ml-finance-python
python scripts for finance machine learning
git clone https://9o.is/git/ml-finance-python.git
06_gaussian_mixture_models.ipynb
(169677B)
1 {
2 "cells": [
3 {
4 "cell_type": "markdown",
5 "metadata": {},
6 "source": [
7 "# Gaussian Mixture Models"
8 ]
9 },
10 {
11 "cell_type": "markdown",
12 "metadata": {},
13 "source": [
14 "Gaussian mixture models (GMM) are a generative model that assumes the data has been generated by a mix of various multivariate normal distributions. The algorithm aims to estimate the mean & covariance matrices of these distributions.\n",
15 "\n",
16 "It generalizes the k-Means algorithm: it adds covariance among features so that clusters can be ellipsoids rather than spheres, while the centroids are represented by the means of each distribution. The GMM algorithm performs soft assignments because each point has a probability to be a member of any cluster. "
17 ]
18 },
19 {
20 "cell_type": "markdown",
21 "metadata": {},
22 "source": [
23 "## The Expectation-Maximization Algorithm"
24 ]
25 },
26 {
27 "cell_type": "markdown",
28 "metadata": {},
29 "source": [
30 "Expectation-Maximization Algorithm\n",
31 "\n",
32 "GMM uses the expectation-maximization algorithm to identify the components of the mixture of Gaussian distributions. The goal is to learn the probability distribution parameters from unlabeled data.\n",
33 "\n",
34 "The algorithm proceeds iteratively as follows:\n",
35 "1. Initialization: Assume random centroids (e.g. from K-Means)\n",
36 "2. Repeat until convergence (changes in assignments drop below threshold):\n",
37 " 1. Expectation Step: Soft assignment - compute probabilities for each point from each distribution\n",
38 " 2. Maximization Step: Adjust normal-distribution parameters to make data points most likely"
39 ]
40 },
41 {
42 "cell_type": "markdown",
43 "metadata": {},
44 "source": [
45 "## Imports & Settings"
46 ]
47 },
48 {
49 "cell_type": "code",
50 "execution_count": 1,
51 "metadata": {
52 "ExecuteTime": {
53 "end_time": "2018-12-27T18:38:53.521649Z",
54 "start_time": "2018-12-27T18:38:53.361419Z"
55 },
56 "slideshow": {
57 "slide_type": "skip"
58 }
59 },
60 "outputs": [],
61 "source": [
62 "%matplotlib inline\n",
63 "import warnings\n",
64 "import matplotlib.pyplot as plt\n",
65 "from matplotlib import cm\n",
66 "import pandas as pd\n",
67 "import numpy as np\n",
68 "from numpy import atleast_2d\n",
69 "from sklearn.decomposition import PCA\n",
70 "from sklearn.mixture import GaussianMixture\n",
71 "from sklearn.metrics import adjusted_mutual_info_score\n",
72 "from sklearn.preprocessing import StandardScaler\n",
73 "from sklearn.datasets import load_iris\n",
74 "from mpl_toolkits.mplot3d import Axes3D"
75 ]
76 },
77 {
78 "cell_type": "code",
79 "execution_count": 2,
80 "metadata": {
81 "ExecuteTime": {
82 "end_time": "2018-12-27T18:38:53.525434Z",
83 "start_time": "2018-12-27T18:38:53.523068Z"
84 }
85 },
86 "outputs": [],
87 "source": [
88 "cmap = cm.get_cmap('viridis')\n",
89 "pd.options.display.float_format = '{:,.2f}'.format\n",
90 "warnings.filterwarnings('ignore')"
91 ]
92 },
93 {
94 "cell_type": "markdown",
95 "metadata": {
96 "slideshow": {
97 "slide_type": "slide"
98 }
99 },
100 "source": [
101 "## Load Iris Data"
102 ]
103 },
104 {
105 "cell_type": "code",
106 "execution_count": 3,
107 "metadata": {
108 "ExecuteTime": {
109 "end_time": "2018-12-27T18:38:53.544225Z",
110 "start_time": "2018-12-27T18:38:53.526619Z"
111 },
112 "slideshow": {
113 "slide_type": "fragment"
114 }
115 },
116 "outputs": [
117 {
118 "data": {
119 "text/plain": [
120 "dict_keys(['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename'])"
121 ]
122 },
123 "execution_count": 3,
124 "metadata": {},
125 "output_type": "execute_result"
126 }
127 ],
128 "source": [
129 "iris = load_iris()\n",
130 "iris.keys()"
131 ]
132 },
133 {
134 "cell_type": "markdown",
135 "metadata": {
136 "slideshow": {
137 "slide_type": "slide"
138 }
139 },
140 "source": [
141 "## Create DataFrame"
142 ]
143 },
144 {
145 "cell_type": "code",
146 "execution_count": 4,
147 "metadata": {
148 "ExecuteTime": {
149 "end_time": "2018-12-27T18:38:53.554360Z",
150 "start_time": "2018-12-27T18:38:53.546058Z"
151 },
152 "slideshow": {
153 "slide_type": "fragment"
154 }
