OU2Uql+pQ7hHEur51hBbpgqmiUUisNRtPs7c3bsAcOjrgppsSlTeplDbZxM69Hn0waL9chl3zSIGAPWdhVLXltBkMxj19P2O/36bnRgRGjYqfn82zuffe+PumpuQ4vHdk4nDLLcnev66SBQrz6OcBnwO2iYgjAfk7rIG/TUQWA7uATxXWxcrht3LWG/sGYvnoQztDbHttG/0H+1k+bzl9e/tYMH0BS+csZeXGlUkqmBXnriC0KET31m72vbuPCWMmANC1uSs20XvmpDPpOLEj1la2q313vbUr4QtkODxctJWxWke2QLKJHXd3x+PiAOedZ48bGIh7347yBpK9Wfc1nFj3j35kvxx6emDmTBg7NjFGv2uXDf+4Of10e71Vq2DChPj1IxEbVnrxxfioAqxRH3AtAhw3zqpeUunmu7sT+x8K2T47nHxy/Bivtt77BZNLHL6eVttmgzGm4j9z5swx1cajux41h33nMBP8VtAc9p3DzKO7Hs14bKAzYOjEBL4VSDon2/a8x3Vt6sq5H8FvBU3r9a2m+dvNhk4MnZiW61vSnpstuTwXJQWPPmrMYYcZEwza10cfTd7f0mKMNZ/GNDcb09QUf+9sa21N30Zra/z4lhZjuroyX9d9TjCYeM1AIPH98uW2Tfc2749IdvfY2mq3Oc/Ge62Wlngb3n562yj0+dcQwCaThY2tm5WxxSa0MxRb+DQ4MpjgDTsebdvoNvoP9se8Z2eRVMTEz3Ha6pjakZUKxjtiyCVfjftYIrBk9pLYvmLF6DV/jg/5eIduTxys1+uOpbtVLrNmWfWKm2nT4Jln4t69nyd7xhnwhF29TThsPXnHyz90CD77WZg/37bvKHBuvNH25a23bNsHXDJfrwd9++1w4YW2j6lEHcbYa3V3J6p9du1KDBENDVnFTWdnXH1zfzz8yfBw/B7b223Mv6srft0zz7SjlWyef7oRVZ16+mroU9A2ui1uuInQNtrmDnFUN86XgFNVKhgIEglH4kVIiHBg8EDSitwV52bWOXv1/dnq4f3y8xTbCKs+30Ouyg7v8bNmWRmi+3y3Zt4Ya3SeeioxlLNjR9zIeePY7hg2xOPsCxbYGLYTGnnpJfjxj+PHNDXZ646kzpaawAsv2DayUe7dfHM85OPMDQSD8WsZk6idX7Ag0dC7tftgvyDXr0+cr8jWMKdaoVrHKp2GMfS5xpXdGSoDEmDL3i2s3LjS13sfiYywZPYSXnzzRR548YFYEZLQH1N7v9n2x+3hO/MAzvZ0x5Yqft6w+vxUnl6meLv3vFWrrIcL9ni3l+2sCD3ppLiXLGJj6Z//fNwoQ6J3fdZZ9vULX4B9+2DPnvhEpYht76yz7LWOOQb2+iThi0SS5ZoO48dbg/ymJ5OJMclfCo4B9eKOuztqn8sus3H/Rx6B7dvj253Vru6Rwuc/H79HsIbeUdQ4SqBt2+Ijk3QG2lHjOLF/h1z/lvmg2StLRz552TumdtAabGUoPERToIl1fesIR8I0BZoISCBBGdMUaIrlkgm9ZI27wbBl3xaCgSBESPB+c+2Psy+bc/JZ7Zsr5bhGVZHO00uXv8Qvw6QjGwRryJwcNe4VocFg3MAZYw2ZNxul2yA/8gice26iMXXaNwaef97+pEMkrtN3G+9g0IZvhlOs6PZ+MfgZeacdd/+Mseqam26yahn3cR0d1mi72z7ySDj//PgoZd26uMH0rg1obc3OG3dGBM6q4lz+lvl4+xUcMRSS66ZmyCfvizsXzlUzryIcCRM2YUYiI8yaMCvh2KtmXhUzflfPvDqW3yZiIlw98+qkfDq59GfN5jVc9NOL+PqDX0+qdqWUCT9Pz82iRVZn7v3H9Z53++2J582ebRc4bdhgY90Q96zFfoYIBKy6xq2pd/a58TPyJ5/sf6wfJ58Mn/qU7dO0adaLP+88e1/ZhnL8GD0apk61uXi8DA3BV74SN97uVbf9/fG+i9jsnO4vESdmn2ptgPdv5CWV954qF02mz0A2FKONPGkIjz7fuLJjvHt397J+6/r4+Sd2xFIUQ2LFqYVnLEw41i9Onm1/vCtsHdzVrpQykG1M16sV9573iU/Y0I3D4sX2tb3dyh29MWljbNz8Jz9JNLaBQLJh99LcbMM1mTx5