4-Probabilistic Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "60895607",
   "metadata": {},
   "source": [
    "# Probabilistic Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "457e24fd",
   "metadata": {},
   "source": [
    "## Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f62b2e40",
   "metadata": {},
   "source": [
    "The probabilistic models use the idea of probability to describe the data or classify new entities. probabilistic models see features and target variables as random variables. there are two types of probabilistic models:\n",
    "   1. Discriminative\n",
    "   2. Generative<br>\n",
    "\n",
    "Discriminative probability models (also called conditional probabilistic models or predictive probabilistic models) use the idea of conditional probability distribution ${p(y\\vert X)}$ which ${y}$ can be predicted from ${X}$. generative models estimate ${p(X)}$, the probability of observing ${X}$, or joint distribution ${p(X,y)}$, which then can be used to drive any conditional distribution involving the same variables.<br>\n",
    "we already talk about discriminative probabilistic models like KNN and Logistic Regression (they can be describe as probabilistic or not), so what are we going to do next is to talk about generative models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c042d83",
   "metadata": {},
   "source": [
    "## Generative Models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51a7f22f",
   "metadata": {},
   "source": [
    "as we said before, a generative model describes how data is generated, in terms of a probabilistic model. we can describe the workflow of generative modeling as this:\n",
    "   * We have a dataset of observations X (with or without labels)\n",
    "   * we assume that the observations have been generated according to some unknown distribution ${p}_{data}$.\n",
    "   * a generative model ${p}_{model}$ tries to mimic ${p}_{data}$. if we achieve this goal, we can sample from ${p}_{model}$ to generate observations that appear to have been drawn from ${p}_{data}$.\n",
    "   * We are impressed by ${p}_{model}$ if:\n",
    "       * it can generate examples that appear to have been drawn from ${p}_{data}$.\n",
    "       * it can generate examples that are suitably different from observations in ${X}$. in other words, the model shouldn't simply reproduce things it has.<br>\n",
    "\n",
    "but how to find our approximate probability?<br> \n",
    "1. first we define a Probability Density Function (PDF). PDF is a function that maps point ${x}$ in sample space to a number between 0 and 1. the sum of all the density functions over all the points in the sample space must be equal to 1 so that it is a well-defined probability distribution.<br>\n",
    "2. we know that there is only one true density function ${p}_{data}$ exists, but there are infinite numbers of ${p}_{model}$ that we can find to estimate our ${p}_{data}$. so in second step we use parametric modeling to find suitable ${p}_{model}$. in this approach, we will assign some finite parameters to describe our ${p}_{model}$ so we will have ${p}_{\\theta}(X)$ which is a probability density function with parameter $\\theta$.\n",
    "3. now to compare our ${p}_{model}$ with ${p}_{data}$ we need some metrics, so we will use **Kullback-Leibler Divergence** (KL), which is measure similarity between two distribution. the KL divergence is always equal to or bigger than zero (if two distributions are the same, it is zero), so our goal is to minimize KL divergence. using the KL formula (and Monte Carlo Estimation) we can show that instead of minimizing KL divergence we can maximize **likelihood** of ${p}_{\\theta}(X)$. the likelihood is the output of our pdf and can define as:<br>\n",
    "\n",
    "    $${L(\\theta\\vert X)} = {p}_{\\theta}(X)$$<br>\n",
    "   so the likelihood of parameter $\\theta$ given ${X}$, is the value of pdf which is parameterized by $\\theta$, at point ${X}$. because of some computational difficulty and also statistical reasons (if you derive the formula from KL divergence, you end up with the log form of ${p}_{\\theta}(X)$) we use log-likelihood which is simply calculated by performing log function on our likelihood so log-likelihood will be:\n",
    "   \n",
    "   $${l(\\theta\\vert X)} = {\\ln}{p}_{\\theta}(X)$$<br>\n",
    "   \n",
    "   we want to find some $\\theta^{*}$ (which is called Maximum Likelihood Estimate or MLE) that maximizes the log-likelihood of observing data ${X}$:\n",
    "   \n",
    "   $$\\theta^{*} = \\underset{\\theta}{\\textrm{arg max}} {l(\\theta\\vert X)}$$\n",
    "\n",
    "now that we approximate our data distribution with ${p}_{\\theta}(X)$ or ${p}_{\\theta}(X,y)$ (because all the above formula can be derived for ${p}_{\\theta}(X,y)$ similarly), we can use it to solve any downstream task like, classification, clustering, outliers detection, generation, etc. let's talk about some of these tasks and their corresponding methods."
   ]
  },
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   "cell_type": "markdown",
   "id": "c2b481f6",
   "metadata": {},
   "source": [
    "### Classification using generative models"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe908266",
   "metadata": {},
   "source": [
    "classification is a supervised task and its goal is to construct a model using the training dataset, to predict the labels of a new dataset. so we will have ${(X^{(i)},y^{(i)})}$. so in order to classify data, generative models try to approximate joint probability distribution ${p}_{\\theta}(X,y)$. in order to approximate our joint probability we use the idea of conditional probability so:<br>\n",
    "\n",
    "$${p}_{\\theta}(X,y) = {p}_{\\theta}(X\\vert y) . {p}_{\\theta}(y)$$<br>\n",
    "\n",
    "the first term is called **likelihood** which is the probability of observing ${X}$ assuming that the true class is ${y}$ and the second term is called **prior probability**. now we need to estimate these two probabilities using our training dataset.<br>\n",
    "\n",
    "* **Estimating ${p}(y_{i})$, prior probability of class $y_{i}$:**<br>\n",
    "we are estimating prior probability with the number of occurrences of class ${i}$ in our training dataset, but in general, we can use other numbers from other sources too. so we will have:<br>\n",
    "\n",
    "$$ {p}({y}_{i}) = \\frac{m_{i}}{m} $$<br>\n",
    "\n",
    "* **Estimating ${p}_{\\theta}(X\\vert y_{i})$, likelihood of class ${y}_{i}$:**\n",
    "    1. Numerical features<br>\n",
    "        when we have numerical features we assume that each class ${y}_{i}$ is normally distributed which means each class has parameter **mean** $\\mu_{i}$ and **covariance**  $\\Sigma_{i}$. both parameters are estimated from the subset of data with corresponding labels. the probability density function for **Normal Distribution** at X is given as:<br>\n",
    "        $$ f_{i}(X) = f(X\\vert \\mu_{i}, \\Sigma_{i}) = \\frac{1}{(\\sqrt{2\\pi})^{n} (\\sqrt{\\vert \\Sigma_{i} \\vert})}exp (- \\frac{(X-\\mu_{i})^{T} \\Sigma_{i}^{-1} (X-\\mu_{i})}{2})$$<br>\n",
    "        \n",
    "   and by doing some math we can derive the maximum likelihood estimation of our parameter as:<br>\n",
    "        \n",
    "        $\\hat{\\mu_{i}} = \\frac{1}{m_{i}} \\sum \\limits _{x_{j}\\in y_{i}} X_{j}$<br>\n",
    "        \n",
    "        $\\hat{\\Sigma_{i}} = \\frac{1}{m_{i}} \\bar{X}_{i}^{T}\\bar{X}_{i}\\space,\\space \\space \\space \\space \\space \\bar{X}_{i} = {X}_{i} - \\hat{\\mu_{i}}$<br>\n",
    "        \n",
    "  2. Categorical features<br>\n",