155 },
156 "outputs": [
157 {
158 "name": "stdout",
159 "output_type": "stream",
160 "text": [
161 "<class 'pandas.core.frame.DataFrame'>\n",
162 "RangeIndex: 150 entries, 0 to 149\n",
163 "Data columns (total 5 columns):\n",
164 "sepal length (cm) 150 non-null float64\n",
165 "sepal width (cm) 150 non-null float64\n",
166 "petal length (cm) 150 non-null float64\n",
167 "petal width (cm) 150 non-null float64\n",
168 "label 150 non-null int64\n",
169 "dtypes: float64(4), int64(1)\n",
170 "memory usage: 5.9 KB\n"
171 ]
172 }
173 ],
174 "source": [
175 "features = iris.feature_names\n",
176 "data = pd.DataFrame(data=np.column_stack([iris.data, iris.target]), \n",
177 " columns=features + ['label'])\n",
178 "data.label = data.label.astype(int)\n",
179 "data.info()"
180 ]
181 },
182 {
183 "cell_type": "markdown",
184 "metadata": {
185 "slideshow": {
186 "slide_type": "skip"
187 }
188 },
189 "source": [
190 "### Standardize Data"
191 ]
192 },
193 {
194 "cell_type": "code",
195 "execution_count": 5,
196 "metadata": {
197 "ExecuteTime": {
198 "end_time": "2018-12-27T18:38:53.562353Z",
199 "start_time": "2018-12-27T18:38:53.555821Z"
200 },
201 "slideshow": {
202 "slide_type": "skip"
203 }
204 },
205 "outputs": [],
206 "source": [
207 "scaler = StandardScaler()\n",
208 "features_standardized = scaler.fit_transform(data[features])\n",
209 "n = len(data)"
210 ]
211 },
212 {
213 "cell_type": "markdown",
214 "metadata": {
215 "slideshow": {
216 "slide_type": "skip"
217 }
218 },
219 "source": [
220 "### Reduce Dimensionality to visualize clusters"
221 ]
222 },
223 {
224 "cell_type": "code",
225 "execution_count": 6,
226 "metadata": {
227 "ExecuteTime": {
228 "end_time": "2018-12-27T18:38:53.608644Z",
229 "start_time": "2018-12-27T18:38:53.563296Z"
230 },
231 "slideshow": {
232 "slide_type": "skip"
233 }
234 },
235 "outputs": [],
236 "source": [
237 "pca = PCA(n_components=2)\n",
238 "features_2D = pca.fit_transform(features_standardized)"
239 ]
240 },
241 {
242 "cell_type": "code",
243 "execution_count": 7,
244 "metadata": {
245 "ExecuteTime": {
246 "end_time": "2018-12-27T18:38:53.724567Z",
247 "start_time": "2018-12-27T18:38:53.609689Z"
248 },
249 "hide_input": false,
250 "slideshow": {
251 "slide_type": "slide"
252 }
253 },
254 "outputs": [
255 {
256 "data": {
257 "image/png": 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yFs9cRnlpOR88/Bn+sgAiwsoFq+mwr0lSZzQeqoqWvgr+H8F7OJJ2BSJVfIa014Ju/kAUgvCKLefwj0WLHwErHcl6FHF3qv265T+hZe9CYAIQAA2gxQ8geWYuS7zV1CAMrepJVf2XiLwYo+u/hVOr+Z1a9mswUtJTGHDmoVVuK1pfzBU9b6as2EcoGEIi3UuqSvGGTfUZpmHsvPLPoeR5wAfBuahkI2lnbr+f9wiw0kEt0BCSdgUAaheiBVcB5RAWtOAypOmYGi+p/t/RwmudY7ayW3ZK1LuaVir7AETEo6rBbTb7Y3FxVR0bqbOwS/h5xB8Ub9hEoNz5caU1SUMsCztsc/HDZyU4OsPYMRqch5PXEuff0Nwq9xOrCeR9B8Gp4GqLuNs7G+yNlc8G4XW1XzMwhe3eXqw8JOuhHYzeqIuaZhkdKSIrgFUi8v02b9zfxzuwSnFcJiKTRGRSfn5+fV22TrLyMrBczo9UXELH/drx1C/38faCZzn8tIMTHJ1h7BhJPh5IrviSlJOq39dKR7yHbWkMAFztwdMNJA1IgdRza7+m9yDAG3mUAplPYDX7A9xd6voyjB1Q06DyY8CxqtoUeAUYLSIHRbbV2ywjVX1FVfuoap+mTZvW12Xr5PChB9NvsLMeQcPK/Il/M/ajceS1yklwZIax4ySpB5L7KZJ5B5L7EZJ0wI4dLxaS8w7S5Fkk522szFuiuOYBSParkHop0uQpJOUk7KLb0bX7YK87DA39XdeXY0ShpgYhSVVnA6jqJ8Ag4G0RGYyTAdXYhmVZHDr4wIo6ygFfgN9Gjk9wVIbhjGPNXreWufnrql0zUxXx7ImknoF49q7TdUU8iPdQJGn/KmLyoaVvYpe8gFbqXhLvgViZNyPJR0HgD/B9A9hgr0UL/1WnOOJFNbxDP8+GrqZB5aCItFDVNQCqOltEjgK+AmqfKrCb6rhfO8IhG4CkFA/7HrZPgiMyEklVeX/mdKauWc3Je+1N//YdEhLHrT+M4usFfwHK6V335Z4jBiQkjsp042UQnAaE0bKPoOloRDxb72OXstUAc3hRvcZYHVVFi26F8i/AyoHsNxFP4+/WqukO4TageeUnVHUF0B94NBYXF5EPgXFAFxFZISIXx+K8idSqUwseHfUvBpx1KMNuGcRVz12S6JCMBHpt6iQe+e0XRs6bw/998wVTVq+q9xiK/X4+nz8XXyiILxTi3ZnT8IdC9R7HdoITcQaQQ6AFEF6z/T6uFmzVQ63bzj5KkMA48H+Pc+eyHi2+K9ERxURNs4x+qOb5IiAmQ/6qWsUctsave7+96d6vbrfYxq7l92XL8EXefMO2zdQ1q+nVslW9xuB1ufBYFiHbuXNNcbvxuFz1GkOV3F0hNA+wgRRwNd9uF3G3RSUZtAxwgXvP+o5yK2pvRAsuh+BcoFKGgu0mYjZOdU1/bRhGFI7p1JkUt/O5y2VZHNS6zQ4dv7iwgKPffZP9XnqWZ8bXrT6V1+3mpRNPoVVGBm0yM3ntpMFYVaysr2+S8wakngcpw5DcTxDZfq2BWNlI9huQdDAkH4tkv5SASLfQTY9DcDYQwBlKdYOkIpm7xh1CtTWVGyJTU9lojL77ewGz1q3lHx07sX+Lljt07JCPPmDamtUozif7D4cMY7/mLeITqFEru+Cf4N/ceZIEaVch6Rci4q3xuESLRU1lwzBi4LjOe3Jc57p1dRSWl1dM6bNEKPI3kD703ZSkX4kGxjkPrCZI2hkNvjHYEVF1GYnIZTU9NgwjPm7rdzjJbjepHg975uRxYOv6K7Ck/nHYa/tir90fu2xE7fsH56O+r9Fw9AtINbQY9X2D7fscO/9o7PUnosHZOxN2XImnG9L0FyTnQyRvlLNKexcS7R3Cth2Oie+ATJDSolL+mryItl1akdc6t07nGPvJON66azjZLZpw69tX0WyPhr3gzkicozt15pfzL2F9WSl75ubhrqE6X6xp4dWgxc6D4gfQ5KMRq+pFllr+I1p4HYgLcEHel4ir5u4xDUxCN16E87m0bMvzBZcizeo2XlIfxMoEKzPRYcRFVA2Cqr5c0+PdxYbVBVzR8yYC5UHssM0j3/1rh2cTrV2az2PnP4ffF2DFgtXcd9qTPD8hJrN4jV1U07Q0mqalxfUa60pLcFsWOSmpW57UyjmFBDRQ7fFa9jZQHlmy6nUypKaeXeM1tWwE2yexA+wCVLUipbyTVi25yhTzRmzV+nFDRJqLyOsi8m3kcdddYb1ATQLlAWb9NpfVi9du9fwvH/1BaVEZZcU+ykv9jHjs8x0+9/qVG7Hczo9dbWXt0oadn8lIrGVFhXyz4C9WFhfH7RoPjv2Jw996jUPeeIV3pk/dsiHjZpwso15IORlx1TCY7e5MRQ4iscAVRap3dyecPEngvBUlgTg5j0QEtcuw15+Gru2Jrh+AVrVOwYipaO4Q3gLexCmnCfAXMAJ4PU4xJVR5mZ8rD7iV/BUbsEM2N791Ff2HOonpcltm43K7CPpDeLxumtehq2evPh1p3q4pa5fmY4eVoTdWnzDM2L3NWLuGMz/9CJcINsonQ89k77zYdi/ml5Xy7ozpBG1nTv1Dv/7Cufvtj4hgpZ2HJg8E9SPumqfLSsZNzqri0CxIGYJ4q04Rv9UxaRej4bVOeoqkw5xppZYX8ezn7OD7BELzARvCa9CSZ5Csh6s8l9qFoAHE1WyHXr+xtWgahDxV/UhEbgdQ1ZCIVF8zspGb9uMs8ldswLfJuZV9594RFQ3CYacdxJxx8/n5o3Hs2bsjFz604+vqNhfZmfbTbJo0y6JLH5MFxKjaiNkz8YW2LHgaOW8Otx/aP6bX8FgWlXtikrZZsCau6BogkRSkyY51fYp4UFcrCK8E33CwUpCMG6vZW3EWsG3PLhsBxQ84e6UMxcq6Z4fiMLaIZoSqVERyifQORjKeFsU1qgRq0iwTO+xM9LMsIbdSplLLsvi//1zIiJWv8OAXt5GWmVrdaVBV3rpnOGe2vZw7jn+YTQUlFdu8KV4OPL6XaQyMGnXMziY5sqgt2e2mY5Oty68Gw2H+2rCeovKqp6IGwmGeGvc7l345kjGLF1a5T5PkFO4+/Ei8LhfpSUk8M/CEeuurVw1ByX9wFnkFoPR11K5USCrlVHB3BNxgNUXSr6n6RMUPbzmH7xPTtbQTorlDuAH4AugkIr8DTYHT4hpVAu3dd0/OvWconz71FS3aN+XmN6+M+tii9cUkJXtISU/h61dGM+Lf/yMUCFG4rogXrn+LW9+6Ko6RG7ua83v0YkVxMb8tW8qA9h0Z2m3fim1lwSCDR7zPyk3O2MKbp5zKAa227tZ5/PdfeX/WdMpDIf5Yvozhp53Bvs22Tw9x1r49OGvfHvF9MVUSwAVszqtkgWx5SxIrHXI/d2Y6SUbV5TsBxAO6uZCPAp6q9zNqVWuDoKpTRKQ/0AXnf3B+FRXUGrTVi9aydM4K9j6wM02aZtW6/7CbT2HYzadEfX5V5T+XvcTod8cilnDhg2fyxh0fEAo4v+ihYJi1S6qvFvXrZ+N5/fb3ycrL4Ja3r6J15x1bzWrsmtyWxT39q85KOnrR36wsLqYs0qX0xB+/MeK0M7baZ/LqlZRXJLET5uavq7JBSBQRF5r1FBTfAmpD5v2IpGyzj4DU/DcrTf7jlN3UAGTcgrjqNh3ciKJBEJErgfc310YQkWwROVNVX4h7dDEw/efZ3HniI7jcFpbL4uWpj8d83v93b/7Id2/+hNpOV9Pbd48gHNySTdJyWZx5+6lVHrt+1UYePfcZAr4Aq/5ew72DH+fVmU9ttU8wEMSTZD71GFukJyVVrAayRMjyJm+3zyl778P8DesJ2TaWwMFt9qjnKGtnpRwNKVNr37EG4j0MaT5lq6mqRt1EM4ZwqaoWbn6gqgXApfELKbY+e/pr/GX+iqmiv3z8Z0zPv3rRWp676vWKxgAgKdmNN8WZgufxehh2yykccOz2BUIACtcWYVmb51sra5asY/ijI1kyeznFGzdxWY8bOSHlLP6v9y2UFpXGNHajcQiGty/CMqB9R07psjfJbjd75uRybxX1Dc7v0YtnB57ETYccyv/OOIe2WbXfHW+mwZnY6w7GXtMNe9NTtR+wEzQwFTv/GOz8Aaj/tzqfp3JjYPtGY6/rh73uSDQwORZhRkXLf8IuuAJ70zM0so4UILoxBEtERCO/kSLiwpmc3Ci06twCj9dD0B/E7XHRvF1eTM+/fP4q3EluAuXOf74I3P3xTaz8ezU/D/+DHkd05cw7qr47AOiw7x6069qGZfNWEvSHCPpDvHXXcN5/6FMGnHUYy+etRBWWzF7OZ898w7l3DY1p/EbDparc+8uPvD9zOulJSbxx8qkVqbNFhIcGHMNDA46p8RwDOnRkQIeOO37twpvA3uA8KH0LTT4hLgVgbDsIG8/FGRQGLfgnNJ+AyPZ3PNFSuwSKbsCptYCTrrrZxLjfPWhwltN1RTn4/0C1DMm8La7XjLVoGoRRwEci8hLOiM0VwHdxjSqGzr9vGBtWFTD3z7848ox+HDbkoNoP2gH7HLQnSV4PoZQwliUMueFE9j+yO/sf2Z0TLj261uNdbhf/+fUBZvwyh9dufY+/py1xnreV1YvWVnwyVFXCwV12tq9RhVn56/hkzmxsVYr9fm4Z/R0/nHdR/Vy88iplkfgVpil9hs2NgSPo1D7YiQbBGWCudEelpZHHce5OCs6tdI1yCNbfnUmsRNMg3ApcDvwfzqv9HngtnkHFUnKqlzvevzZu58/ITufl6U/w+8gJ5LXJ5aATe+/wOTxJHnof3YMZY+ew/K9V+MsCiMCQ609g5d+rKVhTSF7rXAZdPTAOr8BoqMK2vdVbWEirnocfFxl3YhddT9i2WerrQtvsvUmp/agdF5i+9WN3l2rzJUVLXE3R5GOdNNWqkHZB9TOUYinpwEjj6XZmPiWfHP9rxpiphxBnM3+dywOnP0l5mZ/LHjuXEy+v/hY/HArz0eP/Y/6khRx34QAOOrE34XCY4g0lZOVlYNVjYjMj8VSVa7/7mlELF+C2LF4+cRCH7hFFSogYyC8t5eQPX8CilI3+LI5s34kXToj9G5xdNhKK78aZeuqG3M+xPDu/PkdVITQXJAlxd97p80V93dAi8P8Ero5I8pH1dt3axKwegoj0A+4F2kX2F0BVdcc7JnczhflF3HXyo5QWOZkcX7juLQ455QByWmRXub/L7dpuNpLL5SK7WfSDgcauQ0R4ZuCJFPh8pHo8eN31V75kwcYNlIWS2RSwALvKWtCqIae2sCSDp08d++g3r0B2OYvP3K13MnKHiICna0zOtUPXdXeMLKZrnKL5DXsduB6YzFZFRI2arFuWz+U9b65oDADEEvxlAdYtX89fkxbSuWcHWrQ3uVeMmmWnVN1Z893ffzFy3lx6tmjJpb364IrhHWTXpk2xRHCJkORyVQxMq/rRorvAPwHE3pIeO/kUJOu+Hb9Q6fNAZDaOFkBgIngPi82LqIJqCC283vkU7+6EZL9h1i1UEk2DUKSq38Y9kl2AqvL1K6OZ9tNsPF435aVbBuYsSzjs1APxlZZzXb9/IZZgh22e+Ok+k8LC2GETVq7ghu+/pTwU4rdlSwjZYa7qe3DMzt8kOYUvzzyXkfPm0CwtndP26QaAlrwE5d8C/q3GbfF9hGbeu+N3CVZLJ5cRNmgYrDjXBin/EvxjgQCEFqAljyNZJv38ZtE0CD+JyOPAZ2yex4WzgjluUTVSX7/6Ay/f+A7lZX7cSW4ksr7A43Vz1NmHc8OrV/Dabe/hK9kyY+O718eYBsHYYbPz12FHxv98oRATVq6M+TXaZGZx9baNTHg5ld4GIsTp7qlDl5E0eQItvMFpFNIuRzw7Vl9kh2kZW5LkhaBy7iQjqgbhwMi/lQckFKh6Tf1ubObYOZSXOX8soUCI7oftzcbVhexz4J5c+cxFiAitOrXAm+rFX+bHm5JE6z1Nmgpjx/VruweuSl06J+0V+zUCVZHUc1H/aMDlfKJ3tQArC8l8qG7nc7VAcj+IbZA1ST4JSt8Eez1gIelX19+1G4Fochk1nKHyBsbv8zPjlznktsqh437tOHTwgfz22QQC5QHcSW4ufvjs7So9CuaOAAAgAElEQVSqHXfxAJbPX8X4ryfT8x/7Mfia