B6/XL2IngK+80vYhlUefiYMHYefO1PvffTf+uzF2zgLsCMY9qpk5084vOP1wRjozZiSvDcgmM2Sqv2kq3X0xMk9WMHtlQxj6QuPKfkoYd/y+/2B/Qszd71pO7htHV79h4YbYqlUHb9zeu8IWkqtdKWUg1QrLUCh9VSe/804+2cbKFyxITFfQl5iNlGnT4HOfs6oZd7gHYM4ca4RTTYKOG2c9ce8IIhccNU9/v/1Ccs8PlBJndW9/f2J+/bFjk/uxYoWN3btj9f398Zg9ZM7imW28vL09vgZhgU1gmKCUyoZKrtTNRoNZ6p9q1NGnI1ete9emrpienU5M16aurNrwniedotr1asKrIe/qKl5bzc12m1tr7vxceWV67bpbw57NcZn075m08sX6aW5O1Mp7te6p+rF8efw5lkoj7263pSX9GoYyguroS0c6rfvAyEBCtafe3b18/7ffTzh/7VNrGTtqbEyiORQeomd7j+/KWbC5cmZOnMnY1rGxkM0X7rbqA81hU0G8Xmeqqk6pcCswli6F++6Le+9OKmJvyEQEHn88vXbdwdl/+OHw3nu59e3kk22oqbMzcaVrJrK91hFH2PDSoUM2TDV7Nnzve3Ev1+39trXF8+/43fftt8MNN8SzaTqrd7PN6JkN7vi6W/paI1kx1dDniVd50hRoIhwOYzCs61sXU+Fc0H1BUl3YLfu22KRoRAgQoCXYwoLpC9i4a2NS3H7pnKUJ2Sp7d/fSsb4jlt7glr5beGjRQ2rsK0FHh1V45BNz9VNgLF8O//mf8VwyW7YkGjXHyL3wgn11tO8i9gvBL+cM2Dh5rpx0UuJ8QrZk+4XyzjuJ7/0Kg7iVTanUPGC/kJzn6Rh5SF87N1fc8fVgMJ4qusyx9nxRQ+8hk749Vf6bq2ZeFctRE46EY/lm3CUHTxl3Ch889oPcuePO2MKquZPm0nFiB2ufWsuHJ32Y6eOnx74kVm5cGVt9616FOxyOe3luBU7DadsrTSExVz8FxooV8fZ27bKLjMAalcsuswbbydUeCMDcuTa3zOuvw2mnWW/63/89rmJxyOT5++GeGAbeAs4BHgWOyr21zLhXvrpxKlO5OfpoOOUUmzjtrLPg7bftorPBwcR7zSajZ6btDt6/NdTUClo19C4y6dvT7feqbdpGt/EPoX9IaP8T0z8BgNkR/zA+uefJBAXPoy8/yqyJs1j2m2Wx0I4gGAwBAgQDwYTKVk2BJtpGt+W8TkApEvlmR8yk+ujtTVz5uXy53e9kq2xqgs2b4+qbZ56xoZB81TEZuAfYDtwLfLYkVyDZ+3YqW3nZv99OUi9fDj/4QeIXmzPqcfT02Wjhs9W3e//WNWDgHdTQu/Dq21f9dhUHhw/GlDKZ8rxcdMpFPLb7MQbCA6z875WMRBL1x7c9fRuvv/d6wja30QZbRWrtU2sZDMcLjLvTKkQ8w/P2E9pZ+9Ta2MhhcGSQzlAnnR2dauxLSS4rHP2O9fMQHRUH2O2rVydWgeruhg9/2IYnRo2yC6XclMDIX4HNO+6Y0oXAEuDPgX8r9sXWro3r7Z1RTbp7+vGPk0cvH/6wVef4rZBNpZ3PtCK2DlBD78KtbxcR7thhJ8ac3PKp9O/e3O8ABwaSa77uPLAz/mYA+AnweWBU4nGb924mYlLEWz08sivxnz1ChAdefICNuzaqZ18qclnhmO5Yt/fuzvPujv861Zzcq0LLyLeBPmAnMAI0A+8Dri/FxZ54Aj7yEXv/4XB8ojsVb7+dvG3rVvtlkYsWvoL69nKhhj6KE3tfffFqtuzdwt3P3s3L77wc2/+1B7/Gh479ECeOPZFT205l+bzlsbKB3/ivbyQYeTejgqMYCPuoFp4F3gCeAzyLBv0Kj+SCwXBo5BDLfrOM1RevznquQfPMZ0kuHmCq1ZBuD7+7OzHPO9jfBwbsIqxJkypi5AFOwRr7zwKHYz37bwEnOwdkMsa54vbg3YvCAgG7eviPf4Tnnkt//rJlVsXjztHvjKpWr04u6FJJfXuZct8UXDO2GFS6ZqxfHdhUhtuh69IuAN+Vq2n5d2AHEAYi2CQUQeA04JM5dz0jLcGWpMpSfnMNkF0uHYXCPPrVqxOzVa5eDV/6UtyQNzVZr35oKL9J1FxpacmYsfLTwP3AN7Ge/EXAL0vfszhOvP266/yVQO4EcO5n5tSbhfQjpkqFaYqQ+6YsNWOrhWw8UfcxgK3q9N4+MLDnnT2xic9wpqXlUf7qnr/Kz/M+H9gHHCBu6McCf5p7U9kwFB7i07/6NCeNO4np46cza+Iserb3JGj4HdVOqvz7iodU2Q/THet4bV4Pv6cn0chOm2a/CL7//eT0BSLw/vdnTiuQLcceaydAW1vh979Paez/FrgJOA74C2B34VfOHhGrLpo92z83jAh89KN2teratfH8+xAfQe3aFR8xuf+/i6mzz4cyzg3UvKHPJhOk+5imQFMsOVkh5B1eacMa+x5swDMMdABHF9SdtLz8zsu8/M7LsXi+W8XjzDVse22bb/59JQ3e7Ifpltu797njwQsWJJbPe+YZ67kuW5bovTq1Vy+9ND99ux+vvWZ/MvBh1+/HRX/KRiBg4+6bN9vfvftaW+0iKbDHuWlpsV9knZ3+o6Ni6uzzoYxzAzVv6LOpeNS9tZuBkQEMJqE4SMV4GmvkPwI8HH3/gfJd3smXP3fSXEY1jWLZb5Yx6YhJSfl7lDRk8sZSxV791DYzZyZ6osPDNrdLV1difde2Nuvpe5k+3RqKN96w/fHLN+/Q1AQnnGA93H378r17yxFHJC98KoSpU5NHKhMnwiuvxOcvpk61z6ejw15/3z77xbdnT2J8/4QT4IorkkdMbkTs/lSTtw6Z4uj5xtnLODdQ8zH6bLTv7pWkTYGmgr35gnkFu+pkDPAudjXK8eXvRoBAzIsHaA40EzERjdFnQ7r4araxV7/VnGCN8SOPJH9xZHPsRRclLXbKmqam7FMSNzUlh0IKobUVvvzl7Ecr7hXBbpzJYW/c3vvqTl2RLn99pr9lhatSNUyMPlNmytDOEOGI/TAKwnGHH8cr77xSia7GcRv1MdGfCuA28gCzJszi8tMvV9VNNqTyxpx8K05Wy3Q1SZ1RgdfZcqopubMjupU5InD88TZ2PX9+YnUl98gA7OTjCSfYGrAHkiW/ABx2mPVqR42yC7LSOX8TJtjsmCK2KlS+jBljVTT799v7crTv2ZLqC2nMGCu7dO7BMeoXXmjDZE52y56e+CrjdPHxTCO3GtHg17yhh/QVjxztuzPRWHEjX8Usnr04Ia+OkgFv7N1dq9UvN7qfAsebS7211eZk9x63dm2i8frmN61xdl/PL+FXOGzrunrj224OHUqf9tjNa68VHvIBm4f+17+OjyK2bbP3mWp1r1fGmcqj92rr3XF8999qxoz4KuN08fFMcfQa0eDXhaFPR/vkdlZfvJrv//b7vPDmC5WPz1chLYEWLlLRg/gAAAu5SURBVJl2CTOO9akCFEU19lngeHeO0b7wwvhE4cqVVv3h9v76++OjggMHbE56x+t015H9/veTDVp/f3J1pXSGOpPWPdsQbrp2Lr/cvt57b/okZA5OJkgnC6Q3971bUeN44o4G3inysmoVPPusbeOZZ5L7c+aZ/vHvbOPjmY6rpAY/B+re0Pfu7o3ljVEj789QZIg7dtzBPc/dw8emfYwJYyYkpD/Op+ZuxSl3EebeXmvIg0H7vqUlbuQd79zRyDv73X1zjnn44XixbxFrCF94IfFaTU32WrNmZVdtqlxs2GCzV3q/DAKBuKfu90UhEn8e27bFtxuTXKDFobfXhrPuu8+OCLwjluZmmwvH+7f3fi6y+WxkOi7ffEdlpO4NvaPKcZKDQXJ+GcUyHBmOpX1wpz/ORtlUVZR7gsx9vaYmW93JWZW5cmXcOwe7b8qU5EpVzjHhcDyHjUhyOCYQsNtuvtleq1qMPKRW4Hz1q9a7DoXg6afh5z9PHoV84hPxvDOZcvynSknsnnBdvNjfyFdw4rSSpAnc1Qa9u3tZuXElvbt7fbcfGDyAiMQyPyrZ4V5I5cxzBCWYU83dipEq7UA5rjcyYg05WCPf1maNSjAYryu7YkWigXHivN5C3s5EonfbyEj83oqZfiAXgjn8LzkTlCtWwAc+4F+w/IEHrGLowAEbUw8Gk7NPuttzT2I7I4LmZnveqFF2tLNyZWKe+1DIhsKckJjzuejtTT62zqhpjz5VSMHZ7k7z2xRo4q/b/5qbHr8ppqlXUuM26IXW3C075