    "   when we have categorical features, we use **Multinomial Distribution** to estimate likelihood. the number of parameters is all the possible combinations of our categorical values. for example, if we have 2 features and one feature has 3 unique categories, and the other one has 4, the number of parameters will be:<br>\n",
    "d = 3 $\\times$ 4 = 12<br>\n",
    "\n",
    "   then the maximum likelihood for each parameter will be:<br>\n",
    "\n",
    "   $\\hat{\\theta}_{ij} = \\frac{m_{ij} + 1}{m_{i} + d}$<br>\n",
    "   ${m}_{ij}$ : number of time that category combination occur in class ${i}$ subset<br>\n",
    "   ${m}_{i}$ : number of samples in class ${i}$ subset<br>\n",
    "   ${d}$ : total number of parameters<br>\n",
    "   ${+1}$: Laplace Smoothing, because of combination that may not occur in our dataset and to prevent them from becoming zero.<br>\n",
    "        \n",
    "        \n",
    "* **Prediction phase:**<br>\n",
    "    after we estimate our parameters and use them to estimate prior probability and likelihood then we can predict our label of new data with: <br>\n",
    "    \n",
    "     $ \\hat{y} = \\underset{y_{i}}{\\textrm{arg max}}\\{{p}_{\\theta}(X\\vert y_{i}) . {p}(y_{i})\\} $<br>\n",
    "    or use log form for mathematical and statistical reasons:<br>\n",
    "   \n",
    "     $ \\hat{y} = \\underset{y_{i}}{\\textrm{arg max}}\\{\\ln{p}_{\\theta}(X\\vert y_{i}) + \\ln{p}(y_{i})\\} $<br>\n",
    "    \n",
    "   we also can calculate ${p}(y_{i}\\vert X)$, called **Posterior Probability** which is the probability of observing ${X}$ from any of the classes. by using **Bayes theorem** the posterior probability is:<br>\n",
    "    \n",
    "    ${p}(y_{i}\\vert X) = \\frac{{p}(X\\vert y_{i}) . {p}(y_{i})}{p(X)}\\space \\space$   , $\\space P(X) = \\sum \\limits _{i}{p}(X\\vert y_{i}) . {p}(y_{i}) $<br>\n",
    "    \n",
    "**NOTE:** but why use normal distribution? well in general you can use any distribution to model your problem but normal distribution have some properties that make it preferable:<br>\n",
    "   1. it is the most common distribution found in nature, so there is a good chance your distribution is one of them.\n",
    "   2. it has the most intuitive parameters. we normally have a good sense of mean and variance (covariance).\n",
    "   3. another reason, or maybe the most important one, is because of **Central Limit Theorem** which says if we collect several subsets of any random distribution (arbitrary distribution) and calculate all the means of these subsets, the distribution of those means will be normally distributed, and we can perform any statistical procedure on the normally distributed means.<br>\n",
    "\n",
    "so normal distribution is a good choice, but you always can test other distributions on your dataset.<br>\n",
    "by using the normal distribution for estimating our probabilities we will end up with the family of methods called **Gaussian Discriminant Analysis** or GDA. we first talk about the general form of the GDA and then derive other variations too."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aee41b9",
   "metadata": {},
   "source": [
    "#### Gaussian Discriminant Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cfcdd4d",
   "metadata": {},
   "source": [
    "in GDA we estimate our likelihood with gaussian distribution, so for each class, we will have $\\mu_{i}$ , $\\Sigma_{i}$ and again the goal is to model distribution for each class and classify new data. Let's first write the GDA algorithm then code it from scratch and test it on our breast cancer dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c7f6d95",
   "metadata": {},
   "source": [
    "##### Pseudo code for GDA"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bb7754a",
   "metadata": {},
   "source": [
    "1. create class specific subsets from training dataset ${X_{i}}$\n",
    "2. calculate number of samples in each subsets ${m_{i}}$\n",
    "3. calculate prior probabilities $\\hat{p}({y}_{i}) = \\frac{m_{i}}{m}$\n",
    "4. calculate mean of each class subset $\\hat{\\mu_{i}}$\n",
    "5. calculate centered subsets $\\bar{X}_{i} = {X_{i}} - \\hat{\\mu_{i}}$\n",
    "6. calculate covariance $\\hat{\\Sigma_{i}} = \\frac{1}{m_{i}} \\bar{X}_{i}^{T}\\bar{X}_{i}$\n",
    "7. calculate determinant and inverse of covariance matrix $\\vert\\Sigma_{i}\\vert$ , $\\Sigma_{i}^{-1}$\n",
    "8. calculate pdf using multivariate gaussian formula ${f}_{i}(X\\vert \\hat{\\mu_{i}},\\hat{\\Sigma_{i}})$\n",
    "9. prediction phase $ \\hat{y} = \\underset{y_{i}}{\\textrm{argmax}}\\{{f}_{i}(X\\vert \\hat{\\mu_{i}} . \\hat{p}({y}_{i})\\} $<br>\n",
    "\n",
    "by using log function and doing some math we can simplify step 8 and 9, and use this formula in prediction phase:<br>\n",
    "\n",
    "$ \\hat{y} = \\underset{y_{i}}{\\textrm{argmax}}\\{\\ln{p}(y_{i}) - \\frac{1}{2}\\ln\\vert\\Sigma_{i}\\vert - \\frac{1}{2}(X-\\mu_{i})^{T} \\Sigma_{i}^{-1} (X-\\mu_{i})\\}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "377296e6",
   "metadata": {},
   "source": [
    "##### GDA from scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "50bf8437",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.linalg import multi_dot\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0fb4b5a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "X,y = load_breast_cancer(return_X_y=True)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42,stratify=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d9c9c82",
   "metadata": {},
   "outputs": [],
   "source": [
    "# class specific subsets\n",
    "X1 = X_train[y_train==1]\n",
    "X0 = X_train[y_train==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a95bc0cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "#number of samples in each class and all the samples + number of features\n",
    "m1 = X1.shape[0]\n",
    "m0 = X0.shape[0]\n",
    "m,n = X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bcacb808",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prior probabilities\n",
    "p1 = m1/m\n",
    "p0 = m0/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4343c62b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 30)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mean of each class subset\n",
    "mu1 = np.mean(X1,axis=0,keepdims=True)\n",
    "mu0 = np.mean(X0,axis=0,keepdims=True)\n",
    "mu1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8be2f991",
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculating covariance matrix and its inverse and determinant\n",
    "X1 = X1 - mu1\n",
    "X0 = X0 - mu0\n",
    "# cov1 = (np.dot(X1.T,X1))/(m1-1)\n",
    "cov1 = np.cov(X1,rowvar=False)\n",
    "cov0 = np.cov(X0,rowvar=False)\n",
    "invcov1 = np.linalg.inv(cov1)\n",
    "invcov0 = np.linalg.inv(cov0)\n",
    "detcov1 = np.linalg.det(cov1)\n",
    "detcov0 = np.linalg.det(cov0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "14774e0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# prediction phase\n",
    "y_predict = []\n",
    "for i in range(len(X_test)):\n",
    "    Q1 = (multi_dot([(X_test[i]-mu1),invcov1,(X_test[i]-mu1).T]))/2\n",
    "    Q0 = (multi_dot([(X_test[i]-mu0),invcov0,(X_test[i]-mu0).T]))/2\n",
    "    f1 = np.log(p1) - (np.log(detcov1))/2 - Q1\n",
    "    f0 = np.log(p0) - (np.log(detcov0))/2 - Q0\n",
    "    y_predict.append(np.argmax([f0,f1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "332fbdfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9473684210526315"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate accuracy\n",
    "y_predict = np.array(y_predict)\n",
    "accuracy = np.sum(y_predict == y_test)/len(X_test)\n",
    "accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bd59fddb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1ac6ba0ac80>"
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     "execution_count": 10,