4xMUvdGY7ZWbxyenn8XPSxbRNa8Z/dt3qJfrSlIPyPsWQn+Be99G1/8uVqYTf3gZWC0QK76V6BqbqKYtiMgJQDe2lDdCVe+PV1CNQaA8wD/7RArphG0u/fc5HH7awViRnEmWJUz/efZ2DYLL5eKKJ8/niifPT1Dkxq5in7ym7BPjgjnREFcrcLWq9+vGiognUq3N2FY0JTRfAoYBV+NMOR2KMwV1tzb7j/kVhXT8ZQFG/Pt/zPptHpY4g8WB8iBj3v91p6/j9/n56In/8fod77NumSm3aRhG/ERzh3CIqu4nIjNU9T4ReRJngHm3kr9iA0nJHrLyMgHIa52DHXIGpyxLaN6uKe27tyUcdmbmJiV72Lvvzi+IeeD0p5g6ZiahYJhvX/+Rdxc9T0raTizrN3YLGpiObnoYxItk3uvMjzeMWkQzcXlz5YkyEWmFM2m4fjosG4j/XP4S5+91NWe2vYKvXx0NQNsurbnmxUtp1akF3Q/bhzs+vI62XVpz38hbOPCEXpz8z+O49sWdTwo7/efZBMqD2GGbYHmQVX+balC7qulr1zB26RL8oVDtO1cStm3enj6Fe34cxbQ1q1EtRwsugOBUCIxHN5ruycZMVVHddmZXfETTIHwlIk2Ax4EpwBJgeCwuLiLHich8EflbRBpkWsC1S/P54d2xBMuDBP1BXrrhnYptx5x3BG8veJYnf7qPpm2cwbXeR/fgrDuHsGDKIh4+62nWLV+/U9fvdkgXPF5nCqvL46JVp4ZT4MSInWfGj+OsT0dw5TdfMPST4YTs6PMWjZj6CqfmnMude1/DH3NvYHnhUqhIvaxgr0PrMw+SETManI+uOwhd2wO74J+oxndtcDSzjB6IfPupiHwFJKvqTtdUjqTRfh44GlgBTBSRL1R1zs6eO5Y8XjeV0z0lJddcqKa0uIzbjn0A36ZyLEtY+fcaXptZ93zy93x2M5889SXF6zcx+JrjSUmPS4oxI8HemDYZX+TOYFHBRuavz6dblNXNjs57hTSP0wBc3GUKC4veh/TuEJ7n7OA9qn6Suxkxp8X3OSu4AQJ/OIvq4pgjqdoGQUQGqOqPIrJdMn8RQVV3dhyhL/C3qi6KnHM4cArQoBqEnBbZXPb4Obx6y3skpSTxrxHX17j/xtUFFcVybFt3uosnJS3Z1EDYBQTCYQTwuFxVbm+Rls4mv9/J7GMrealphGwbW5Wkao7ZLMW9ZUGYW5S9kj8D6YVkPQaSBEmHx+Q1aHA+WvKCs+4g43rEqjonlxFL297ZxfdOr6Y7hP7Aj8BJVWxTdn5guTWwvNLjFWxZBFdBRC4DLgPYY4/ElAAcdNXxDLoquvUCrTq1oEWHZqxZ7NRQPnxo7NIJGI3TG1Mn8+jvYxHgkaOO4dRIGojKXj5xEDeN/paCch+3HHIY41Ys47Yx32Orcushh3Fxr+oTVabmPEK48DosQoiAEIDgBPC+HfXq4bnr8/li3lw6ZGdzWtfuWNscp3YJuvFM0BLAjYbmIbkf7ciPwagDybwL3XieU+PB0wu8/eN7vZrSX4tzn3maqsb8f15EhgLHquolkcfnAn1Vtdqlg40l/bWvtJzfR04gNSOFg07qbdJW78ZKAgF6v/I8wciYgMdyMeef19SYiM5WpdsLT+OPzFjzWBYTL/0/Mquom1xxjF0E+UeDFgEucHfCyvsyqhiXFxUx8P23KQsFSXG7uXD/3tx0yKFb7aPB+ejGYZHUDwDJWC1mRHV+Y+eohpwiP5JZ56pv0aa/rvGdSp2RqKvqFEHtVgBtKz1uA2yfY7cRSklL5h/nHM4hpxxgGoPd3PYfuKKrP2Jvs1ttZUssKwvJ/RiSB0HK6Uj2W1HHOG3taja/z/hCIcYsXrj9Tu4OIE1wquemgPeIqM9v7BwRN2Jlxb0EKEQ3y2i0iNwkIm1FJGfzVwyuPRHYU0Q6iEgScAbwRQzOaxgNRobXy40HH4rbsvBYFvcf8Y+t7g5+W7aUi7/4jAfG/oQv6AwMWyI8cORReCwLt2Vx7YGHkJVc+9oTcbfDavJvrKx7dyilRPdmzSsS5SW73fRru/26U5EkJO8zJOMmJPNupEndJ0oYDVetFdNEZHEVT8ekQI6IHA/8F3ABb6hqjRmyGkuXkbFrUFXemDaFHxb9Tf92Hbis9wHb9a1XxR8Ksba0hJbpGRWDyL5gEEtkqyI3iwsLOOGDdygPhfC6XBzXeS/+c+yWsarlRUV8OmcW2akpnNFtv7gWyJm6ehUfzZlF55wczu/RC3ec7mxVFfyjnOym3mPA3ujMpBELybwfSUBRm91BzCqmqWrcFqGp6jfAN/E6f6J8/epoPn/2W9p1bcP1L19OWpZJoNUYvT19Ko//8SuBcJgZa9eQ6fVy1r49ajxmWVEhp370Ab5gkJyUVD4fdja5qamkeLafrrxgw/qKN15/OMz0tasBZ6FZaSDA6Z8MZ0NZGS5LGLt0Ca+fvN2Ev6h8s2A+H8yaQde8Ztx4cL8qG5aeLVvRs2X88xNp6XNQ+pqzTmLT8yDq9I+Ds4Cu2YR66RoxqhZtcrvuQFe2Tm73TvVH7L7m/PkXL17/Fv6yACv+Wo3L7eL2965NdFjGDpq2ZjUP/foz4Uo1B2bnr631uBcnTaDQ58MG1paWMGL2TP55wHaT5wDo1bJ1Rfpql1gM6rIPvy1byuVffY4/HMYCQqqEwvD78mV1fh03j/4OXyjE5FWrCNph7umfwMz1vq+cGTOAUxSn0gpc3QQEAG8CAjMguprK9wBH4DQI3wADgd8A0yBUYc2itRUDyaFAiGVzY1+4xIi/N6dNqWgMANyWxUl77VPrcakeDy7LwrZtXCJV3hlslpeaytdnncd3fy+gTWYmR3fszCFvvFKxQG3zjHOPZbFvlIvUtjV/w5aV8v5wiBlrE5z6xNMTwqtwiuwoeA6AUGS2kvcIRExjkEjR3CGcBvQApqrqhSLSHHgtvmE1Xr2P6YE31QsCdlgZcsOJiQ7JqIM2GZl4XS784TAey+LKAw7koDZbJsWt2lTMnT+OpsDn48ZDDuWwPdoDcHXfg5i4cgVz1+fTu2Vrzuy+b43XaZWRyUU9e1c81kqzkLwuF0e270jbzCyu7Fv1XUZtDm3bDpdl4XW5OLjZCm7rswi7LAVJGZSQrhnJug+18iC8CEk9D5IOgMA4QCDJrNlJtGgGlSeoal8RmQwcCWwCZqnq9qtr4qyxDCoXb9jE1B9n0bpzCzr33K3yAO4yfMEgt/wwiimrV3FMp87cdfiRWw0on/DBO8xfvx4bJcXt5pcLLiUvNXWnr/vzksX88+svCKnNsG77cv8RR+30G/fyoiJmrvyOo7MfxCV+nGmjx4K9Ajz7Ihk34kz0M3ZVMRtUBiZFktu9CkwGSoAJOxlfozb959m8euu7pDVJ47qXLqNlh+Z89szXvHvvx2TkpnPvpzfT36xQbtRSPB6eHVj93d3y4iLsyKd5EWFtyaaYNAhHtO/AtCuuIhAOk54UmzfptllZtHGXoJs2J0bzgf8LwIbgTBRBMhtkbkmjntU6t0xV/6mqhar6Ek4iuvNV9cL4h9YwrV+1kTtPeJj5ExcybcxM/nXiI6xYsJrXb/+AksJSVi9cy4PDzBztXd0Z3fYlxeUm2e2mdXoGe+bmxezcSS5XzBqDCp4+bPn852HLn74fgrNiey2j0aq2QRCROSJyp4hU1JpT1SWqutuuV18yezkXd70Ovy8AOEnI1i7Jp7SoDMvacltfUliaqBCNenJ0x87YOGkmFHYoXXVNwjE6z7YkqQeS8zqkXggZt+KsOE4GUiDFJE80HDV1GZ2Js3r4exFZD3wIfKSqu0R6ibp4664P8W3yVTx2e90cd9EAOvdsT9eDuzBn3HzssM3Fj5ydwCiNuijw+cgvK6Vjdk5Ui7KeHPc7/rAzG2hVySa+X7iAQXtXv6hKVbnn5zEMnz2TpqmpvHXKaeyZu2U1sS8Y5PzPP2Hy6lV0zM7hwyHDYtIFVZkkHYAkHeDE4z0SAr+DuzOSVGvX8javJQzqR6yt49PAVLT4budamQ8iSTWv2TAanmobBFWdDkwHbheRg3DqKv8pIn8DH6rqq/UUY4PhTfUiloWGbTxeN4OuPp5L/30OIsIj393JklnLychJryiW4yvx4fK4SfJ6WPn3aqb/PIfOPduzV29T4Lsh+WP5Mi79ciSC0D67CZ8MPZNkd811L7KSvU797MikjNq6eCauWsln8+YQsm3WlJRw25hRfHr6WRXbR8yeycx1a1FgaVEhz4z/g/uP/MdOv7bqiLstuM/Y4eM0MB0tuAi0DPUegzT5DyIWqqHI85FFZgUXQrOJOGVPjMYiqvXpqvqnql4PnAdkA8/FNaoECYfDvH3PCG488h6+fGnUdtsvefQcWndugVhC76N7cNFDZ1bMALEsi477tatoDF668W0G51zI4Ozz+d9z33FFz5t54bo3uaH/3Yz/Zkq9vi6jZv/+fSy+UIiyUJAlhYX8vGRJrcfc2/8o9szJJdnt5qS99mZAh5ob+fJQiM2digqUBYNbbQ/a4YoEdratBMLxrYxVG9s3CrvwFuyykVsl6NPiuyMLyMIQ+AUC4yMbyp2vih19Wy86MxqFaBamHYDTfTQEp3zmK8DH8Q0rMT558ks+fvIL/GUB/pq0kLzWuRx80pbb6aZtcnlj7tOoao1TAVf+vZovXxxFOBQmHArz/HVvVBTNAfj29TEceHyvuL4WI3qZ3q0/7Wd4ax/QbZmRwbdnR1+r+OA2bdm3WQumrlmNJXDX4VtXvRrWbV9GzJ7JyuJiMrxeru6buFlq6v8Zim4GyqF8FApI6uAajxErHU0+Fvw/O094B2zXpWQ0fDVVTHsYp5uoAKeGcj9VXVFfgSXC/IkL8Zc5A8aB8iCLZy7bqkHYrLZ54dumvK7cGCSlJJm1CQ3MI0cdw0VfjGRFcRGnd+3OIW1iX4jJ43Lx/qlDWbmpmCbJKdt1MWV6k/n+nAtZX1ZKTkpq3JLLRUMDU4DNn/Z9zsKxSIMgmfdXdBmR1B+StiyYk6ynIBhZJ+Q5oH6DNmKipjsEPzBQVf+qr2AS7dgLjmDCt1NQVSzL4uCTetd+UBVadmzOqdedwEePf4Ed3jJrREQ4+tzDOePWQbEK2YiBNplZfH/OBXG/jojQJjOr2u2WCM3S0nfqGqoBCEwGKw/x7Fmnc0hSP7T0LZxGIRm8R1Xa1gOaTQAtR6ytkzaKWJDUt+7BGwlX60rlhqQ+VirPHb+ABZMXsf+A7uyxd+ta91dVZv46l5LCUvocuz9J3i2DkYHyAP/9v1f49dPxCNC+e1v++9uDpmjOLsQfCjFp9UqapaZvNWsIYMzihcxbv54BHTqyT17TuMeiGkA3DIHwCtAwZNyKlVa3GW/qH48GfkeSeiNxLttoxF+0K5VNg7CTXrnlHb588Xvn01+XVjz758O4KhVFt22bSaOm4/cFOPCEXls1GJWtX7WRRdOX0rlne3JamOLljYE/FOLk4e+xalMxYVXuPvxIzui+HwAfzprBg2N/wh8O43W5+HzYOds1GLGmgYlowWUVM32wmmM1+7ViUNikld59xTJ1hVGDL1/8nvJSZzbF8nkrWT5vFe27bUmCZlkWfQf2rPEcC6cv4frD7sJyCWrDs+MfieruxEisSatXsmrTJkojM4aenzi+okH46q95W7KWqjJuxbK4NwhYec6dgfMAXM0ZPmsG9/3yIy7L4r/HHs8/OnaObwxGo1bTSuVeNX3VZ5ANWdO2eUhklbKqkt28+j5iX2k5n/33az5+4outVjN/9fJofCXllBb5KCvxMerNH+Met7HzmqWmE1ZnjMhCaJmeUbGtb+s2JEcK0VgidK9j+uodIe4OkHkPWK3B04PSlMe495cf8YfDlAWDXPvd11XUeDaMLWq6Q3gy8m8y0AdnkZoA+wHjgUPjG1rj8NBXt/PkJS+yaWMJlz52Lll5mdXue+s/7mfBtMWgyrevj+G12f/BsixatG9KUkoSAV8Ab0oSLdo3q8dXYNTVnrm53HX4kTw/8U9apWfy3+O2lL+86oCDSHZ7mL52NUP27kaveqhGBmClDoHUIQCEfL6tGoCg7aTjU983UPIMWC0g+zksa+cGsuNJ7RLQMsRl/ibqQzTpr4cDD6nqzMjj7sBNqnpB/MPbWkMcQ9hWOBRm9Du/UJhfzNHn9Se3pTMeEAwEOT75rK32/c+vD9C9394EA0Ge/r9XmfrjTPoe15Ornr0Yl9us8DR23qO/jeWt6c5CyFv7Hcb5XVNgY6VZblZrrGY/JSi6mtm+0VB0A6CQfDSS9ZQZB6mjmA0qi8g0Vd2/tufqQ2NoEP59wXP8+sk4QsEwGdnpvL3gWVIzUgA4rfnFFOUXV+zbf9gh/OvD6xMVqrGbyC8rxSVCTkoqdskrUPJEpa0WVot5CYutJva6w8COlC2VFCTnQ8RTfb4oo3rRNgjRzH+cKyKvicgRItJfRF4F5u58iLumP7+chL8sQDgYJlAeYMns5RXbht1yCpbb+ZG73C5S0pOrO43RQK3aVMxGXxkAy4oK+b+v/8flX33OooKNCY6sek1T08hJiawa9m69QhpXu/oPKFqVi/aobv3YiItoGoQLgdnAtcB1wJzIc0YVuvTphMcbGZpRaN25RcW2QVcPpM8xPbBcFnvs05qLHjwzQVEaO0pVuWX0dxz1zhsc8sYrjJg1g2GfjGD0ooX8sGghwz4ZHrfU1bFkefaE7NfBvT94B0LqBWjZx2jlPEQNhGQ9DpIFuCDtAsRtZkjFW1TrEEQkBdhDVefHP6TqNYYuo9LiMt69/2MK1hQy9KaT6by/SVOxK1haWMjAD96mPDKVNM3twRcOVeQ/8lgW4y+5gibJKYkMc4fYG87eUhzH0wXJGdEg++hryx1m1C5m6xBE5GTgcZyKGh1EZH/gflU9eefD3PWkZaZyxRPRJz0zGgev27XVjJ1kj4f9WrRg2po1qNqkeDwM+ehDTtunG1f06dvg38DULoPgFCCybiE4C7QEJKPG4xKhof8sdyXRdBndA/QFCgFUdRrQPo4xNVh2I+gSMOKjRXoGNx9yGF6XiybJyTw78ETePGUIDxx5FD1btqI0GGRxYQHPTRzPz0sXJzrc2kkKWLk4bwEWWE1A0mo7qloanOGku9DEpu02dk40K5VDqlq0O7fSwUCQewY9xqRR02nZqTmPj7mHZm1jV0PXaBwu6tmbi3punfDw1H26MXLe3Ir6BbYqK4qLqzq8QRERyPkA3fQEoEjGTU5yujqwix+HsvdABDw9IPst86m+kYrmN2CWiJwFuERkTxF5FvgjznE1KD9+8Bszf52LqrJm8Tpeu/W9RIdkNCAX9+xNsttNelISKW43R3dsHBXxxL0HdtZ/ue7PY+n+yucM+egDCny+2g/cVtnbgM9JiR2YCuHltR5iNEzRNAhXA91w0mF/CBTjzDaqMxEZKiKzRcQWkR0r6BpDvtJy/nXyowzOvYCHz36aUDBU5X6hQKiipoHaSsAfrHI/Y/d0RPsOfHnGOTxx9HGMPvdCWqQ3vH746nw+bw5jFi/EFwoxc91anvrz9x0/ibVNjiar+vQtRsNWa4OgqmWqeqeqHqCqfSLf7+wctVnAqcDYnTzPThnx6EimjJ5BSUEpf3w+gW9eHVPlfgPOOpTWe7UkKdlDRk4aF5rposY2OuXkckynPfl4zix6vfI8x7//NksLCxMdVq2K/X7CkcHykG1TUL7jdwiS/Qq4u4KrHZL9DGIahEYrmllGewE34QwkV+yvqgPqelFVnRs5d11PERMb1hQSCjif9oOBEIXrqv4DTklP4cXJj7FxdQFZTTPxJNVcgN1ovEoCARYWbKRDkyZkends4eCsdWt5dsI4fKEQReXl3DT6Wz4e2rA/PAzaex9enzqZYn85IsKVfQ6s/aBtiKcLkvd5HKIz6ls0g8ofAy8Br1ExR23XMOS6Exn78TgA3Elujruo+jbOsizyWsc5fbGREGHb5s+Vyyku93PHj98TVkUQRg47i47ZOVGfp6DchxX5kKPAhrKyOEUcOzkpqfx43kUsKiygdUYmmV5vokMyEijaWUYv7uiJReQHoEUVm+5U1f/twHkuAy4D2GOP2Na6bd+tLe8uep4V81fRrltb0jJNUfDdjapyyZefM3HVCgLhMKHI1GIB3pw6hQcG/CPqc/Vt1YYO2TksKtiIrcpNhzSOhMBet7teKroZDV80DcKXIvJPYCTOwDIAqlpj8hZVjf4vqebzvAK8As5K5Vics7LMnAy6HtylTscW5hexdkk+7bu3xZtiPlk1RvllpYxbsaxi2uhmHpeLvLToPyAEwmHclsWnQ89k7vp8mqam0TKj8QwuGwZE1yBsXnZ7c6XnFOgY+3Aaj9l/zOe2Yx/AsiwyctJ5ccpjZGQ33LzyRtUykry4xGJzb2iS5cLrdtG7ZWsu63VAVOd4evwfPDfhTzwuF88cd4KpSmY0WrU2CKoa82Q8IjIYeBZoCnwdSad9bKyvE0/v