Z4g816vrS15MtUvm6KDe6WtuxB4c3OyJNDZFg7HJY4jI/aYefOspv7II5MXWzlhoGLgTIRmO5rYssUa0fb2+LM6dCjxmNdes7LQ+++3IZexY1M/L/fzDgbh6qvjMftQyD5/d5oJx3Nva4s/A2exVIN4+TVt6FOFFNzhGrChmoiJ8PbA2yw6Y1FSwjLFct6U85g+fjqQXKIwnbKp6ij3BFmmNAf9/dabzdRGe7s1WO7UCjffnCgRdOL+7gVXfvf57LPxsoROdVUvTtHt/fvj2w47LFmrD/H0C+edF++XH44BdhOJxL16p8i2X4oHh74+W2krFemkrWC/WPwkj97Sj1u2WJmlnxS23HM8JaamF0xl69EHJEBzoDlW/SkgAYYjpSnQUMu0Blu1LGExKJaXWEg7XqmngzMh7CT18iYKW74cbrop7i0bE1f8tLTEwx1OvwKBREXQlVfCrbfG3zupG7xFPtyS0mAwsY2uLv8J2GzuN13iMu9cijMa8i6cct9flXv5DbFgKlVIwb3dXYLv5qdujuWomX7MdLa/UcCCjxolKEFObTuVyUdO5sU3X2RM6xi27tuKwTASGan+idZaINcRhaMgARtbdsI827bBiSdag7RsWe4FTlavhuuvh5ddo9dzzrGl+B57LB4iclItOAqXyy+P92ffPrjzzrhR7Oy0P+7C3ffdZ1MQLF5szz/vPKv7HxUttDAwYO/FXeTDMa6nnWZTGUybZksiLlhgNe5f+IJdkOUspspk+N2jKPCf9HaHyB5+GP7wh+TRkncCvYoXQeVCSTx6EbkY+AE2Ae9PjDHfS3d8OdIUe73/1RevtrLL8CAREy/X1wgECNDa1KrpiauB3t7k4teBgP1xr/70S4vgbcc7L3Ddddnp2Zcvhxtu8G8rH883VbqGrq74Ii+/0YCz3/s8nH3pjH0uaSe87TsjlVxTWFQBFfPoRSQI/BD4KPAy8KSI3GWMqaj77Of9zzh2RszrX/vU2oTarfWMOz1xx9QOFp2xCEiOyytlIBRKXgwViSRPnI6MZF/gZGDAzglkY+QBbr890dB7veOPfxw2bbIjA3csG9KX5vM6kT091lg7o4E77khM2dDTE4+ve3HOTUW2oyi/53311ekTz1Wpkc+FUoRuzgSeN8a8CCAivwAuw9YWrijeCUXnfe/uXra+ujXNmfWFk57YW1R84RkLK921xqOjwyppsvHo06mHHCWK40W7J1jd7fopb5wFWt62HI/+nnsSjaO7L37qJm9fHBYssK/OpGxbW6KhnznTFvv2wzk3HdksXPI+79bWuGIn17ZqiFIY+uNJrE3wMnCW9yARWQosBZji6I4rRGhnKCGj5fTx0xnTPIZNezf51m49b8p5DIwMsOedPbz63qsJE7uHNx/OuFHjeHfoXd4dfjfrTJkBCSBGOLzlcA6NHMp5snjC4RO4/PTLmTVxFvc9dx973tnD4tmLAejZ3sPMiTMZ2zo2NmfRMbWj9hZC1SOOB5wqRr92rS0l6LfK09vOhg3WaLnVLCecYHPYO+22tSUW6BCx2na/tkIhuwK3qytx/1VXxfvi5/m6z3endvB65M57Z36gvz/xy23qVFscJZsYfbZ4n7e73GAdU/QYvYh8CrjIGPP56PvPAWcaY65LdU41lRL0ltZzlDsOXmVKuvQA3qLhTYEmBEkw4u54ufu8j/zrRxKOE4TmYDOCMBIZiZU8HImM5B1br8nUBkp61qyBa1zlLf1i27mWQnQXJvfGs4tJDcXGq4VsY/SlMPTtQKcx5qLo+xUAxpiVqc6ptKGH9MWy20a3sWWvTabkF8dOl/Crd3cv3Vu7Y+cCsfezJs6Kedd+56367Sr2vLOHjhM7GNs6NraAyV0SsdBFTJqsrA5ZsyZRReNHLjpxtyqo1B5wnenXS00lDX0T8CxwAbbExpPAFcaYp1OdUw2GXlEUpdaomOrGGDMiIl8E/hMrr1yXzsgriqIopaUkC6aMMfcC95aibUVRFCU3aj57paIoipIeNfSKoih1jhp6RVGUOkcNvaIoSp2jhl5RFKXOqYp89CLyOvBSpftRAY4B3qh0J6oAfQ4WfQ4WfQ5xMj2L9xljxmdqpCoMfaMiIpuyWexQ7+hzsOhzsOhziFOsZ6