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "miss_classify = np.where(y_test!=y_predict)\n",
    "plt.scatter(X_test[:,1],X_test[:,2],c=y_predict,s=10)\n",
    "plt.scatter(X_test[miss_classify,1],X_test[miss_classify,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7134c8c0",
   "metadata": {},
   "source": [
    "the blue points are the samples that our model miss-classified"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5305c5f5",
   "metadata": {},
   "source": [
    "##### GDA in scikit learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d0085a47",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "76d4251d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9473684210526315"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qda = QuadraticDiscriminantAnalysis()\n",
    "qda.fit(X_train,y_train)\n",
    "qda.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "856dba97",
   "metadata": {},
   "source": [
    "same accuracy so we should be happy now :)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a578b05",
   "metadata": {},
   "source": [
    "**NOTES:**<br>\n",
    "* what we discussed was a general form of GDA and it is also called Quadratic Discriminant Analysis (QDA) because it will create a quadratic hyperplane between our classes.\n",
    "* in QDA because we have to calculate the inverse of the covariance matrix, we may end up with the singularity problem, especially in the case of high dimensional data, the common techniques to fix it are:\n",
    "    * Apply PCA to reduce dimensions\n",
    "    * regularize the covariance matrices\n",
    "    * use Pseudo inverse\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3225b968",
   "metadata": {},
   "source": [
    "##### Linear Discriminant Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c906f909",
   "metadata": {},
   "source": [
    "Linear Discriminant Analysis or LDA is special case of GDA, which instead of using covariance matrix for each class, use same covariance matrix for all classes. we can use this formula for calculate the covariance matrix:\n",
    "\n",
    "$$\\Sigma = \\frac{1}{m}\\sum\\sum(X-\\mu_{i})(X-\\mu_{i})^{T}$$<br>\n",
    "\n",
    "in prediction phase, we can also use these formula:<br>\n",
    "$$ \\hat{y} = \\underset{y_{i}}{\\textrm{argmax}}\\{\\ln{p}(y_{i}) + X^{T}\\Sigma^{-1}\\mu_{i} - \\frac{1}{2}\\mu_{i}^{T} \\Sigma^{-1} \\mu_{i}\\}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f0fe4d5",
   "metadata": {},
   "source": [
    "###### LDA from scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f7ca37ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "#class specific subsets\n",
    "X1 = X_train[y_train==1]\n",
    "X0 = X_train[y_train==0]\n",
    "#number of samples in subsets and original dataset + number of samples\n",
    "m1 = X1.shape[0]\n",
    "m0 = X0.shape[0]\n",
    "m,n = X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "192a23b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prior probability\n",
    "p1 = m1/m\n",
    "p0 = m0/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "283f9641",
   "metadata": {},
   "outputs": [],
   "source": [
    "# mean of subsets\n",
    "mu1 = np.mean(X1,axis=0,keepdims=True)\n",
    "mu0 = np.mean(X0,axis=0,keepdims=True)\n",
    "# centered subsets\n",
    "X1 = X1 - mu1\n",
    "X0 = X0 - mu0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "063fce34",
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate covariance matrix and its inverse\n",
    "XX1 = np.dot(X1.T,X1)\n",
    "XX0 = np.dot(X0.T,X0)\n",
    "cov = (XX1+XX0)/(m)\n",
    "invcov = np.linalg.inv(cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8a90cb96",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prediction phase\n",
    "y_predict = []\n",
    "for i in range(len(X_test)):\n",
    "    Q1 = (multi_dot([X_test[i],invcov,mu1.T]))\n",
    "    Q0 = (multi_dot([X_test[i],invcov,mu0.T]))\n",
    "    f1 = np.log(p1) - (multi_dot([mu1,invcov,mu1.T]))/2 + Q1\n",
    "    f0 = np.log(p0) - (multi_dot([mu0,invcov,mu0.T]))/2 + Q0\n",
    "    y_predict.append(np.argmax([f0,f1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2ab89039",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.956140350877193"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#accuracy\n",
    "y_predict = np.array(y_predict)\n",
    "accuracy = np.sum(y_predict == y_test)/len(X_test)\n",
    "accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9a5ad3e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1ac6dd1ca60>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "miss_classify = np.where(y_test!=y_predict)\n",
    "plt.figure\n",
    "plt.scatter(X_test[:,1],X_test[:,2],c=y_predict,s=10)\n",
    "plt.scatter(X_test[miss_classify,1],X_test[miss_classify,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "949a5688",
   "metadata": {},
   "source": [
    "###### LDA in scikit learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "621f0dd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4c3ac70b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.956140350877193"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda = LinearDiscriminantAnalysis(store_covariance=True)\n",
    "lda.fit(X_train,y_train)\n",
    "lda.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8646a463",
   "metadata": {},
   "source": [
    "**NOTES:**<br>\n",
    "* in LDA hyperplane will be linear\n",
    "* like GDA, in LDA we will have singularity issue\n",
    "* we can also use LDA for dimensionality reduction (see dimensionality reduction chapter)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70e5dc93",
   "metadata": {},
   "source": [
    "##### Naive Bayes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71f7954e",
   "metadata": {},
   "source": [
    "A Naive Bayes classifier is another variation of GDA which assumes that all the features are **independent** from each other. with this assumption, we don't need to calculate the covariance matrix and we just need variance which is very computationally preferable. also, we can calculate the likelihood of each feature separate from each other and our total likelihood will be the product of each feature likelihood, so we can treat each column separately. but of course we will lose some accuracy. so we will have:<br>\n",
    "\n",
    "$${f}_{i}(X) = \\prod \\limits _{j} ^{n} {f}_{ij}(x_{j}) $$<br>\n",
    "\n",
    "$$\\hat{y} = \\underset{y_{i}}{\\textrm{argmax}}\\{\\ln{p}(y_{i}) -\\frac{1}{2}\\sum \\limits _{j} ^{n} (\\ln \\sigma_{ij} ^{2} + \\frac{(x_{j} - \\mu_{ij})}{\\sigma_{ij}})\\}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f58dc5d5",
   "metadata": {},
   "source": [
    "###### Naive Bayes from scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fe9a119e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#class specific subsets\n",
    "X1 = X_train[y_train==1]\n",
    "X0 = X_train[y_train==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "138571ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "# number of samples in each class + number of features + overall number of samples in training set\n",
    "m1 = X1.shape[0]\n",
    "m0 = X0.shape[0]\n",
    "m,n = X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3cc49efb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prior probabilities\n",
    "p1 = m1/m\n",
    "p0 = m0/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "972ed66f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# class specific mean\n",
    "mu1 = np.mean(X1,axis=0,keepdims=True)\n",
    "mu0 = np.mean(X0,axis=0,keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e434706d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculating variance\n",
    "X1 = X1-mu1\n",
    "X0 = X0-mu0\n",
    "var1 = np.var(X1,axis=0,keepdims=True)\n",
    "var0 = np.var(X0,axis=0,keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c780caf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prediction phase\n",
    "y_predict=[]\n",
    "for i in range(len(X_test)):\n",
    "    f1 = np.log(p1) - 0.5*np.sum(np.log(var1) + (((X_test[i]-mu1)**2)/var1))\n",
    "    f0 = np.log(p0) - 0.5*np.sum(np.log(var0) + (((X_test[i]-mu0)**2)/var0))\n",
    "    y_predict.append(np.argmax([f0,f1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d87cd3b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9298245614035088"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#calculating accuracy\n",
    "y_predict = np.array(y_predict)\n",
    "accuracy = np.sum(y_predict == y_test)/len(X_test)\n",
    "accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "5355ca60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1ac6dd8ee00>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "miss_classify = np.where(y_test!=y_predict)\n",
    "plt.scatter(X_test[:,1],X_test[:,2],c=y_predict,s=10)\n",
    "plt.scatter(X_test[miss_classify,1],X_test[miss_classify,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73c474b8",
   "metadata": {},
   "source": [
    "###### Naive Bayes Scikit learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "5c9e8182",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "11206136",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9298245614035088"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nb = GaussianNB(var_smoothing=0)\n",
    "nb.fit(X_train,y_train)\n",
    "nb.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c190427d",
   "metadata": {},
   "source": [
    "**Summary**<br>\n",
    "so we talked about 3 classification algorithms:\n",
    "   * GDA which uses multivariate gaussian\n",
    "   * LDA which uses multivariate Gaussians with equal covariance\n",
    "   * Naive Bayes which assumes all the features are independent of each other<br>\n",
    "\n",
    "and each method has its pros and cons, so for different problems, we can choose the different variant of Gaussian methods."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f240c5f",
   "metadata": {},
   "source": [
    "### Clustering using generative models - Gaussian Mixture Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c7db264",
   "metadata": {},
   "source": [
    "clustering is the task of finding groups in our dataset. the idea of the Gaussian Mixture Method (GMM) is that we have ${k}$ number of components in our dataset, and we approximate each group with Gaussian distribution (in other words we map ${k}$ distribution on our data), so each component will have $\\mu_{i}$ and $\\Sigma_{i}$, and the goal is to find these means and covariances. so we will have:<br>\n",
    "\n",
    "$$ f_{i}(X) = f(X\\vert \\mu_{i}, \\Sigma_{i}) = \\frac{1}{(\\sqrt{2\\pi})^{n} (\\sqrt{\\vert \\Sigma_{i} \\vert})}exp (- \\frac{(X-\\mu_{i})^{T} \\Sigma_{i}^{-1} (X-\\mu_{i})}{2})$$<br>\n",
    "\n",
    "$$p(X) = \\sum\\limits _{i} ^{k} f_{i}(X) p(c_{i})$$<br>\n",
    "\n",
    "so like before we have to use log-likelihood estimation and maximize it to find our parameters. but there is a problem because our data is unlabeled we can't directly find our parameters, instead, we use the **Expectation-Maximization** method to find the maximum likelihood estimation of our parameters.<br>\n",
    "\n",
    "**Expectation-Maximization Algorithm:**<br>\n",
    "Expectation-Maximization (EM) algorithm is 2 steps iterative approach that starts with an initial guess for our parameters then:<br>\n",
    "   1. Expectation Step: given parameters we compute posterior probabilities $p(c_{i}\\vert X)$ via Bayes Theorem:<br>\n",
    "   \n",
    "       $${p}(c_{i}\\vert X) = \\frac{{p}(X\\vert c_{i}) . {p}(c_{i})}{\\sum \\limits _{i}{p}(X\\vert c_{i}) . {p}(c_{i}) }$$\n",
    "       \n",
    "       and each component is modeled as multivariate Gaussian distribution. these posterior probabilities are our weights and we can think of them as how much each point is assigned to the $\\mu_{i}$ (contribution of each point to cluster ${i}$).\n",
    "       \n",
    "   2. Maximization Step: we use the calculated weights to update our parameters $\\mu_{i}$, $\\Sigma_{i}$, $p(c_{i})$.\n",
    "       * re-estimate $\\mu_{i}$ with the weighted average of all the points\n",
    "       * re-estimate $\\Sigma_{i}$ with the weighted covariance over all the points\n",
    "       * re-estimate $p(c_{i})$ with fraction of weights that contribute to that component<br>\n",
    "\n",
    "after some iteration our $\\mu_{i}$ will converge to some values, and those values will be the centers of our clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39ca1093",
   "metadata": {},
   "source": [
    "#### Pseudo code for GMM - EM algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d78dd17a",
   "metadata": {},
   "source": [
    "1. Randomly initialize $\\mu_{i}$. we can select uniformly random values from the possible range of X\n",
    "2. initialize covariance matrix. $\\Sigma_{i} = {I}$ (identity matrix)\n",
    "3. initialize prior probabilities $p(c_{i}) = \\frac{1}{k}$ (equal probability)\n",
    "4. Expectation Step:<br>\n",
    "\n",
    "    $ W_{i} = \\frac{{f}(X\\vert \\mu_{i},\\Sigma_{i}) . {p}(c_{i})}{\\sum \\limits _{i} ^{k}{p}(X\\vert \\mu_{i},\\Sigma_{i}) . {p}(c_{i}) }$<br>\n",
    "    \n",
    "5. Maximization Step:<br>\n",
    "    * $\\mu_{i}$ for next step:  $\\mu_{i} = \\frac{\\sum\\limits _{j} ^{m} w_{ij}X_{j}}{\\sum\\limits _{j} ^{m} w_{ij}}$<br>\n",
    "    \n",
    "    * $\\Sigma_{i}$ for next step: $\\Sigma_{i} = \\frac{\\sum\\limits _{j} ^{m} w_{ij}(X_{j} -\\mu_{i})(X_{j} -\\mu_{i})^{T}}{\\sum\\limits _{j} ^{m} w_{ij}}$\n",
    "    \n",
    "    * $p(c_{i})$ for next step:  $p(c_{i}) = \\frac{1}{m}\\sum\\limits _{j} ^{m}w_{ij}$\n",
    "\n",
    "6. repeat step 4,5 until we reach the maximum number of iterations or some threshold:<br>\n",
    "    \n",
    "    $$\\sum\\limits _{i} ^{k}\\vert\\vert \\mu_{new} - \\mu_{old}\\vert \\vert ^{2} \\leq \\epsilon$$\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80a6ceac",
   "metadata": {},
   "source": [
    "#### GMM from scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "924820a2",
   "metadata": {},
   "source": [
    "**NOTE:** as you already saw in other chapters, when I code algorithms from scratch I try to code as simple as possible because our purpose is to learn algorithms and don't distract by code complexity. but because we already work with covariances and means, I code a little, seriously a little, more complex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5d472b0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.mixture import GaussianMixture\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3bfa849e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-15.0, 