3v9xRenMcDjM2I/HccJlRyc4KmNHpXg8vH7yYO75eQxet5tHjzqGrk2jL8ayetMmXpo0gbAq4VCIm0d/x9TLr4pjxPGh9kbwjQRJh5TBiMksuluqtkEQkQGq+qOInFrVdlX9rK4XVdWROF1QjVZ28yxcHhfhYBgRIbOGSmlGw3ZQm7aMOueCOh3r1CCr9LgRlqhUDaDrB4O9HnCBfyyS/XyiwzISoKY7hP7Aj8BJVWxToM4Nwq7g8ifOY/WitSyZvZwjh/Wj36DouheMXUvrjEzO69GTN6dNwRLh4aOOSXRIOy68DLQICDpf/oQuDzISKKr01w1FY0h/beyeSgIBPJaF1x3NsFzDonYpmt8fdBPgBk9XrNyPEx2WEUMxS38dOdkJOOkrKlbqqOr9dQ/PMHYt6UmNt89drDTIHY6WvAiSiWRcm+iQjASJZqXyS0AqcCTO4rTTgAlxjsswGqTZ69aywefjwNZtGuXdQHXE3Rlp8mSiwzASLJrf6ENUdT8RmaGq94nIk+zm4wfG7umNqZN5ctxvWCK0zszif8POxut2o6pMWbOKEn+Ag9vuQZLLlehQDaNOomkQNme7KhORVsAGwNSFNHY7L0+eiC9SQnNlcRHT166hb+s2/Pv3X3l3xjQsgS65eYw47QxcVt1qCxhGIkXzW/uViDTBKaM5BVgCDI9nUIbRELXKyKj4gwmr0jzNWYj4zoyp+EJBSoNB5q7PZ3FhQeKCrERVGb9iOT8s+ht/qOrU7oZRWTQL0x6IfPupiHwFJKtqUXzDMoyG57njT+LGUd+yrrSEaw86hHZNmgDQPC2dZUWFKM587NyUhpET65HffuGDmTMQgY7ZOXx2+lnmzsWoUU0L06pckBbZtlML0wyjMWqdkcnw04Zt9/zrJw/m1h9GUez3c8eh/clOSUlAdNv7YOYMykJOeveFGzeysGAje+Wa0q9G9Wq6Q6hqQdpmu/3CNMPYrGN2ToOse9AyI4PFhQXYqtgoeakN487FaLiqbRBU9cL6DMQwjNh67aTB3D7me4r85dzW73ByGkhXltFwRbMOIRe4BzgU587gN+B+Vd0Q59gMw9gJ7Zo04YMhpyc6DKMRiWaEaTiQDwzBWZSWD4yIZ1CGUZNlRYWMmDWD6WvXJDoUw9ilRLMOIafSTCOAB0VkULwCMoyaLCrYyMnD30NVUYh5/QFVZcLKFRT7/Rzerj1etxtblRcm/skvS5cwoH1HrujTt8Z64GqXoMX3Q2ghpF2IlXJizOIzjHiKpkH4SUTOAD6KPD4N+Dp+IRlG9X5cvIhgOEwwUupy+KyZMW0QHv1tLO/PnI4ItG+SzchhZ/Px7Jm8OGkCvlCIOfnraJaezpB9ulV7Di2+G8pHAUEougN1d0Q8XWMWo2HESzRdRpcDH+CUz/TjdCHdICKbRKQ4nsEZxrY65+TitpzUEMluN92bRV/MJhrvz5pOWWSR2eKCAhYWbGROfn7FCmVfKMTc/PyaTxL6CyeVNCAuCC2JaYyxFAiHeX/mdF6YOJ51pSWJDsdIsFobBFXNUFVLVT2RLyvyXIaqmqowRr06on0Hbut3GL1atuKcfXtw5QEHxfT8rTIysSLdQTZK09RUTt57b5LdblIiXyfuVUsN7pSzgRScnJBe8MY2xli6ftTXPPTrz/x3/B+c+OG7+ILBRIdkJFCt9RBE5GJVfb3SYxfwL1W9L97BbcvUQzDibXlREbeP+Z5Cv49bDzmcw9q1B2De+nymrllN75atolrcpYEpTuGZpMMQV26co667fV98htJII5DuSeLDIafTrVnzBEdlxFos6yEcJSJDgIuBPOAN4JedjM8wGqS2WVm8d+rQ7Z7fO68pe+c1jfo8ktQL6BXDyOJjv+YtmLxqJSE7zJEtF9EhZRyqAxHxJjo0IwGiyWV0logMA2YCZcCZqvp73CMzDCPuXjrhFJ6d8CfHNn2JHk3mYJX9hPrfhdyPETF5j3Y3tf6Pi8iewLXApziZTs8VEbPk0TBqEQyHeX7in1zz7VeMW76syn3mrs9n1rq1JKqUbYbXy+2HHk7PJlOx8IGWOYPitlnjsTuKpsvoS+BKVR0jzuTrG4CJOCU1DcOoxqO/j+XDWTMoD4X4YfFCPh929lbjDw+M/Ynhs2YAMLDzXjxxzMCExCkiqNUK7FWADeIBKzshsRiJFc09YV9VHQOgjicBszDNMGoxfuUKyiPTVS35//buP8qK+rzj+Puzu/xYCMFQwSpI9RSMRsQQgZocisnRKCQWGxWDyUmsxlDaE0sSU21KqzHWpqm2JcbGFJRgLEXjMdFK/AGx/ohyiCgC8ktAg4LxCKiACIi7+/SP+V6y3HN3l73sMveyn9c5e5iZe2fu813uzjPznZnnK+4Q5oAAAAzxSURBVFZt2bzvtfcbG/npsufZ3dDA7oYGHli7hu179uQVKuo3G7qPgW6jUL/ZSJVRsdUOrRYTgqSrACJih6Tiq2wufGe5aMqpa6Uc44cMpb6uGzVkt7GOPGbgvtdqa2qor+u233zPHMdoVt1gavrdRs0fzEHdhucWh+WrxdtOJS2JiI8VT5eaP1R822nXtbexkSnz7ueJV37L4L5HMOf8iRzTp7Ifg4kIHly3lt9ue5txQ4YypN/+t58+89om/nbBwzQ2NfHPZ57N2HSLq1lH64jbTtXCdKl5s071wNo1/Oa1jQSwccd2/vXpXzN93GfzDqtVkvhsKw+xjR44iCf+4vJDGJFZ61q7hhAtTJeaN+tUexsb933pIoI9jR4j2KyjtZYQTpW0Q9I7wPA0XZg/5RDFZwbAhBNO5Li+R9Cjtpa+PXpy5elj8g7J7LDT2ohptZ31oZJuJBuicy/wEnBpRGzrrM+z6te7e3fmfeHLvLFzJ/3q6+mR4wVYs8NVXo8iLgCGRcRwYC3w7ZzisCpSI3F0nz5OBmadJJeEEBHzI6LQCbwIGJRHHHZ4eGjdi4ydPZNz597Jujc9sqtZuSqhWMllwEN5B2HVacu773Ll/IfZtGMHq7ZsZvK8+/IOyaxqddq5t6RfAX9Y4qVpEXF/es80oAGY08p2JgOTAQYPHtwJkVo1e2vP7v2Gs9y6a1eO0ZhVt05LCBFxVmuvS7oEOBc4M1qp7BURM4AZkD2Y1qFBWtUb8qF+DBswgFVbNtMUwZSRo/IOyaxq5XJ1TtI44GrgjIjwIZ2VrbamhjnnX8SS139Hn+7dOal/xw6padaV5HW7xi1AD2BBOt1fFBFTcorFqlxdTQ2jB/q+BLODlUtCiIgheXyumZm1rBLuMjIzswrghGBmZoATgpmZJU4IZmYGOCFUtD273mP71h15h2FmXYQTQoVaeP9iLjjyUiYN+ktu+sqPaOXZPTOzDuGEUKF+8Ncz2bvnfRr2NvD43QvZsOLVvEMys8OcE0KFquvWbDiKCGq7ueSzmXUuJ4QKddUdX6NXn3pqamv43NTPMPjEgXmHZGaHOR92VqhTzziZ+7bdQVNjE7V1nTZ4nZnZPj5DqGCSnAzM7JBxQjAzM8AJwczMEicEMzMDnBDMzCxxQjAzM8AJwbqoFZvfYM4Ly1j/1pt5h2JWMfwcgnU5T736CpPn3QeAgJ9dOImTBxyVb1BmFcBnCNbl/HzNSvY0NLCnoYHdDQ088tL6vEMyqwhOCNblDOt/FPV12clxfV0dJx55ZM4RmVUGdxlZl3PJqSN45733WLjpVc7546GMH3JC3iGZVQQnBOtyamtqmHr6J5jKJ/IOxayiuMvIzMwAJwQzM0ucEMzMDHBCMDOzxAnBzMwAJwQzM0ucEMzMDABFRN4xHDBJW4BXmi06EtiaUzgdye2oLG5HZXE7Dt4fRUT/tt5UVQmhmKRnI2Jk3nEcLLejsrgdlcXtOHTcZWRmZoATgpmZJdWeEGbkHUAHcTsqi9tRWdyOQ6SqryGYmVnHqfYzBDMz6yBOCGZmBhwGCUHS9ZKWS1oqab6kY/KOqRySbpS0JrXlF5KOyDumckiaKGmlpCZJFX2LXTFJ4yS9KGm9pL/LO55ySZolabOkFXnHUi5Jx0p6TNLq9H2amndM5ZDUU9IzkpaldlyXd0ytqfprCJI+GBE70vTfAB+JiCk5h9Vuks4G/i8iGiR9HyAirs45rHaTdBLQBPwX8K2IeDbnkA6IpFpgLfBpYBOwGLg4IlblGlgZJI0FdgI/jYhhecdTDklHA0dHxBJJfYDngD+vtv8PSQJ6R8ROSd2Ap4CpEbEo59BKqvozhEIySHoDVZnhImJ+RDSk2UXAoDzjKVdErI6IF/OOowyjgfUR8XJE7AXuAs7LOaayRMSTwFt5x3EwIuL1iFiSpt8BVgMD842q/SKzM812Sz8Vu4+q+oQAIOkGSRuBLwLX5B1PB7gMeCjvILqYgcDGZvObqMId0OFI0nHACOA3+UZSHkm1kpYCm4EFEVGx7aiKhCDpV5JWlPg5DyAipkXEscAc4Gv5RtuyttqR3jMNaCBrS0U6kHZUIZVYVrFHcl2FpA8A9wJfL+oNqBoR0RgRHyU76x8tqWK78eryDuBARMRZB/jW/wF+CVzbieGUra12SLoEOBc4Myr44k47/j+qySbg2Gbzg4Df5RSLAanP/V5gTkT8PO94DlZEbJP0ODAOqMgL/lVxhtAaSUObzU4A1uQVy8GQNA64GpgQEbvyjqcLWgwMlXS8pO7AJOB/c46py0oXY28HVkfEv+cdT7kk9S/cMSipHjiLCt5HHQ53Gd0LfJjszpZXgCkR8Vq+UbWfpPVAD+DNtGhRld4t9Tngh0B/YBuwNCLOyTeqAyPpM8B0oBaYFRE35BxSWSTNBT5JVm75DeDaiLg916DaSdIY4NfAC2R/2wB/HxEP5hdV+0kaDtxB9p2qAX4WEd/NN6qWVX1CMDOzjlH1XUZmZtYxnBDMzAxwQjAzs8QJwczMACcEMzNLnBCs3SQ1puqyhZ+yKoNKmi3pwjbe811JHfIgnKTHiyuwSvqOpO8VLfuopNXt3HaHxVkuSV8s+n9pSm3pJemXqZruSkn/0sL63SX9RNILqTrnJ4temyFpbdrOBWn5Fekp9QfT8xtIGiOpap8d6Mqq4kllqzi706P4nS4iOrs21VyyulHfbrZsEtlT7wdEUu0hiLNNETGHVPJE0inA/RGxVFIv4KaIeCzttB+VND4iiutlfTVt5xRJA4CHJI2KiCZgGrA5Ik6QVAP0S+tcDgwHrgfOkTQP+Eey36FVGZ8hWIeQ1FfZWAIfTvNzJX01Te+U9G+Slkh6VFL/EutfI2lxOtqckZ5U3e8sQtIGSdel7bwg6cS0vLeyMQAWS3q+UFNJUr2ku5SNMXE3UF/8uaky6zZJf9Js8UVk1U6RdKukZ1VUyz7Fco2kp4CJRXG21JbHJX1fWX38tZL+NC2vlXRTatNySVek5adJekLSc5IeUVYS+kBdTJbsiIhdEfFYmt4LLKF0Nd2PAI+m920me7CwcEZ1GfC99FpTRGxttl43oBfwPvAl4MGIeLsdsVqFcEKwctQXdU18PiK2kxUWnC1pEvChiJiZ3t8bWBIRHwOeoHStqVsiYlSq319PVtOplK1pO7cC30rLppGNJTEK+BRwo6TewF8BuyJiOHADcFoL25xLOqKVdDrwZkSsK2w7IkaSHQWfkZ48LdgTEWMi4q52tKUuIkYDX2/2e5gMHA+MSLHOUVbH54fAhRFxGjArtQFJUyS19RT751O79qOsjMKfkXb8RZYB50mqk3Q82e/rWP1+sKbrUzK+R9JRadlNZOXa+wNPA5cAP2ojNqtQ7jKycpTsMoqIBZImAv8JnNrspSbg7jT930CpQmWfknQV2ZFmP2Al8ECJ9xXWfQ44P02fDUyQVEgQPYHBwFjg5hTbcknLW2jPXcBCSVeSJYbmO9KLJE0m+1s5muwourCduymttbY0j/+4NH0W8OPCeBgR8ZayipjDgAXpBKMWeD29/uMWPheAdLazKyJWFC2vS227OSJeLrHqLOAk4FmyMjALySrv1pGdUTwdEd+U9E2yRPCliLgTuDNt/1qy3/d4SV8mKyd+ZepysirghGAdJvUtnwTsJtsRbmrhrfvVS5HUk+yocmREbJT0HbKdeinvpX8b+f33V8AFxQPzpB1pm7VZ0mduAM4ALgA+ntY/nuwsZFREvC1pdlFc7xZv6wDa0lL8xXEKWBkRH28r/hKKk1rBDGBdREwvtVJKSN/YF4C0EFhHVl9rF/CL9NI9wFf2CzYbunZURFwn6Rmy3+ENwJnAgjLaYDlwl5F1pG+QjWx1MTArdXtA9j0r3E30BbJhBJsr7DC3Kqt/3+qdRyU8AlzRrK9+RFr+JNmgSaQj7uGlVweyHeh/AC9FRCGRfZBsp789dZGMP4BYymnLfGBKOoJHUj/gRaC/pEJy6ibp5LY2lJLyRNI1kGbL/wnoS9ZV1dK6vVJXG5I+DTRExKpUiv0BsoJ5kO3ki4eyvJ7sYjJk3WRBdmbYq62YrXL4DMHKUa9sBKiCh8m6Gy4HRkfEO5KeBP6BrJ/8XeBkSc8B28n6t/dJdeJnklW23EBWiro9rierUro8JYUNZP32twI/SV1FS4FnWtnGPcAPgCuaxbVM0vNkXT4vk/WRt6rMttwGnJDifx+YGRG3pIvUN0vqS/a3Oh1YWbh+0ELX0VhgU/MuIUmDyK6zrAGWpLx5S0TcJmkC2dnMNcAA4BFJTcBrZBeIC64G7pQ0HdgCXNps+yNSPM+nRben9m8EKnpQedufq51ap5O0MyI+kHccZtY6dxmZmRngMwQzM0t8hmBmZoATgpmZJU4IZmYGOCGYmVnihGBmZgD8P6edVk/wunreAAAAAElFTkSuQmCC\n",
258 "text/plain": [
259 "<Figure size 432x288 with 1 Axes>"
260 ]
261 },
262 "metadata": {
263 "needs_background": "light"
264 },
265 "output_type": "display_data"
266 }
267 ],
268 "source": [
269 "ev1, ev2 = pca.explained_variance_ratio_\n",
270 "ax = plt.figure().gca(title='2D Projection', \n",
271 " xlabel='Explained Variance: {:.2%}'.format(ev1), \n",
272 " ylabel='Explained Variance: {:.2%}'.format(ev2))\n",
273 "ax.scatter(*features_2D.T, c=data.label, s=10);"
274 ]
275 },
276 {
277 "cell_type": "markdown",
278 "metadata": {
279 "slideshow": {
280 "slide_type": "slide"
281 }
282 },
283 "source": [
284 "## Perform GMM clustering"
285 ]
286 },
287 {
288 "cell_type": "code",
289 "execution_count": 8,
290 "metadata": {
291 "ExecuteTime": {
292 "end_time": "2018-12-27T18:38:53.881811Z",
293 "start_time": "2018-12-27T18:38:53.725574Z"
294 },
295 "slideshow": {
296 "slide_type": "fragment"
297 }
298 },
299 "outputs": [
300 {
301 "data": {
302 "text/plain": [
303 "Text(0.5,1,'Clusters | MI=0.56')"
304 ]
305 },
306 "execution_count": 8,
307 "metadata": {},
308 "output_type": "execute_result"
309 },
310 {
311 "data": {
312 "image/png": 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\n",
313 "text/plain": [
314 "<Figure size 432x288 with 2 Axes>"
315 ]
316 },
317 "metadata": {
318 "needs_background": "light"
319 },
320 "output_type": "display_data"
321 }
322 ],
323 "source": [
324 "n_components = 3\n",
325 "gmm = GaussianMixture(n_components=n_components)\n",
326 "gmm.fit(features_standardized)\n",
327 "data['clusters'] = gmm.predict(features_standardized)\n",
328 "fig, axes = plt.subplots(ncols=2)\n",
329 "labels, clusters = data.label, data.clusters\n",