GhG0VRlDpHDb2iKEqdo4a+sqypdAeqBH0OFn0OFn0OcYryLDRGryiKUueoR68oilLnqKFXFEWpc9TQlwkR2Ski20SkT0Q2RbcdLSIPiMhz0ddxle5nKRCRdSLymoj83rXN997FcqOIPC8ivxOR2ZXreXFJ8Rw6ReSV6OeiT0Quce1bEX0OO0Tkosr0uviIyGQReUhEnhGRp0Xky9HtDfWZSPMciv+ZMMboTxl+gJ3AMZ5tq4CvR3//OnBDpftZons/D5gN/D7TvQOXAPcBApwNPF7p/pf4OXQCX/U5djqwFWgFTgReAIKVvociPYeJwOzo70dgCxVNb7TPRJrnUPTPhHr0leUyYH309/XA5RXsS8kwxjwC7PdsTnXvlwHdxvIYMFZEJpanp6UlxXNIxWXAL4wxg8aYPwLPA2eWrHNlxBiz1xjzVPT3d4BngONpsM9EmueQirw/E2roy4cB7heRzSLiFPI8zhizF+wfHTi2Yr0rP6nu/Xhgt+u4l0n/4a8HvhgNSaxzhe8a4jmIyFRgFvA4DfyZ8DwHKPJnQg19+ZhnjJkNzAf+l4icV+kOVSnis62eNcA/Ak4GZgJ7gf8b3V73z0FExgA9wDJjzNvpDvXZVjfPwuc5FP0zoYa+TBhj9kRfXwP+AzvketUZgkZfX6tcD8tOqnt/GZjsOu4EYE+Z+1Y2jDGvGmPCxpgIcDPxoXhdPwcRacYat1uNMbdHNzfcZ8LvOZTiM6GGvgyIyOEicoTzO/BnwO+Bu4BF0cMWAXdWpocVIdW93wUsjCotzgbecobz9Ygn1vw/sJ8LsM/hMyLSKiInAtOAJ8rdv1IgIgKsBZ4xxvw/166G+kykeg4l+UxUeua5EX6Ak7Cz5VuBp4G/j25vAzYAz0Vfj650X0t0/z/HDkGHsV7J4lT3jh2e/hCrKNgGzK10/0v8HH4avc/fRf+RJ7qO//voc9gBzK90/4v4HP4EG3L4HdAX/bmk0T4TaZ5D0T8TmgJBURSlztHQjaIoSp2jhl5RFKXOUUOvKIpS56ihVxRFqXPU0CuKotQ5augVRVHqHDX0iqIodc7/B33k1z27RQcNAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114363278>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11446d550>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1145f24a8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1144fd748>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114747f28>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114813278>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for k in range(1,9):\n",
" k_means = KMeans(n_clusters=k).fit(data)\n",
" visualize_k_means(data, k_means)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Determine the optimal number of clusters"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the best number of clusters? "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Within-Cluster Sum of Squares:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1f013550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Ks = range(1, 10)\n",
"inertia = []\n",
"for k in Ks:\n",
" k_means = KMeans(n_clusters=k, random_state=0).fit(data)\n",