15.0)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ps6NjjsPMNWsoi6TPwKpUJtrso1QHURFLP7zVGAgn4uRTe15Ec5RHo3ywagWReJyDBw+hd25ei55ftS0N/kp1EFOHDuPFhfOJ1xik0T8/n54t3Ob/yepVXPHGqxgDIpAQh+v2P5CLJzaqT1G1Y9rso1QH8Yv9J9MtmEPAdutsXssix+vlz4cf1ewRP8u3FPPJ6lUUVVZSHo1yxZuvUhmPURGLURmPEUkk+Mvnn7Jgc2FL3IpqB7Tmr1QH0Ts3jxnn/Zhn58/ji3U/MLSgO+ftPoGBXbs2+ZxbwyEufvVlFhYVYlsW0USC/XcZmHYNnWgiwYsLFzCmly5sszPI+jh/Y8wqoAxIAPG6xqLqOH+lWteFr7zIpz+sJubsSGhnG4OVfBDUdOKo0ezRtx8iwpHDR7BLl6Y/eFTLac/j/A8VkaJWupZSnU5xZSXvr1qBiHDY0OH0zKm/D2BbOMysH9akBH7A7VNIE/i9xuKtZUt4Z/lSAO6a9Qm/mnwwP5kwsWVuQrUqbfZRqhVEEwnWlm6jRzCHroFAvfsnHIdn53/PU/PmEkkk2KVLFzZVVBC0bc4Zvwcn7robVrKd/6VFC/i/96bjsSwQuOnD97hlylROG5uai2hDWRm3fPw+H65ahW0ZDh86gvq6Cgzu4md+j03MSeA4qS0Fd376MYcNGcbggoJGfDfc78f/vp/DcwvmIyKcNmYc5+4+AZ9H02W3ltZo9lkJlOD+Dj0gIg/WeP9S4FKAQYMG7bV69eqslkep1vbf777lzlkzEYS443DU8BH8+fCjCNiZl4S8+q3X+GDlilrj+gGCtpdjR47kriOOYWN5GYc+/giRGjV1v8fD8aNGM3PNagK2zWljxvH4d99QXBnCqbaW5fbgnkkXv58TR+2Gg8PzC+bXagryWha/2H8yl+21T4O+F+DmTzr3pef4duMGwsn7C9g2E/r043+nnKbpKpqgva7kdaCITASOAa4yxhxc/U0ReVBEJonIpF69dKFstXN5b8Vy7vj0YypiUSpjMaKJBNOXL+fGd6cDEHccPlmzijeXLqG4shKAhZsLeT9D4AcIxWO8sXQJy7cU8/aypWn3iSQSvLRoAZsqylm9bSt//fxTikOpgR/cwF9XqE04DrccOpUhXbulfUoI7lDQxvh87Q98t2ljVeAHCMfjzC3cyGdrf2jcyVSTZb3ZR0TWJf8vNMa8BOwDfJzt6yrVHtz/1Re1gngkEeeNZUtY8MRmlm4pBtwatAF+vv9kcr0+6vtEboAv169zm2Iy7Ft9e6KO81nG4MnQwTu0oBsARwwbwd2fzaz1vsdYHDl8RJ1lrembjesJx2o/2EKxGN9sWM8BAwc16nyqabJa8zfG5Bpj8rd/DRwJzMvmNZVqTzZVlKfdHnecqsAPbpqGqOPw/2bN5MWF8+tt+vAYi57BHKYOHe629TeD17K4YI89Cdq164ILijYz+dEHmb1+HRdNnIRtWe7DwhgCts01++zHsG7dG3ytUCxGUUUlXk/tMgdtL71yc5t1L6rhsl3z7wO8lPxFtoEnRUSzUKlOY1L/AbyxdHHG2nlNCRHmbNpY5z4G8NkeDhkyFJ/HwyUTJ/HQN7OJJj9hWJZFwqnZwJNZJJHgtDHjmDxwMFe/+RrlsWjVe44IG8rLuOG9d3BEsI1BRBBg6pBhXD6p4W39769cwTVvv45JXrMmj2U4dsSoBp9PNU9Wg7+IrAD2yOY1lGrPrt3vAD5YtYJQLFbV9FJfJ2t1Po8Hgzs6xm/bGAy9c3N54PhpVSNjfr7fZI4YNoLXlyxCBPYbOJAr33g1bYBNx7YsRnTvQc+cnIzHbC97rNpD7I1lS9j28gs8dtKpVSOPMimqrOTqt15LaeffLmDb9MrJ5f5jTyDf37L5iVRmOtRTqWZYWlzMiwvnUxGLcsTwERw4cHBKk83Qgm68eua53PPFZ3y1fh398vPxWhZfrFvboE8De/frz+8PmcqQggK+2bCe8miUEd27kRC3Vr496I7r3YdxvfvgiLCqpISBXbqyrGRLg+5hcNcCAGIJp96hnzV9vu4H3l2xjCOHj6xzv7eWLSGebu6AZXHhhL24bv/JjR7lE47HuP/LL3h+4XwccTh25K78fL8D6OKvfyit0uCvVJM9NW8ut378AbFEgoQILy5awCGDh3DvMSek1ISHFHTjL0cdW/V6aXExJz3zP0Lx9Fk6q5u3uZDBBQX89oN3eXnRAhIiOCJ4LYsu/gB3HnEUhw4ZBsB7K5fzm/dnUFxZWWcHb00byst56OuvGNi1K/3z8lm1bWuDj407Di8vWpgx+M8v3MSD33zFh6tW1kpIt/34gG03OvCLCOe99DzzCjdVfVp58vu5zFyzmjfPPh+vzheolyZ2U6oJSkIhbvnofcLxeFWgrYzF+Gj1Kj5avbLOY0f26MF/Tj6VMb16Y6h7qGVFLMaN777Dq4sXEnOcqk8LMcehOFTJ1W++xvItxcwr3MRP33qdwoqKRgV+9xpR7pz1CdfPeIdN5ek7qOuSrvMW3Db+055/mteWLKYsGk27D8CUIUMbfc2v1q9jYdHmlGaqmJNgQ3kZM1Ysa/T5OiOt+SvVBJ/+sBrb8tRqI6+MxXh9yeKq2ngme/UbwOtnnYeI8MW6tZzz4rNp+wECts0by5akHYYJbl/Af+bOYWs4nHGfhkiIUBHLHKAzybG9/Gi3cbW2iwi/fX9G2jb+6owxjOvdp9HX/b5wE/EaaSnA/f7P2biBY0fu2uhzdjZa81eqCfweO237uJUcAtlQxhj222UgE/v2T/t+RTRaZ1BPiLBqawlLi4saPKKoOQxuO73XstyZw2PHceCgwbX221xZQVGost7zbe9vaKxdunTBa9Vu2gnaNoOTcxNU3bTmr1QTHDR4cNqZrX6Ph9PG1K4J1+cfx5/I4f95lPJoNOUTQEPC+adrVtc72qalnLLbWPYdsAvl0SgHDRrM8O490u6X6/WRSFMzry5g21y3/4FNKsdhQ4aR5/MRjqeOovJ5PJwwanSTztnZaM1fqSYI2F4ePH4aOV4vuV4fObYXv8fDlXvvy4S+/Rp8ntJImH9+9QXH/u9xKqLROtv/M3EgbWdqNuzTfwA/GjOOH0+YmDHwAywr2VJnp2v3YJA/TT2SY0c2bVy/1+Ph+dPOYmK//lWfRMb06s0zPzqTLjpctEGyntitMTSfv+poKpLr3FbGYhw0aAj98vMbfOz6slKmPf0/toZDje6kbSvDu3VjYt/+lEYjfLtxAz2COVwycW+m7Tq6asTOXZ9+wr+/+yZje3+O18vXl1yJvxHNY3UpjURwxKEgEGyR83VE7Tmfv1I7pVyfj+Ob2Mzwp5kfURIOtUpbfUtZXlLC8pKSqteFFRX85v3prNpawrX7HcDS4uKMgd8AftvmD4cc1mKBH9CafhNp8FeqjXy4alWHCvyZhOJx/jH7C6YOG86sH1anHYUDMKZXb2477Ah279O3lUuo0tE2f6XaiN/eeSYixR2HHz37FF+s/QFPms5nn8fDSaPHNDjwR+Jx1peVNmv4qqqb1vyVaiNnjB3PI99+3SoBLmjbGdcHaCkxJ8Fna39IO0LJEUlJ2haJxymNROgeDKZkJU04DnfNmsl/5n6b7Pw2HDFsGOfvvid79uuvC720IA3+SjVDZSxGSThEn9w87EamVr5mn/353/ffZQz+AdumZ04Ofz3qWIZ27cZpzz/Nmm1bG9057Pd4+Nm+B/D52jV8uHpVo45trEgigc+k/z7MK9xEr9xc7vz0Y574/jtEhKDXy68POJgzxrlLTt775ef8d+63KX0Gry5ZzFvLljKiew+eOPk0ugU7b8duS9Lgr1QTRBMJbvrwPV5etABjDD6PhxsnH1IVxKqLxOM8NW8ury1ZRCC5Bu8xI0axrqyU0kgk7fm9xuLJU05njz59q2q7L59xDvd8MYu3kqt3rS8va1BZI4kEIsJJo8dkPfgDRKV2m3/ccfjzrI/5av1a/vf9d1XBPZJIcMvH79MtGODwYSN49Nuv035CiTkOS4uLuOG9d3jg+JOyfQudggZ/pZrgpg/f45XFC6vSO4TjcW75+H165roLrGwXSyQ444VnWFJcVBXwvtu4kU/WrObNpYsznj+BsFvPXlWB/5FvZnPHpx9X1fobO6nrni8/Y7cePRt1TEtbs3UbT1QL/NuF4nHu+eIzDho0pM5kd3ERPli5gnA8Vuf6x6phtMNXqUaqiEZ5edGCtEHs/i+/SNk2ffkylm0pTtm3Mh7jhYXzidTRBt8tEKgaDvnWsiXcMfOjlOaexo4SCsXjfFPPIjHZ5rFMxnKvLy8jYNv0yc2r8xwJEWKJumcOq4bR4K9UI5WEQ1gZ2rXXl5emvP5o9UoqY7Vrs/Hkso3pGOCMsbtXvb7ni8/oKGNe7ORaxOlEEgliGfo3xvbqjTGG3x40BX8dM4M9lqULvrQQDf5KNVKmzl3LGPaskdqhd24u3kZ2BBcEglw8ca+q1xvKGta23x7k2F4m9O2XdrgnuA+Hmt+PoG1z/QEHAXD0yFH89ajjMj5A+ubV/clANZwGf6Uayevx8KsDDkxZ8Nzgjs75+X6TU/Y9fez4Bi+wbnAfFjPO+3FKqoJRbdxW3xiheIzeubmctOtuad+POQ5ThgxlTM9eFAQCTB44iKdOPSNl/P/RI0Zy4KDBtR6wAdvmsr0avmawqpvm9lGqiWYsX8Z9X33OxvIyJvTtx3X7H5g2UL+3cjnXTX+LaCKRMd+Nz7K4eOIkrtx7P3K8qZ2Zi4s2c8yT/8nKPWSDz/LQMzeH9Wk+sQRsm9sOPYKTdxtT5zmKKyv58SsvsKKkBI9liCUSnDR6DLcddkSrZTDtSJqS20eDv1ItKJZI4IjUyl0TSyR4c9kSfv3uO7XG9dvGcPb4Pbh5ytSqfecWbsQ2FuP79MUyhreXLeVnb71OLM0wyvbGa1nYlpV2yGbQtvnm0qsalNtHRFiwuZAN5WWM6dWb/vldslHcnYImdlOqjWwLh/ntBzOYvnwZCRHG9erDnw4/kt169gLcpqJpu+7Gf7+bw/eFG4lV6+z1ejxcMGEiAB+vXsU1b7+OI4KIkOP18eAJJ3H0iJHMu/Ia3l+5gmvefoOY0367gPP9/owjmfbo06/BSd2MMYzt3YexTVjpS9VP2/yVaiZ3MfHnmL58WdU6u3MLN3LG80+zubIiZd9Hp53M1KHDq3LQD+5awL+nncrQgm5sLC/jijdeoTQSoTwapSIWY3NlBee/9DyhWAyvx8NRI0Zy7zHHEbBtgradsWO1Lf1sn/1THm7bBWybw4bWvbylaj1a81eqmb7btJEVW0tqBbxYIsFT38/lmn335/vCTTww+0tWbi1h7/4DeOucC+gWCFIQCOyYwbtoYdrUDY44zFixjBOTnahHDh/JzJ9cwvTly9gaDnP/l59TUcfkqNaUY9uM6d2b08eM44WF86uafryWRUEgwOlja8+AVm1Dg79SzbRq69a0QxMjiQRLtxTx3srl/PSt14nE4wiwdEsxLy9ayMtnnpOSp6Y4VJk2z0/ccdgaDqds6x7M4cxx7lyAh775qt0E/4QIwwq684cpUxnfpy+PzfmGsmiEI4aN4MpJ+2ru/XZEg79SzTS6Z8+0NfaAbbN777789v0ZKaN84o5DeSzK3Z/N5N5jTqjafuDAwTw1b26tSWHbF3lP55sN6ymp8WBoK0Hb5vSx46seaKeNGdek9YxV69A2f6WaaXTPXuzTfxf8nh11KcsYcr1epg4bVqvWDm56hreWLeXsF57lo1UrATho8BD27NsvZf6Axxj65uZRFk1NAJdwHP4882NOf+7pLN1V/Qbk5VctpD4gvwvXH3AQvzv40DYrj2qcrA/1NMYcDfwd8AAPi8gdmfbVoZ6qo4rE49zz5Wc8M/97IvE4U4YM5cYDD6EgEGTig/fXmbM/aNvceOAhnLv7BGKJBC8unM+dsz5hWyRSlQsnaNtcttfenDN+QtWoorYepO2zPCy6+tqM75dHozw9by7vrlxOz2AOF0zYk73779J6BexE2t04f2OMB1gCHAGsBb4CzhKRBen21+CvdkbXvv0Gby9fWucDINfrZXZyUfOPV6/iyjdfrdX84/N46J2Ty9qy0gxnaV1ey2Lx1T9P+155NMqJT/+XjWXlhBPxqhnQ2x9yqmU1Jfhnu9lnH2CZiKwQkSjwNDAty9dUql25feqRHDhwMH6PJ2POGjCs2rYVcGcOp0sGZ4ANDczhn22WMUwZMjTj+09+/x0by8oIJ9y+DsHNLPqnmR9REY22UilVXbId/AcAP1R7vTa5rYox5lJjzGxjzOzNmzdnuThKtb4cr5eHTzyZ98+/iDE9e6fdJ+4k6BHMASDP70s7ft8RafQqXs1hZ3hU+T0eegRzuPmQqRmPnbFiGeE0n3Q8lsW8wk0tVkbVdG3e4SsiD4rIJBGZ1KtXr7YujlJZ0y8/n1/WSAgHbnPO5IGD6ZnjBv9TdxuLN01a43QTp+rS3Olf8TS9CscNH8nNU6by2LRTeOL7Odzw7ju8vWwp8Rpl6558kNWUcISugUAzS6ZaQraD/zqg+hi1XZLblOqUDkl2BOd6veR6ffg9Hg4cOJi/HnVs1T4juvfg5kMOw++xyfX6yPOm/yRQF9uYRqeSbgi/10tXn59Tn3uKh76ZzbML5vHLGW9x1gvPpPRp/HiPPWs95Cxj2KVLF3btQFlKd2bZ7vC1cTt8p+IG/a+As0Vkfrr9tcNXdRaReJxV27bSI5hTVeOvqTQS5tMf1uD32Fzz1mtU1rHyV3V+j4fRPXuxcPNmovXkALKAxnyeGNW9B+vLyiiPpbbbB22b3x18aNXEM4BHvv2a/zdrJj6PRUKEfnn5PDbtVAZ00QRtLa3dJXYTkbgx5mrgHdyhno9mCvxKdSZ+2663BtzFH+DIYSP4cNVKGtqIY4Bbpkzl5N3G8tyCedz68QdVM4vTsSwLpxHNSQWBYNqF40PxOE/Pm8vJo8dUJW67aM+9OG3MOL4v3Ei3QDBlTWLV9rI+w1dE3gTezPZ1lNrZhOMxzn7xOZYUF1HZwPQNuT4fo3r0xLYszhq3OxP69uO5+d/z6pJFbA2Fcao9BoK2zYjuPZhXuKlBcwb8Hg8njNqV+ZvTd9jO31zIXg/9g2v3PYCLJ7qV0C5+P5MHDm5Q2VXravMOX6VUeo9/N4dFRZtrp3sg8x9uLJFgaLduVa9369mL3x9yGG+efT7Duncjx+slz+f2NZw8egx3H3E0wRqLx2y/hsEN+AHbxmd5GNurN+8sX0qmTyEJESpjMf76+ae8uXRJk+5ZtR7N7aNUO/XyogVpV/7yeTzcftgR3PTR+1REo1W19qBtc/4ee9LF746miSUSvL5kMa8sWUjQtvntgVPoEgiwsbyc3fv0qVoc5aXTz+Evn8/k87U/kBAhz+vj8GHDuWTiJH4oLeXr9ev45+wvmLtpI3ERvMlF2gO2nXbBllA8zr9mf8GxI0dl61ujWoAGf6XaqXSLxIOb6G3Pfv15+YxzuPPTT/hy3VoKgkEunTiJM5IpkxOOw09eeZE5GzdUNRl9vHo15+8xgV9PPjjlfCN79OCfx6Wfe7lLl67c+N70lDH7McfBwv1U8X3hprRDUAsrKmptU+2LBn+l2qkzx47n9pkfpdSuDdAvL5/BXQswxvCv49MH7fdXrmDOpg0pfQWheIzH5nzDueMnNHjETXEoxKaK8lrbHWDl1hJyfb5aiessY5g0YECtY1T7om3+qoo4FUh8DW4mDtXWzhi3OwcOGkzQtvF5POR6vRQEgvzzuBPrHTXz/soVaVNEWMYwa+2aBpchYNtkGg6e7/Pz24OmpIznt4whaHv5xX6TG3wN1Ta05q8QiSGlt0LoJcADxiB512Dl/qTh54ivQsruhOgXYPIh9wJMzgUYo/WLprItiweOP4nvCzcxe/06eufkcviw4Q1aA7dbMIhtWbVm3nosq1ELquT5fBwyZCgfrVqZ0rwTtG0u2GNPTtltLH3y8vjHV1+wrrSUSf0HcPU++zGkoFsdZ1XtQdZTOjeGTvJqG07prVD5HFD943sQ0/U2TPD4eo+XxEak6DiQCnZMGQpC8ESsrrdmocSqPitKtnD8U/+t1WHcxe/ni4sub/Ai6uAuTv/jV15gSXERHssilkhw/KjR3DH1SDxZmEWsGq/dpXRurLYO/iICkXeRyifAKYXA0ZicczFWbpuVKR1xyiGxBjx9MVb35p1LosimSaQG/iR7JFbPN+o9h1N6B1T+F6jZzODD9PoQ49Hp/G3htcWLuOG9d9wALeC3PTxy4ins3qdvk863sGgz60tLGd2rFwPydZZue9LuZvh2NFJ2dzKIhdwN5cuQ0MvQ80WMCdZ1aKsQEaT8b1DxKBgvSBQJHInp+ieMaeLaqE4ZGSf4Jwobdo7YN9QO/IDxQ3wZaPBvEyfsOprDhw1n9vp1+G2bvfr1b1ZNfbeevditpyZf3Flo8E+SRCFUPgZU7+yMQGI9UvkKJvfMNirZDhJ6DioeAyIgyWX9wjMQk4fpekv9xyeKkNDzEF8B3j0xwWlgdQMrH5zi2gd4x1d96VS+ChX/AGczeMdj8q/HeMe6b9ojIPY9UCOPjETBo6M+2lLQ6+WgwUPauhiqHdIGu+1i37q16VpCEP2wtUuTXsVDVH0qqRKB0EtVI3REIkjl8zglV+JsuwmJLXS3xxYgRUdA+f0QfhnK7kCKjganBPL/D6ieZtcAQUz+LwFwKh6F0t9BYgVIGURnIcVnV53b5F4IxlejXD7w7YOx0y88rpRqW1rz3y5j27kFVtPaSFucsyXTGyCVCAmk+AxIrAYJARYSegnpcitUPpzskN0uBE4MKf8LVtfbEKsbUn4/JH4A7+6YvJ9hvLu6D5Xye6n90Akh5X/HdPsXxh4BBQ8ipb+DxFrAgsCxmC43Z+GboJRqCRr8t/PuBaYgGTSrt4H7MDlntVGhavDuBdGPoGYaLqsHmK5I5X8hvoodnbeO+3Xp70nbJk8cwu9C19sw/gMx/gNr75LYCJIhLXD066ovjX9f6PkOSDkYP6bWJwGlVHuizT5JxliY7o+DZxgQBJPrjlfvegfGu2tbFw8Ak389mCC1fmzORqT4VAjVHK65nUWtB0bVSevpKLZ6kNoPUo1UIrLjQWmMwVj5GviV6gC05l+NsQdher2JxJeDUw7e3dpVIDPekUjBY1ByRu034/PI+Cw3AvbuEJtLaqesH4Kn1X1NKxcxAZDKNO86kFgP9i4Nu4FqxClzR1LFF4E9BhOchrHyGn0epVTTaPBPw9jD27oIaYnEofTXZKzF4+B21lZ/34DVEwJnQGxO6u4mB3Ivqv/CVn9ILEvzRgKJr8I0MvhLfA1SfBoQTjazBZGK+6DH8xgdHaRUq9Bmn44k/HayQ7U+vmSzVS5YfaDgfii/lVoPDQljItMbcLpDMr8Xeb0B5alx2dKbQbYlAz+4nc8lbooJpVSr0Jp/ByLh6aTvuK3ODz1nYOJz3DH83kkQ/RJJuwBHCAm9AoFpEJudnJA1zB2iWT1xmG8ihB4H0qwh62xt3D2IQHQWtSeWORD5pFHnUko1nQb/jsTqSv1Lbscg/Aom79KqLWJsMjYViYUUnwyJVSAOGAs8A6H7ExirKwDGvzeCh9rBP4gJHN2EG7FJ24ls9NdRqdaizT5tTBLrkYrHkYrHkHjdTTom5zSgvg7oBJTfgxOpliPJuyeQZgKbCQKOW+OXStw2+EqIr0BK/7hjN6sA8n+BOxHM7DjWOwoCx9Z3i6mXNAYCx6Qpjw8C9SeRU0q1DK1qtSGn4n9QdkfylUDZ3Uj+dVi5P067v/HujuRfD2V3JnP7xEk/tDMKW3+G5J4L3olIbHGNCV4AXgicBKHnqd2UFIPwm4jcWdX8Y+X+BPHugVQ+Bc42TPBoCBzf6NFQIgKBE90mHikDLDAe8AzD5N/YqHMppZpOg38bkcS6ZOCPpL5RdjfiPxRjD057nJV7HhI8AaJfuYE4OjPDBTa7SeDw4zax1GwqEoivJHMfQurELgl/gFQ8CE4h+A4A3/5NCvxS+lsIvY47Y9jjliNwDqbLr+tdoEQp1XK02aethGeQvh0+AeF36jzUWAXgPxSic+q5iOB+MkjXRxCH2OeZD/XuWxWMnYrHkK3XQuxrN/1D6AWk6EQksbGe69cQ/RLC2wM/uA+YOIT+V0fqCqVUNmjwbzNC5vH6da+xIInNSOktQBYXyQ64wztFwlD+V1Jz+8RBKpDyB1PLJYITno5TfDpO4cE4JVcgsbk73g+/BZKumcoD0Y9b/h6UUhlps08bEZNP+iYXDwSOyHxcYjNSdEKyvTxbC/F4MNs7ZOMrIO2CP3GIfrajXJJASi5KDuNMimxEIp9Awd8xganJrKk1J6EBxpC2Q1oplTVa828D4myDTBOacs7B2MMyH1vxSDLw1zfevzksSCZ5k/D7pO9UBjz9dnwdfsVdv7eWKFL6e0Qcd/2AdKOVJI54+iNOSXMLrpRqIA3+bSE8I8MbHjeZHMmadHwZklifukt0JnUHfk/yX6Da60Z2pFp9MPZQxNkCFf/KsJMPk3tx1SupfIFai7ls52wFpxDjHQd5V+B2QgeAIFWdviUXI4UH4Wz9ZdXaBEqp7Mla8DfG3GyMWWeMmZP817gB4TuzWmmjt3PctvTIJ8jmA5HiHyGbj8IpOnnHQ8DqU8/JE7hNKFby/wSNbh5y1rsLtUQ+y7DADW4yNv8B1TbU9YARBD9O2d+SK5Hhfmqwx1E14UvK3f/D05P9GUqpbMp2zf+vIjIh+e/NLF+r4/BnypXjAe84pOQqd1lFqQQiEF+IbDnXbTrJvQi3xlyXMFBJ05uGHKTiP8lJYOlY4B2TssXknErGdnv/Ee5KYBWPgpTgLo+5EuJfUWuoK2EIvYJIze1KqZakzT5ZJhJBQi/ibLvJHTLpbMXYgzKsDiZQ+RK10yg47nKLsa/d2nb+DW7SNpq4aHtDhF9FvLu76/DW4oB/SuqmwIngOxi3Gacaew/IvQIiH5Gx76AWSTMpTSnVkrI92udqY8z5wGzgOhGp1aNnjLkUuBRg0KBBWS5O6xJnC1L8I3cMu1QCAaTsHsQ7GpzVaY5IuGPp0yVQEyCxCQAr9ywk5xQkOgdKLqHhQbUxbDeLaNomI+N27gam7NhiPNDtHxCbg0Q+BIlB8CQs7ygk/B5ifDsWna+PVQCmW/NvQSmVkZG0w/gaeLAx7wLpqrC/AT4HinCjx61APxG5sK7zTZo0SWbPnl3XLh2Ks+33yfQJNYN5muGOVew0+wP4MD3fTsmdL4nNSNmfIPwm7oc4nzts0h6TfIhkSgBnJf/V1x8QwG06StORa++O6fEkUvkMhF4F48XknJlM+ZD6gVLiy5Cik8i4IljqicF0B8vvniv3El3kRal6GGO+FpFJjTmmWTV/ETm8IfsZYx4CGp/4vaMLv0P6QF5XwM0QsO1xKYHfia+F4uOq5cRPLuTS9e8Y30Sk6EfgZEoU52S+Too6PlFIFNlyPsQWVO0npfMh8imm4M+p+5o80n8farC6uyuoSaH7vKl4FIm8Cz1ealcrqim1M8jmaJ9qg8A5GZiXrWu1W5lGymS0fQhkelL5IhJb6r4ouaha4N8uBqU3g+mG6TXDzdOfrZa9xFqIfUPKA0JCEH5rRxm3b654jHofNv5p4FSS+ukgAvF1dQyNVUo1VTY7fO80xnxvjJkLHAr8PIvXap+CP6JWB2gmpgt0vSvz+/G5SNktSPGpOFsucUfLpOMUI+X/QkouBGKQ/zuwsrE0YnmG7QKxr1I3RT6s51wWRF4j/SeNSiS68zQFKtVeZK3DV0TOy9a5OwzThbRNPKZrchRNCLed3oYuv4Py+3CHaKYTT6ZwJnMmTwASUHE/VTXo8NtgWnNd3ARYPVI3SX1DTuv6VOAHXddXqRanuX2yRCSeDMJpAptnBASPcZtNPMMhcDhsOTvN8MZMHcMZZtJWqd504oD80JiiN1McsXdPnfLl3QMiTSyDsTHBk1uiYEqpanScf7Y4JRnGyAOJ5Vi552MV/A0r/6cQ+WBHrT6Fnw75fC46FGfrL3bk6sm9kCbfR8G/MZ4e9e+nlGoUDf7ZYnV118NNxzMw9XV8JbVnugIYt4mow3Eg/DZSfDZObA1svZKm/ap1xfJPaOGyKaVAg3/WGOODnAuonYohgMm/JnWTd880+wFIcjZvDjuyYXaUIY9xcDbC1kvd1b8aNMa/BkvTPCuVLRr8s8jkXQt5FydTMXjA6g1d/4SpkdvHBKe5nxRSmkYC4NsXK2capuc7kHuZO3Qz/3fJjuQOQKKQWE39cwoyJIVzypH4mpYulVKKDtmg3IFIOSZ4OpJzJYYwmJy069QaKxd6vOiuuRueAcYP3r0hsRKncDJ4J2DyrsV4RwLg2COh5Dyyl9PfQ/2dyg2RoGH1i+2zjWswhoZ8YpBEIVL5H4h+DfYwTO5PMPaIRpZVqc6lWekdWtrOkt5BnC3I1l8mFzexwNML0/UOjG+fBh3vVD4DpbexY9y7ARPEdH+u6gEgsUVIyRXgrGv5G7D3BLt/siM609DTajy7grM+uchMTRYNm02c7tA+mF4fYYzl5vgPv4vEF2I8QyBwDMbKQeJrkOJTkhPeYrhrIvgwBQ9g/Ps17bpKdTBNSe+gzT4tTESQLT+G6Oe4wSgCibXIlksa1IQhEoeyu0id8CQgIfeTQZLxjsb0ehsCx9LiP0ZjY7r+BdP1bvAeQP2LwTiQc0WG/Xy4o5Yak4HU5z7sCv7iBn6nBCk6Dtn2f1DxAFJ6K7L5MDfwl92dXAtg+6eghPu9Kv0t7alio1R7o80+LS3+PSTWUDuXTRypfBLT5Ya6j3c2ZVjkXCD6DVLxBBAG/xSMPQJT8DecRLGbRyj8tjtXIBEGWZrmHA3hB/8hbvNUYCr4D0M2TaTOxeITG6HibtLPSQi7Hd9Wb0j8AJ6hEHoREovT7OsD317g2x8TPAXj6e3eedldkFjHju9pJUjYfRjEF5P2k0ViA8g2MAWNuHelOg8N/i0tsYH0NfFY5pQM1UgiTMZ2btmClN0JJKDsHiTnbKwuN2CMHwk9C4lVyQdHE5tZMODpick5K7XcdQV+ANI192w/ZQ7GuzsmeELVJiexFkJLa5fTeDE5Z2MCR6VuT5sgz3Ezl1rdM+TJM3UsRqOU0uDf0uwxGdIZeMF0RRLFdU9aKv9jHScXdjQHxaDy3ziV/3PTKTiFNChzZkYG/EeCdxKy5UzEKXc7ndMuyl7juIxZSo07MilwZOrWnFOR0HPUzuUj4DsozXkyNWsl3Ml0tfggcCTGZHGxG6U6OG3zb2HGHgiBY6g9bj8OkRnI5ik45f/IfILYt424mgARt7O1QYHfAB43pUSt8nkgugjK/x/El4KzASKvgmyq43z1tOV7hmN6PFcrCBvvGMi/FrdtPwc3k6kFGGTLeUjkk9TzBI4n4xKRte7bC769MF10HWCl6qLBPwtM1z9B/nVgDWbHt3j70oQRKH8AiXyW/mDJ5ocxC7zjMPnXU7u2HgdZTfqZxml4hmO63gLe8Zn3CRyP8aQuOC/OFiQyC3wHQPDMZFqLZFOVVED8e6TkKpzQ9KpjTP51YA9PPihs6lzD2DMIpAIpOhqn5Bokvrxh96NUJ6PNPllgjAeTez7i3R0p+UmahG0ht/PXv3/tg4PTIPQ/mt5uX5cExBYjFQ/QvKUfLXfB9sBJEJ1bO4XzdhX/QILHYuwh7iiosjuh8gkwvuT3RMjYSVz2Jwi6zUXGyoMeL0P0U4gvRsSB8n+Sti8isQISyXNGpiPRj6HHCxh7eDPuV6mdj9b8s0kqyDhMUkrTbjb514I1lB3NKRaQC7k30CKpHYwNsUXNPIkHIYBsPgRCT9WxXxQp+5v7ZfgVqHwSiCTnAzjUuaKZs94d9lr1ugiJLUASG8EeROaHY/VzOu6ooLJ76r8lpToZrflnk3dC5lz20dk4G3cH/wGY/P/D2O7i9cbKR3q+CpUPQfRbsEdA7lVYnjyc4BQoOrqOC25/0GSYMQvVatzN4DsIyu6kQZ8eYl8kL/tv3PULGsh0YftCOBL5DNl6OUgCiLrrInt6u0NMieLejw93ZFLNe3Ma2Y+iVOegNf8sMlYu5Jyf4d0YEIbIh0jxqYizBcAdZbPlTKh40B1pE3oatpyOOFuw7GHUtcwjiNsubrrXVaqm3UwVGyRCg/sGnBBOyZWQqKvjuAYThNxLMcYgkkC2/jw5gzc5BFYq3fMFz3Y7g737Qu6VZOwU9vRLv12pTkyDf7bV1fQDuE0TIaTSbT6RsrvdiUtSCYSTk7ZWIdtudnfvcmM91xOQ4rp2aHjZ07G6J+cyNPQ8lRB5F6SEBj14TBByL8HkXuy+ji8i/YMmDLHZWAV3Y/X4L1b+lRA4jtqjj4KYvCsaWFalOg8N/lnnDmGsWxQis9wvw69Qe5JXHCLvIuJg5ZwF/lPqOFecun+szQn+Psi/Gfx7knltYov0NfDtnbvby5bue2KD/ySsvKurJcCzydi+b1KvY7reknwAuOkhMF2gy/9h/FMy35JSnZQG/ywzwRNpUEdtbC4i4QwreoEbAN0gaHW7A/JvpXaXjR/8hyYnVdW1cHxDm368pP6KRKH09+CbCiZQ4zxByLnUfTjUNRQTAXss6X/14hB+0R0ZJA4iMbBHpW/GMkFMzpmpm4wfq+AOTO/PMT3ewPT+DCvnjIbdqlKdjAb/LDO+CZD7Y9zmiDoeAsYD4ffd4F3rx2LAtw/G7Aj2Vu4ZyYVecpPrBfjAP8VdCN5/JJheGa6TC8ELqTtAw45O4xq1bimCbVdB7lVuWU0X8AyB/BshvgDKbgbSj2RyecAzjMwpoyPItl8hm3ZHNo1Hin8E+de7K5qZXNzvYwD8h0PgxPS3aOVh7F0wJtPEMKWUpnRuJRJf4Xbuht/LMC7ej8n/FeI/AoqOpNZImtzrsPIvq31eiUJ8NXh6IKHpUHab2xwiDjtG12z/GSeHjdqD3P99u0N8CZADxCH6ifsQwrhrCjghMo/Q8WL6fI9JLlUpkQ+Rkquof40BP1i5kOzgrm37A7Ja05fJhR4vY+ILIFHkPgi9u9ZzHaU6j6akdNahnq3E2MPAHgaeocjW+UDNPPnJ2n1iOZKuWabiPiT3DIxVkHqU8YF3JBJbAGW3446jr95B6qVqTL3JcVfXis9330p8D8HTsbr8BgCJr3aHRVq9EPyw9ZI6ughiSOQzTGCye2z4Axq8uIxTV6K4NEntJAah592ZvkqpFqHNPq3NfzB4dyNlyKYJQuAIjHdXJPwGaWvbxobIzKqXEl+NhF51x8CLg1Q+S9rAaXxQ8AB0+RNuU0u1B4OEoPJxnNK/IyIYezAmeBLGP9ltrqqvryL06o6vrYYsNO+FrneAPbIB+1YXhVi6FNBKqabSmn8rM8YD3R93g3Xo5WQa4zOqtV97yZgp09huoC/9DYRer9ZEUwDeUWQaFWOkHIl+lBwrn0bl/UhsLqbHI9XKaUO3+5At52S+mcTaHfsHT0YqHqbOBHP2rljB4xCrB1JyCQ2eK4DfbaJSSrUYrfm3AWN8WLnnYvV8HqvHU+DdCyLv4YRn1jEvIJnuOPQShN7Ebd6pdPd3NkBsKW7bfc3D4uDbF6xe1Pnjjn2CE343tZy+vaHrgxkOsMA3dse+9lDocmvdNx5f4O7r3w+6PVBHearfvwXGjwmelWFfpVRTaPBvQyJxnK2/QIqOddf83XohhF8ltQYfAIKYgr9jrFyk8glqNws54Gx2M19WjeIx7td5P3XXD4gtot5kcdtuQ2q0x1vBKeA7kFq/KiaAqTZ7WRIbITKdOoeYmrwd5/UfALlXUHvUUSA5Wqlb8uspmB4v1r0GglKq0ZrV7GOMOQ24GdgN2EdEZld770bgItyG5mtE5J3mXGtnJBWPQvhd6mz+8AzE9HgKY3VJHpRhQXVjQdfbMfGFSPgtMHmYnDMxvr2R2FyIz21AgdYjRUe4WTCrpUQw3f6JbLspOQEt4Q4j7Xobxt4Fic1Hyu93F3vPOHwzKXB8apHzfooYD1Q84nZSW90g79dYOemHcCqlWk5z2/znAacAD1TfaIwZA5wJjAX6A+8aY0aJSD3RYecnEofwG0joVYh+Sb3t3olVOwI/uAvFVDxMrc5dk4uxR2K8u2KCJ7kTpKKfIaHX3VE8DfrWCzhbkNLbMN3u27E5vgoi71A19l9KYNvPcRK/clMvE6FBM4dj81KLbCxM3tVI7pVuf4