330 "mi = adjusted_mutual_info_score(labels, clusters)\n",
331 "axes[0].scatter(*features_2D.T, c=data.label, s=10)\n",
332 "axes[0].set_title('Original Data')\n",
333 "axes[1].scatter(*features_2D.T, c=data.clusters, s=10)\n",
334 "axes[1].set_title('Clusters | MI={:.2f}'.format(mi))"
335 ]
336 },
337 {
338 "cell_type": "markdown",
339 "metadata": {
340 "slideshow": {
341 "slide_type": "slide"
342 }
343 },
344 "source": [
345 "### Visualize Gaussian Distributions"
346 ]
347 },
348 {
349 "cell_type": "markdown",
350 "metadata": {},
351 "source": [
352 "The following figures show the GMM cluster membership probabilities for the iris dataset as contour lines:"
353 ]
354 },
355 {
356 "cell_type": "code",
357 "execution_count": 9,
358 "metadata": {
359 "ExecuteTime": {
360 "end_time": "2018-12-27T18:38:53.941470Z",
361 "start_time": "2018-12-27T18:38:53.883043Z"
362 },
363 "slideshow": {
364 "slide_type": "fragment"
365 }
366 },
367 "outputs": [],
368 "source": [
369 "xmin, ymin = features_2D.min(axis=0)\n",
370 "xmax, ymax = features_2D.max(axis=0)\n",
371 "\n",
372 "x = np.linspace(xmin, xmax, 500)\n",
373 "y = np.linspace(ymin, ymax, 500)\n",
374 "X, Y = np.meshgrid(x, y)\n",
375 "\n",
376 "simulated_2D = np.column_stack([np.ravel(X), np.ravel(Y)])\n",
377 "simulated_4D = pca.inverse_transform(simulated_2D)\n",
378 "Z = atleast_2d(np.clip(np.exp(gmm.score_samples(simulated_4D)), a_min=0, a_max=1)).reshape(X.shape)"
379 ]
380 },
381 {
382 "cell_type": "code",
383 "execution_count": 10,
384 "metadata": {
385 "ExecuteTime": {
386 "end_time": "2018-12-27T18:38:54.168687Z",
387 "start_time": "2018-12-27T18:38:53.942611Z"
388 },
389 "slideshow": {
390 "slide_type": "slide"
391 }
392 },
393 "outputs": [
394 {
395 "data": {
396 "image/png": 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\n",
397 "text/plain": [
398 "<Figure size 432x288 with 2 Axes>"
399 ]
400 },
401 "metadata": {
402 "needs_background": "light"
403 },
404 "output_type": "display_data"
405 }
406 ],
407 "source": [
408 "fig, ax = plt.subplots()\n",
409 "ax.set_aspect('equal')\n",
410 "CS = ax.contour(X, Y, Z, cmap='Greens', alpha=.5)\n",
411 "CB = plt.colorbar(CS, shrink=0.8)\n",
412 "ax.scatter(*features_2D.T, c=data.label, s=15)\n",
413 "fig.tight_layout();"
414 ]
415 },
416 {
417 "cell_type": "code",
418 "execution_count": 11,
419 "metadata": {
420 "ExecuteTime": {
421 "end_time": "2018-12-27T18:41:22.966672Z",
422 "start_time": "2018-12-27T18:41:22.588241Z"
423 },
424 "slideshow": {
425 "slide_type": "slide"
426 }
427 },
428 "outputs": [
429 {
430 "data": {
431 "image/png": 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\n",
432 "text/plain": [
433 "<Figure size 432x288 with 2 Axes>"
434 ]
435 },
436 "metadata": {
437 "needs_background": "light"
438 },
439 "output_type": "display_data"
440 }
441 ],
442 "source": [
443 "fig = plt.figure()\n",
444 "ax = fig.gca(projection='3d')\n",
445 "ax.set_aspect('equal')\n",
446 "CS = ax.contourf3D(X, Y, Z, cmap='RdBu_r', alpha=.5)\n",
447 "CB = plt.colorbar(CS, shrink=0.8)\n",
448 "ax.scatter(*features_2D.T, c=data.label, s=15)\n",
449 "fig.tight_layout()\n",
450 "fig.savefig('gaussian3d', dpi=300)"
451 ]
452 },
453 {
454 "cell_type": "markdown",
455 "metadata": {
456 "slideshow": {
457 "slide_type": "slide"
458 }
459 },
460 "source": [
461 "### Bayesian Information Criterion "
462 ]
463 },
464 {
465 "cell_type": "code",
466 "execution_count": 12,
467 "metadata": {
468 "ExecuteTime": {
469 "end_time": "2018-12-27T18:41:24.746013Z",
470 "start_time": "2018-12-27T18:41:24.678667Z"
471 },
472 "slideshow": {
473 "slide_type": "fragment"
474 }
475 },
476 "outputs": [
477 {
478 "data": {
479 "text/plain": [
480 "2 794.71\n",
481 "3 801.55\n",
482 "4 853.82\n",
483 "5 845.19\n",
484 "6 962.57\n",
485 "7 1,001.98\n",
486 "dtype: float64"
487 ]
488 },
489 "execution_count": 12,
490 "metadata": {},
491 "output_type": "execute_result"
492 }
493 ],
494 "source": [
495 "bic = {}\n",
496 "for n_components in range(2, 8):\n",
497 " gmm = GaussianMixture(n_components=n_components)\n",
498 " gmm.fit(features_standardized)\n",
499 " bic[n_components] = gmm.bic(features_standardized)\n",
500 "pd.Series(bic)"
501 ]
502 }
503 ],
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