" inertia.append(k_means.inertia_)\n",
"plt.bar(Ks, inertia)\n",
"plt.title('Within-Cluster Sum of Squares')\n",
"plt.xlabel('Cluster Count k')\n",
"plt.ylabel('Error')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Percentage of Variance Explained"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1f122e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.spatial.distance import cdist, pdist\n",
"\n",
"ks = range(1,10) # Range of cluster count k \n",
"\n",
"# Fit the kmeans model for each n_clusters = k\n",
"k_means_var = [KMeans(n_clusters=k).fit(data) for k in ks]\n",
"\n",
"# Pull out the cluster centers for each model\n",
"centroids = [X.cluster_centers_ for X in k_means_var]\n",
"\n",
"# Calculate the Euclidean distance from \n",
"# each point to each cluster center\n",
"k_euclid = [cdist(data, cent, 'euclidean') for cent in centroids]\n",
"dist = [np.min(ke,axis=1) for ke in k_euclid]\n",
"\n",
"# Total within-cluster sum of squares\n",
"wcss = [sum(d**2) for d in dist]\n",
"\n",
"# The total sum of squares\n",
"tss = sum(pdist(data)**2)/data.shape[0]\n",
"\n",
"# The between-cluster sum of squares\n",
"bss = tss - wcss\n",
"# This follows from the fact that tss = within-cluster sum of squares + between-cluster sum of squares.\n",
"\n",
"# elbow curve\n",
"plt.plot(ks, bss/tss*100, 'b*-')\n",
"plt.ylim((0,100))\n",
"plt.grid(True)\n",
"plt.xlabel('Cluster Count k')\n",
"plt.ylabel('Percentage of variance explained')\n",
"plt.title('Variance Explained vs. k')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Shilouette Score:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1e71f710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.metrics import silhouette_score\n",
"\n",
"s = []\n",
"ks = range(2,10)\n",
"for k in ks:\n",
" k_means = KMeans(n_clusters=k)\n",
" k_means.fit(data)\n",
" s.append(silhouette_score(data, k_means.labels_, metric='euclidean'))\n",
"\n",
"plt.plot(ks, s)\n",
"plt.ylabel(\"Silhouette Score\")\n",
"plt.xlabel(\"Cluster Count k\")\n",
"plt.title(\"Silhouette for K-means\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Hartigan Rule:\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def hartigan_K(data, threshold=12):\n",
" \"\"\"\n",
" 'list_of_tuples' is a list containing the points you want to cluster\n",
" 'threshold' optimizes goodness of fit values\n",
" Hartigan recommends setting threshold to 10, but Chiang & Mirkin confirm up to 12\n",
" returns integer, \"correct\" number of clusters\n",
" \"\"\" \n",
" inertia_list = np.zeros(len(data) + 1) # initializes for maximum possible clusters\n",
" num = 0 # counter\n",
" H_Rule = threshold + 1 # simply initializes above threshold to meet 'while' condition\n",
" \n",
" # NOTE: 'inertia' is equivalent to the sum of within-cluster distances to centroids\n",
" \n",
" while num < len(data) and H_Rule > threshold:\n",
" kmn = KMeans(n_clusters = num + 1)\n",
" kmn.fit(data)\n",
" inertia_list[num + 1] = kmn.inertia_\n",
" if num > 0:\n",
" H_Rule = ((float(inertia_list[num]) / inertia_list[num + 1]) - 1) * (len(data) - num - 1)\n",
" print('k={}, H={}'.format(num, H_Rule))\n",
" num += 1\n",
" \n",
" if H_Rule > threshold:\n",
" num += 1\n",
" # NOTE: if while-loop reaches the number of K-Means clusters equal to the length of list_of_tuples\n",
" # without hitting the threshold, then function returns trivial solution that there are N clusters\n",
" # (where N is the number of points under observation)\n",
" \n",
" return num - 1 "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"k=1, H=33006.98608114748\n",
"k=2, H=1303.7793604071974\n",
"k=3, H=1516.1728593448447\n",
"k=4, H=1381.735661629919\n",
"k=5, H=1733.4844033305608\n",
"k=6, H=662.1126967486157\n",
"k=7, H=350.75237466138384\n",
"k=8, H=617.1329342659591\n",
"k=9, H=421.1173631740277\n",
"k=10, H=406.5804351771144\n",
"k=11, H=416.8955261064009\n",
"k=12, H=362.84126685539223\n",
"k=13, H=268.0986265446576\n",
"k=14, H=376.79250950835444\n",
"k=15, H=248.9447268836972\n",
"k=16, H=226.38879767516693\n",
"k=17, H=185.65530642910906\n",
"k=18, H=191.8693177888545\n",
"k=19, H=145.59881362029617\n",
"k=20, H=210.95991507388356\n",
"k=21, H=161.5512299419221\n",
"k=22, H=195.21709743460372\n",
"k=23, H=156.42882039212276\n",
"k=24, H=125.93954025322607\n",
"k=25, H=167.8606728704937\n",
"k=26, H=119.8879408188638\n",
"k=27, H=223.48717969820447\n",
"k=28, H=65.44257204515195\n",
"k=29, H=162.37657240138034\n",
"k=30, H=170.8192731833724\n",
"k=31, H=65.35696340152566\n",
"k=32, H=195.77143090288106\n",
"k=33, H=29.43858884956867\n",
"k=34, H=139.71302113473672\n",
"k=35, H=98.40681862560261\n",
"k=36, H=111.88434490461884\n",
"k=37, H=92.54939400233751\n",
"k=38, H=155.5924843864272\n",
"k=39, H=78.23527913880022\n",
"k=40, H=95.09664615266315\n",
"k=41, H=62.88245645849113\n",
"k=42, H=105.62113726990547\n",
"k=43, H=119.27139183204469\n",
"k=44, H=100.56588807097297\n",
"k=45, H=102.48092233385731\n",
"k=46, H=78.36494108635938\n",
"k=47, H=58.310525120606286\n",
"k=48, H=115.59511991518754\n",
"k=49, H=30.153525751253508\n",
"k=50, H=93.8432475985359\n",
"k=51, H=60.0538323805475\n",
"k=52, H=77.017005051429\n",
"k=53, H=57.70526530638853\n",
"k=54, H=97.30799415088985\n",
"k=55, H=146.5339327759247\n",
"k=56, H=20.280811743746234\n",
"k=57, H=35.055323990746615\n",
"k=58, H=111.63760008594201\n",
"k=59, H=73.46186425913484\n",
"k=60, H=37.70109121330057\n",
"k=61, H=71.58763162108372\n",
"k=62, H=15.50552866656769\n",
"k=63, H=94.09957511683425\n",
"k=64, H=84.99243443931567\n",
"k=65, H=35.62311902363756\n",
"k=66, H=120.78559143956336\n",
"k=67, H=19.197115200930405\n",
"k=68, H=78.51716023633182\n",
"k=69, H=45.70217913713537\n",
"k=70, H=35.61189066066217\n",
"k=71, H=87.27002119997172\n",
"k=72, H=35.80918849022347\n",
"k=73, H=71.90047454836504\n",
"k=74, H=67.647449779252\n",
"k=75, H=23.31903490098106\n",
"k=76, H=78.11795047032751\n",
"k=77, H=-11.542781367279975\n"
]
}
],
"source": [
"k_h = hartigan_K(data, threshold=12)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"53"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k_h"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1fb18be0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k_means = KMeans(n_clusters=k_h, random_state=0).fit(data)\n",
"visualize_k_means(data, k_means)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.14.4"
}
},
"nbformat": 4,
"nbformat_minor": 4
}