TJqTazVymVTc0K/iKyEEj3BzsNeFpEIsBKY8wyYB8gwwomnYOIg5RcBtHZNDjDpUlN5GZyL3Jr9omNyXN4ARvT9a4dY+5ji5AtP6bqwSIRGj6r14HIR6nlLr2lxpoEcbcvYfvQ0oaKL0ScEozVLfWejJWcwKWUai3ZGu0zAPi82uu1yW2dW/RTd9HxBqc29kPw9JQtxsqHnq9A6HUk+il4BmCCZ7jLR7L9AXMJSKZJVA1gavxaxL7JsGMjAn+V9jOpUKnOrN7gb4x5F+ib5q3fiMgrzS2AMeZS4FKAQYMGNfd07ZpEPsrcZg/sGOIZBJxkrv+f197LBCDnR5icH6WeP7Eeic0HKc9w+txk849x29ftocmmp+qTs7wQOKHGccHM52wMewTGqivdtFKqtdQb/EXk8Cacdx0wsNrrXZLb0p3/QeBBcNM7NOFaHYcpwG2mqTkT1uuO1PHtB76DMYTdQGkPadBpJbYI2XotJNbhjujJMNbeu0dyYfOEm49HtiFbznXH64vjdhp7hmHyf5V6XPAMd/nFlJq+352xHF9Jg5eE7Hpbw/ZTSmVdtpp9XgWeNMb8BbfDdyTwZZau1WGYnJORigepFfyNH9PjGYypL9labeKUuwE8w7KQO64RxASOw9iD3M7g8JtI9HPwHw32cIxsdVcN806q1Ydj8n+OJNZA5OPk+rtR8E+GrndB6S0Qfiu5fftKWmlmGuPBeHbuT3ZKdSTNHep5MnAv0At4wxgzR0SOEpH5xphngQW41dCrdKQPGM8ApOvdUHo97sgZd/lB0+2BJgV+wA28mZaKrGpGygF7VwhOQySEFJ/pJoOjEvdXIIFgg6cP5F6NyUldL8AYH6bb/Uh8DSRWgmdo1bKTFNyFODdCYj14BiGlf4DwG9SaU+AZmjpqSSnVpjSrZxsQCUP0Gzf7pnfPlFTNVfs4WyD6tTsxyrePmxYi3bnK70PK0y1QbsDeA+wBGP9UCByFMV6c8geg/D4yd9YGIf8XWLkXNO3eEhuQopN3rESG101h0e2xZL4gpVRL06ye7Zw429zlGqNfujXh3PPSBn6n4hEo+6vblIK4Ha7d/p0+jbF3j2S2zhodySaIyf+Fm0qhutBr1D1KJwTl9yA556QtW32Mpx/0ehupfNrNEGoPxwTPxti7NPpcSqns0eDfSiRRiBSfBE4ZbvD9HAk9D93+hfHvv2O/6NdQdg8QddvWAaQCKbkQen1c+xOAb7K72lVsETs6XgNgj3Fz+tRkaq5xm66wUXC2QRNTKhirAJN3eZOOVUq1Ds3t00qk/B5wtrKj1h0HQsi2G6ne9OYu5J5m9IxUph1vb4yF6f4fyLvCHcHjGQp5V2G6P5Z2tqzJOYt6V/EyNmj7vFI7Na35t5bIB6QdgukUg7MJPMmpFM420k+EMuCkH2tvTACC08Dq4TYB+Q91F3lJJ3gKRD+D8AzcXDw1O4uDkHuhLoGo1E5Og39rMXnA5jRvOG7A3r5b4Bgk9mXt3PsSB1/6/hyn7B6oeAg3/XHyw1y3BzC+fWoXw1iYgruR2FKIfeOO4Am/7j6ATC7kXoLJvbRp96iU6jA0+LeWnPOh7E5SUzvY4Ns/dQhk8HgIPZ1cuSqE2zLng/xfu6kdapDoV25WzKo8Psn/Si6H3p9n/ARgvCPBO9IdDJr/S9xPAF5NrKZUJ6HBv5WYnLOQ+Hx36UPjw51lOwxTcFfqfsYH3Z9wJ2GFp4PVFZNzFsabfiUrCb1Axhm20Vngn1J/2Yyh3iUblVI7FQ3+rcQYC9P1diTvpxBbAJ5+GO+YDPv6IHgSJnhS/SeWOtIpS1MSrymlOgMN/q3MePpBtYVSmn2+wHFI+APc2brVSAx8B7TYdZRSOxcd6tnR+Q9z8+xUdRrbQAC63Jy2j6AliIibTC46252trJTqcLTm38EZY0HBfRCdhYTfBSsfEzwJYw/LyvUkvgYpudgdHYQHcJD8mzH+fZDQS5AowQQOdLOTGq1bKNVeafDfCRhjwD8Z45+c1euIOMiWC8BZT0o/Q+lvkKokcjEk/LybdqLbwzpfQKl2SqtmquFi34JspXYHcww3jXNywphUQnSOO7JJKdUuafBXDeeU0PC1gENIqNkLvSmlskSDv2o438Q61g5II1OKCaVUm9PgrxrMWN0h7zI3xXSVAG7Hb82dczA5p9ferpRqF7TDVzWKlXc14t0dqXgCZBv4jwLfeCi5HHCSC8SLuwi8/4i2Lq5SKgMN/qrRjP9gjP/glG3SeyaE33cfCL59MfbwNiqdUqohNPirFmFMEILHtXUxlFINpG3+SinVCWnwV0qpTkiDv1JKdUIa/JVSqhPS4K+UUp2QBn+llOqENPgrpVQnpMFfKaU6IQ3+SinVCTUr+BtjTjPGzDfGOMaYSdW2DzHGhIwxc5L//tX8oiqllGopzU3vMA84BXggzXvLRWRCM8+vlFIqC5oV/EVkISSXEVRKKdVhZDOx21BjzLdAKfBbEfkk3U7GmEuBS5MvI8aYeVksU1vrCRS1dSGySO+vY9uZ729nvjeAXRt7QL3B3xjzLtA3zVu/EZFM6/RtAAaJSLExZi/gZWPMWBEprbmjiDwIPJi81mwRmVRzn52F3l/HpvfXce3M9wbu/TX2mHqDv4gc3tiTikgEiCS//toYsxwYBTS6gEoppVpeVoZ6GmN6GWM8ya+HASOBFdm4llJKqcZr7lDPk40xa4H9gTeMMe8k3zoYmGuMmQM8D1wuIlsacMoHm1OeDkDvr2PT++u4duZ7gybcnxGRbBREKaVUO6YzfJVSqhPS4K+UUp1Quwj+O3uaiEz3l3zvRmPMMmPMYmPMUW1VxpZijLnZGLOu2s/s2LYuU3MZY45O/nyWGWNuaOvytDRjzCpjzPfJn1eHH5FnjHnUGFNYfc6QMaa7MWaGMWZp8v9ubVnG5shwf43+u2sXwZ8daSI+TvPechGZkPx3eSuXq6WkvT9jzBjgTGAscDTwj+2jpDq4v1b7mb3Z1oVpjuTP437gGGAMcFby57azOTT589oZxsI/hvv3VN0NwHsiMhJ4L/m6o3qM2vcHjfy7axfBX0QWisjiti5HttRxf9OAp0UkIiIrgWXAPq1bOlWPfYBlIrJCRKLA07g/N9VOicjHQM3RhdOAx5NfPw6c1JplakkZ7q/R2kXwr8dQY8y3xpiPjDEHtXVhWtgA4Idqr9cmt3V0Vxtj5iY/nnbYj9dJO+vPqDoBphtjvk6mW9kZ9RGRDcmvNwJ92rIwWdKov7tWC/7GmHeNMfPS/KurFrU9TcSewC+AJ40xXVqnxI3TxPvrkOq5138Cw4EJuD+/u9uyrKpBDhSRibhNW1cZYw5u6wJlk7jj23e2Me6N/rvLZmK3FDt7moim3B+wDhhY7fUuyW3tWkPv1RjzEPB6louTbR3yZ9QYIrIu+X+hMeYl3KaudP1vHdkmY0w/EdlgjOkHFLZ1gVqSiGza/nVD/+7adbNPJ0gT8SpwpjHGb4wZint/X7ZxmZol+Ye13cm4nd0d2VfASGPMUGOMD7eD/tU2LlOLMcbkGmPyt38NHEnH/5ml8ypwQfLrC4BMSSk7pKb83bVazb8uxpiTgXuBXrhpIuaIyFG4aSJuMcbEAIeGp4loVzLdn4jMN8Y8CywA4sBVIpJoy7K2gDuNMRNwP1avAi5r09I0k4jEjTFXA+8AHuBREZnfxsVqSX2Al4y7JocNPCkib7dtkZrHGPMUMAXomUw/cxNwB/CsMeYiYDVwetuVsHky3N+Uxv7daXoHpZTqhNp1s49SSqns0OCvlFKdkAZ/pZTqhDT4K6VUJ6TBXymlOiEN/kop1Qlp8FdKqU7o/wMwymycoQVPzAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,y,centers = make_blobs(n_samples=600,n_features=2,cluster_std=[1,1.5,2],return_centers=True,random_state=42)\n",
    "plt.scatter(X[:,0],X[:,1],c=y)\n",
    "plt.xlim([-15,15])\n",
    "plt.ylim([-15,15])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "fc552507",
   "metadata": {},
   "outputs": [],
   "source": [
    "m,n = X.shape\n",
    "k = np.unique(y).shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2617d0f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#initializing our mu\n",
    "np.random.seed(42)\n",
    "x1_mu = np.random.choice(X[:,0],k)\n",
    "x2_mu = np.random.choice(X[:,1],k)\n",
    "x1_mu = x1_mu.reshape(k,1)\n",
    "x2_mu = x2_mu.reshape(k,1)\n",
    "mu = np.concatenate((x1_mu,x2_mu),axis=1)\n",
    "mu.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9ad30c63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-15.0, 15.0)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pQ/D288KwGrTr3YqoU7HsXrOPB6dPwp7pYEr3h7j+4REkRCUydOKVvPnn85w9cp6J7R+kZZdmDL1zIMH16xBcP/8lJtKS0/nqxe+xWAx+S/tGVgUTNZIEf1GkuMgEPrh/JndMG0eD5iXP4XOxQbcNICEqiSeGTuPTXe/QqKXzuYCbuxt3v307rbtfeOPw8PKg26COPPH1A/jV8aXJJY1Z8+MmlsxaQb8xvXn4k3s4fyyKpV+voteIbmTa7PjW8SUhKoEvnp1Lg+Z16XtDL0IbBzP+6Ru4ctwV1G9WeIJZbz8vXl/6LPFRiRL4RY0lwV8UKeZMLJsW/sWQO64sl+APMPiOAdRrGkbDFvVIiE5k/S9bCIsIYfCE/lgseRdz6TSgA5k25+ze04ecM4RXzl3HgLG96T6kC3f+xzlD1Opm5d3VLwFQv2ldWnVvkb19/FPX5ypTa018VCJ1wgLy1NexX/tyuU4hqioZ6imKxTTN7MXSy9Oy2avZu/EAv360BKXghfmP5hp7n9Md7R4kvE1Dug7qyAcPzsQ30IdWXZty+sA5Zh18P9ex9kw7Qz3HEVSvDnNPz8i3vOVz1vL67e/z3vpXaNG5ablfmxAVRYZ6Cpcpz8B/6uBZnhw6jX9/PoVZz80hLCKUt1a8wOFtR/n4/77E1Jpe11z4fxx5Ioq1P21m4PgraNiyPv1vupy2l7Xk/ftnctmI7qTEp+apw+pmZfR9Q2nTo2WefWt/3sR/xv+Pm5+9gWYdI9i4cKsEf1HrSPAXFc7d042AUH+8fD15f9OruHm44eXjSd2IUGa/8iMv3/Q2c07PwK+OLwBrftzEJ499zcy972b312dm2Ik6Ec0ll7eh6SW58/QkxiaxedF2Jr91W75dSAEh/pimScyZWLx9vTi574zrL1qIKka6fUSVcmj7Udb/spnxT9+Q/WnDYXdw7lhkrgljOZmmydY/dtKxf3vcPdz4+YPf+ejhL/hoy2t53hiEqImq2kpeQpRYi05NueXZm3J1M1mslgIDv8PhYMkXK3jm2ldZ/f0GAIZOvJK3V7xAkw5lWyAkJTGVT5+YTfQZyUYuah4J/qJactgd/OeW/3FPl0d5686PuP3FMVw+ugfgzBDarlfrUg/TPLT9KDfVv5MVc9bywzsL2LfxYHk2XYgqQfr8RbVkS7exfdnfNGhRj/a9W3Pdg9fg7uFWLmX7B/nS9JIIOvZvz7cnpxMQ4l8u5QpRlUifvxBCVHPS5y+EEKJYJPgLIUQtJMFfCCFqIQn+QghRC0nwF0KIWkiCvxDVTGJGOlMW/sre6KjKboqoxiT4C1HNxKWls+bEcY7Fx1V2U0Q1JpO8hKhmIgID2T55iiw0I8pE7vyFqIYk8IuykuAvhCjQZ9u28PiyxZXdDOECLu/2UUodA5IAB2Av6RRkIUTlORIXx7G4+MpuhnCBiurzH6C1jq6guoQQJbQ/JpqvdmzjqT798XK7kCBv2pVXV2KrhCtJt48Qgp3nzzF/315i0vIuiSlqpooI/hpYopTaqpSadPFOpdQkpdQWpdSWqCgZtyxEZbixXQf+mnQvPm7ufLljGxl2e4HHPrt8GU8t+6MCWydcoSKC/xVa6y7AUGCKUqpvzp1a6xla625a626hoaEV0Bwhqo+0zEwSM9IBSLHZCg3Kr61ZxbTVK4osc290FCcTEvJs97BaWXn8KC+vXlHoBDKbw06Go+B2lERSRgZJGRnlUpYoGZf3+WutT2d9j1RKzQd6AKtcXa8QVYndNPli+18MadGSRv4BxT7vzl/nczY5iT9vnciIOV8R7h/IF6Ouz/fYU0mJmNrMte1sUhI+7m74e3heKPOX+QR5efHFyOsJ9vbOdfyIVm1oFxpGq+CQAtv06lWDi93+ooz/cR4a+HXcLeVWpigelwZ/pZQPYGitk7J+HgS86Mo6haiKziQl8sa61VgMgwmduhT7vEldumf3w9/ZuRv1fHwLPPa9odfk2TZq7mzah4Yxc+R12dv+O2Q4t8z/npdXr+CdwcNyHW8xjEIDf3mb0v0yNFVnQanaxKUreSmlmgHzs15agW+01tMKOl5W8hI12anEBOr7+mHJsTj9hlMnOZEQz47zZ3l5wNXlPnlr0aEDWJXCoWFIi5YAmFrzy/69dKnfgPCAwHKtT1SOKreSl9b6iNa6Y9ZX+8ICvxA1XSP/gFyBPy4tjdt++p6vd25nzYkTLrn/HdqiFWtOnuDBxb+RYrMBMHf33zy2dAl20yzwvB3nznLbT9+TkJ7uglaJqkBy+whRSep4efHpiNG0DQ0jJKvv/dU1K9l4+hTzx4wvt3oe6XUFY9pfgo+7OwB9w5twX4/LaOhX8ML051OSORATzXd7dvHFjr/4dewt1PHy4q31aziXnMwbVw8pdXs+3rIJhza5t/tlpS5DlJ2M8xeiEvWJaJId+E2t+XHfnuw79PLi7+FBu9Cw7NcN/f2Z2uMyPKwF3/sNat6S9RPvpl1oGC2DQvDMOjYhPZ1tZ89w/bxvKG2X8fpTJ1l38mSpzhXlR4K/EFWEAno1bEynevU5GBNT5vJOJiRw/6IFRKWk5Npuczgwixm4ezcO5/OR12XP+n1xwFXc1qkLdTy9StUmm8PBxC5dmVXAiKXSiEpN4UxSYrmVV1tI8BeijF5a9SfXz/umzOUopZg2cBALDu5n7u6defZHpiQzfctGNp0+xZxdefcDaK35bs8ujsTFciIxnj+PHeFcSnKuYwZ99Tk3/ziP7p98VOibzD2//cyHmzfm2X7LpZ349NrRxX44rbXOHsu/5PBBJv4yn42nTxXr3OKYvOBnbp7/XbmVV1tI8BeijJoE1KFJYGC5lOXr7s4ft0zg37375Nm3+sRx3t6wjulbN/Hq2lX53r2nZGby7PJlzP57B5c3jmDn3fdhNQyeWb6UDLudxIwMWgQHM6BJM9qFhhLg6YGpNff89jO/HtiXp6zt587y/qYNZbqm+fv20OPTjzgSF8vAps15d/BwujdoWKYyc3qqTz9e6D+w3MqrLeSBrxBldEvHztxC53Irr6AHsaPbtKNnw0aEeHuTZLNh5HPn7evuzqLxt1I3az6AoRTbz51l/r493NutJ3+dPcOq48e4s3M37uraHYBMh4NDsbF5Zv1+OeoG7l7gfFOY2qP0D2c71q1H08A6nExMoFmdIIa1bFXqsvLTtX75vZHUJhL8haiiEjPSsRoWvLP62w2lsmcHe1rd8j3nQEw0QV7euTJzjutwKde1aYeH1coQn5Y0CfwX7ULDSMzIIDYtlSAvbyZ06sL1bdvnKe/ubj2o7+tXpuuo5+vHuZRkdp47R7+IpmUqS5QfCf5CVFGj536Du8XCZY0ak2yzZQ+vPJWYwIID+6jr48vuqEie7jsg+5wbv5tDr0aNmX7NyOxtDy1eyM7zZ/lw+EhaB4dwNGvt3+dWLGPbubO8OGAgL6xcTougYHo0bJR9Xobdzrgf5jKyddsypXTwcXdn48S7cbNYSl2GKH8S/IWoIk4kxPPuhnU81ac/7hYL17Zqy3ub1+NltdLAz5+/I8/zyuoV9Alvwn83rmNQsxbsjnYGf5vDwe7I8/xvyHAa+V/cbaQ5kZDA3+fPsT8qikf+WMTAps0Zd0lH0u12rmnZho5169M+NIxnly/l0rr1uKFdBzysVqYPH0mL4OAyX5sE/qpHgr8QlexATDTjfpjHxM5dWXz4IBM7d+W1tas5EhfLzGuvo1O9evh7eLL6+DFOJibg6+7Gc30HMO6SjmQ47JxKTGDdyRM8vXwp390wlqPxcfh5eBCW1e//zuDhvDpwMB5WK/N2/02zOkG8NOAqNJo1J46RnGmjQ1hdADadOY3dNLmhXQcA+jXJ3U2TYbdnzw84Hh9PPV/fAucLTF34KxrNB8OuddU/nSgDGe0jRCWr4+lFx3r1GNS8BTvuvo/2YXWZ2uMynriiH30jmmRn5OwT0YQ1Eybxw949fLv7b5RSvL9pI1d/9TmXNWzMfwYOwsfdnXt++4WPtmwiLi0tu45/AvRN7S9h8c23E+rjw+nERJYcPsSJ+Pjs434ffxuvDByUq33rTp6g/6xP+XHvbjp9/D7bz50lIT2dIbO/4N0N6wq8rsb+ASXKYCoqltz5C1HJQn18mHntdbm25ex7v9js627C+u230KQJj5w4wd316uETGEr4+PF8tXM7AJtOn+a6ed+w/LaJec43tWb8j/Oy32ysRu57wHPJSTy/8k/GtL8Em8NBXR9fgr28aREUzMjW7WjsH4C/hwfP9ruSyxo1LrCdj13Rt8B9ovJJ8BeiCtBas+3cWdqHhhWadgHA97vv4N57ITUVBfiePYvjrruIT0vjpttvp21IKGmZmcQXIylbZEoyDy9eyPP9B9ImxLmY0u+HDrL86BGiUlI4FBvD9slT+eGmfwFwad162eeO63ApANNWryAmNZW3L0oPLao26fYRogrYFx3F2B/m8t2eXUUf/NRTkJp7rV1LWhrGU0+x9ewZgry86BPRhBGt2+R7uqEU314/hssbR/DvP37neEICiVkzcM8nJzNt9QoyTRN/Dw9+HntzkTN5Mx0mmaYjz3abw8Gq48dwFJI9tCDx6WnM2vEX6fbMEp8rikeCvxBVQLrdTv+IpsWbAHXiRL6bA6IiuXvBz8VaynHHubOsPXGCPVGRfD36huxupjAfH6YPH8mo1m24t1tPmgTWyT7n1/37uOabL/Mknutavz4xqWnYHBfeAGLTUuk/61Mm/vIj607mbW9sWipzdu0k05H3TQNgzYnjTFu9krUnTnDXr/PZHxNd5DWJkpFuHyHK4HxyMosPH+Rfl3TM03d+sbTMTKyGkWfY49qTx/lhz27WnzqB1SjGkMjwcDh+PM/mM4GBWAzFf7Ie2Manp7Ho0EGub9se9xx1ZtjtjPtxHiFe3mybPBWtNSuOHiHDdLDt7Bnq+fry9uDhgHOi2c/793Fju/ZYDQN3qzXPJ4Ekm4349LRcWT4NpQjx9uHGdh3yfS6w5PAhnl2xjEvr1suVcfQfw1q2pmVwCFal2HrmNGeSEmldgSuM1QYS/IUog98PH+CV1Su5IjyCZnWCCj126OxZtAwO4ZMRo3Jtf2nVCixKse6Oyfh5eBR4vs3hYOa2rYTc/C9GvfUO1px9+t7eOF5+mdmjb8ge4rns6BGeW7GMdiGhdKxXP/tQU2sa+PrRu3E4+6KjeHDxb5xISKCxfwABnp7U9fHh9k5dAecd+EurltMyKJihLVsxtGUr7KaJwzSzF6b51yUd+dclHXO1NdDTi1/G3lzgtVzftn2BgR+cbx6tg0P4ad8e7FrTKkgCf3lz6TKOJSXLOIrqJtPh4ERCPM2Dip4INXPbViICAhnYrHmu7ZEpySgUoT4+hZ5/JC6Wq7/6HIsyePz4Ke74/gc4cQJHo0bseehBOjz4UK67crtpsj86irYhoSRn2jCUwXMrlnJXl+60CQllwKzPcJgmp5ISaRoQyLCWrQj08mJiZ+dqgB9v2cTyY0d4rt+VtAkJzS579NzZeLu5Mfu6m4r1b3QwJoYMhz17LkFJ7ImK5JO/tvDygKuyF6MReVW5ZRyFqOncLJZiBX6AOzp3zQ78iRkZHImLBSDMx7fIwA/QrE4QT/ftz7gOl3LHm2/BsWNgmnzy4/dc76Y4mXghMdufRw/zf0sW0TIomJ/276XHp9PZdvYMSw4f5kBW//mMa0bx0oCrGNW6LfNuHMeWs2dYfeJCd1J8RjqH4mIJ8fbJDvzrT56gWWAdRrTK/2Fyfv79xyLuW7Sg2Mfn1C40jHcGD5PA7wLS7SNEJXhh5Z8sPnyQ7ZOnFvmsIKcJWd0xAK+sXsGBmBjeHzaCTvXqZy/GnpCezoID+9l05hS9Z85wpk/Wmt1Rkcy7YQxts7pamgcF0bROnexZvFc3a87CgwdYeHA/w1q2plejcObs2klcelr2m9OHWzZyPCGet3IM60yx2XhlzUru6NQl3zfCtwcPy/UwWFQNcucvqrfZs6FJEzAM5/fZsyu7RcVyT7cevH7VkBIF/ov5e3ji7+GBr7s7rYKDGfv9HNadOM7sv3ew4OB+vh59I0NatGRQ85b0jWjK9K2beGfDOhLS0zmXnEznj9/n8s8+zi5v1o7t/HXuLC+u/BOAvhFN2DZ5Kq1yPGidPnwk7w4axi/79/LDnt1sPnOKyNQU5u/bw66oyDxt3Hn+HFvPnsmeQyCqDunzF9XX7NkwaVLuMe/e3jBjBowvvwXQq4MzSYmM+X4u6fZMMux27u/Zm4mdu+Z6BnA4NoZATy/G/TAXH3d3EjLSaRccyvvDnbl3Umw2Ptq8kX5NmtI9xwzjhQf389Kq5fw05mbq+vry5LIl/Lh3N6bWXN44gs9HXZ8r509ODy9eyLKjh9k2eWq+6w+I8lGaPn/p9hHVVz6TnUhNdW6vZcG/gZ8/qyfcxfQtm/hyxzZaBgXnGZL5T5fMAz174+PuTv+Lk7Y57Hy2fSuGobikbl0SMzII8/Glrq8vrYNDs9cIeLJPf9qFhvHpX1t4acBVLDy4n4716ue7CM20K6/msYy+EvirILnzF9WXYUB+/3+VglLMKi0Ph2JjOJeczBXhEWUqZ9b2vwjy8mJE67YlOu90YiL//uN3XhxwFS2CCh96ajdN4tLTuHX+9zx5RT8WHNzPsfg4vhp9I48t/Z0/jx5l2+QphQbuxIx0enwynZsv7cTTffuXqK2i/MhoH1G7hIeXbHsF+M+alTzwe+lGtuQ0Z/ffzCtOqocc4tPTuHfhz2w4fZLbfvqeL3dsA5x5g47ExeaahPX1zu20+/C//HpgHxbDIDothbo+vrQKDsHdYuH2Tl15qk+/7MCvtWbb2TOM+2Eu0Tk+bfl7ePLjmH/xQM9eZb5mUbGk20dUX9Om5d/nP21apTXp1YGDiU1Py3ef1prEjAwCPD2LLOenMeNL3FUSk5rKkbh4/t3rcpYdO5o9wubTbVt4fe1qnu47gK1nTvPKwEG0Cw3D3WIhMjmZKd178vjSxXSt35BzKcmsOn4MU2va55iA9dyKZfx6YB/ebu6kZtoA7+x9BU3UElWb3PmL6mv8eOfD3YgIZ1dPRESlP+wN9fEpMA3B/H176PnZdA7FxhRZjofVWuLVr2LS0lh7xySCvHx4oGcv7uzi7AWYu+tvgr28MYCFhw7w6/69dKnfgF333M9Dl13OI4sX0bFuPe7q0g0FKOCxpYt5be3q7LL7N2nKje06sGbCXdlDSkX15vLgr5QaopTar5Q6pJR63NX1iVpm/PjsyU4cO1alH/R2a9CQWy/tlO+D0bI6nZTIzfO/Y9b2v3h/83pmbtuavc/fw5N6fn6MbtuelkHBuRZ397BamT92PH3Cm/D+5g38Ou4W+kQ0Yd4NY3knayz/0iOHmLpoAeEBgdzw3bfZawCL6s2lwV8pZQE+AIYC7YBxSql2rqxTiKoqPCCQJ/v0zw6+55OTS5XuOKcUm43/bVyPm2Hw/tBrSLJlkGLL5O1BQ7OPGdm6DaNat8XX3Z0n+/Tj3Y3rOJ2YmL2/dXAIdu3gXHIym06fBCAiMJBgb2fXjs3hwGGaJGSkE5WaQlqmpFmuCVzd598DOKS1PgKglJoDjAT2uLheIaq088nJ9J/1KQ/07M3d3XoUeNyoubNpGhDIO0OG59p+ICaaZJsNrTXvb95Ay+BghrZohb+HJxkOBwGeXtnH3tapS/bPvm7uhHh5Z2f5jElNZdaOv1hz4jinEhN4de1qfhqT+9PTsJatGdayNQBTul9W4mvNsNtxt1iKXBdAVCxXB/+GwMkcr08BPXMeoJSaBEwCCK/EURpCVKQQb28e6NmbQc1bFHpcjwaNiAjIuw7uY0sXsyvyPDe068Ctl3Zi+pZN7IuKYtu5s3wyYlSBD4s712/A91mrcgHsjDzH9K2bebR3H8Z2uJQrmzbP97zSSsvM5PLPZzC2/aU8enmfci1blE2lj/bRWs8AZoBznH8lN0eICmExjELv+P/xZJ9++W5/d/Bw3t+8gX4RTXhm+TLS7Zk0rxPE6aRE7KZJzsTQP+51rhXwxtVD85QzoEkz1k6YVKzEcqXhYbVyfdv2eSaUicrn6uB/Gsi5kkOjrG1CiFJKy8wkIjCQN64eAkC/iKa4WyzZ+fUvti86ip3nz6O1RimV/f0fhQX+UXO+prF/AO8NG1GqthpK8VSf/qU6V7iWq0f7bAZaKqWaKqXcgbHALy6uU4gaa3fkeTrP+IA/Dh/K3ubl5lZg4AdnOobFN9+OUorv9uyi84wPiEpJyXWMwzT5eud2Np06xbsb1mXPEVBKsebk8QKXWxTVl0uDv9baDkwFFgN7gXla692urFOImqyRfwA3tuuQPbFKa81P+/ZwKkcu/8K0CgqmX0RTfC/Kj386KZGXVi3ns+1b+Xjrpuw3h3u792RIi1b5Zh/9eOsmBn45kwy7vYxXJSqD5PYRohqLS0uj12cfM6FzFx67vG+ZyjocG0ND/wCSbTZCvL2LPH7RwQP8vH8vHwwbUegnD+F6pcntI8FfiGpuf0w0jf0D8M4xeUvULpLYTYgaKDEjg6u/+pyf9+/Nd3/r4JBKD/ynExOZvmWjrNhVjUjwF6KKsxoGQV5e+FWBdWwLmpG8/NgR3tmwrtjPHkTlk24fIWo4u2liKFXmBVUWHtzPY0sX88u4W2gaWCfXPlNrziUn0cAFeYtE0aTbRwiRx7BvZnHforKvMdAiKJirm7Ug2Cvvw2BDKQn81Uylz/AVQrjW8JataXLRnXpptAoO4e2sTJ+i+pPgL0QN90DP3pXdBFEFSbePyKYd0eiUL9DaVvoyMvejzaRybJUQwhUk+IsLMlagk14H+6Gij82H1mnomBvQSW+Wc8OEEOVNun3yobUddDrK8K3splQsr9Eo964oa+kyMCrlBYFvgrVtOTdMCFHe5M4/HzrhKXT0VVSlYbA5aZ2GmfRftONcuZarlKXUgT+7DM/BKKusyyBEVSfBPx/KazR431l1Vx6yH4WUGWDbVKHVam1DZ+6q0DqFEK4hwT8fyuMyDN87K7sZBVJu7VChK8Cz4BzrBX1q0RkrMCMvR9tPlLzi1G/QMTeh7UdKfq4QokqRPv9qSllCC9yndTo6aiDaexyG79TcO40wsLaC0jzP8BwBygcsESU/VwhRpUjwr5HcwKMPWC/Ns0e5tUMFfV7KcjMgaRooC3hdV7YmCiEqlQT/asxMneMcleR5NRgNsp9RKGVBBbxa/hUadcBzqIzmEaIGkD7/akprDekLIfU7dNTVkPG7y+tUygvcr0Sn/ejyuoQQriXBv5rS0Vc7+96D5oDvfeDWo1jnmcmfYEZfi9aZpavYtg7Sl6B1/ql9S0LbdmBG9kFn7ilzWUKIkpHgX1159AX3nhgWPwzfe1CW4OKdZ4SCUY/S/uqV/7Oo0D9Rqhz+6xj+zjcwVcsm0wlRBUg+fyGEqOYkn38tZqb9ghn/RKnP1/YTmDH/kjH8QtQSEvxriszdkLmt9CkpdDI4Tju/CyFqPAn+VYCZ8AJmwtOlPl/rNJTHFWCJQMdNKqSe5zCT3svnfBtYW2KErUS55Z0bIISoeST4Vwk2KEMOfdJ+RsdNBksYuF0CgJn2B2b0dWgzx52844zz6yI65iZ01GDM1G8LrUZre7klkzNjJ2AmvlQuZQkhSk4meVUBRsC0shXgOQJlBIPHwByjcDSQezimEfSJc4/OhLRfwPMqlBEAXjdC8kxIXwHe4wqsRidPh5TpELoCZQkpW5uNEOfIIyFEpZDgX41pMxZUAMrwAc+rc+0zvAaB16D8z7NtgsRnUJjgfSOGz3i09zig8CymymsYWnmBEVSMtiWC8iswM6oR+EaRZQghXEe6fSqZmfwJZuJrJT5Pm3HoyP7o5A+Kf462YybPhLgJ4H07eI3K3qeUUWQKa2VthuE7sdAx/lrbnJPIIi8DmQksRJXlsuCvlHpeKXVaKbU962uYq+qq1uy7nV8lpQLAdzLKczAAWpto7Sj0FB3/IKR+CqoueI2AzO1oRyRaa0z72UJn/ZoJz2FGjyxm49zBvTe4l2jYsRCiArm62+cdrbUs6FoII/DdUp2nlIHynZL9WsfdAToNFTy34JO8rgf3Lhg+d6B1Bvp8N/C6FuXRB+LvR1s7oEIKuFt368DFzxDyb5c7KuT7El2L1uno5M9Q3tejLPVKdK4QonSkz78KM1PnoaxNUe7diz7YYxCQnmuTztyLjn8QFfhflFsbDM8BwAAAlPKAoM/A0gTQ4H45eAwpsHjD+0bgxtJeyoU2OWLAPIdya39ho/0YpHwI1vqSKlqICuLqPv+pSqmdSqmZSqk6+R2glJqklNqilNoSFRXl4uZUPdp+CjPpPedY+4slv4NO+bJY5Rg+/8LwuSP3RuUGyhudvgQz8ZU85yj3HihLGMpSFyPoc8jcgpn8Yf7tNBPRmfuK1ZbC6KRX0LH/wsw8ixn3AKY9EuXWBhW6DDxHl7l8IUTxlCn4K6WWKqV25fM1EvgIaA50As4Cb+VXhtZ6hta6m9a6W2hoLRz6Z1vjHD7pOJVnlwr5DVWGUTHK2gIjZD44ToJta9EnmDHOr3zopDfRMTeidXq++4vdJt8HUIEfQPo8yFjk/AKUpV7VXTNZiBqoTN0+WuurinOcUuoTYEFZ6qrOtP0kOvYWVMDLzpm4ZI3WSXgcfB5Eha7Isyyj1umgTZThWeb6ixpWqbUdzPMYQTMLPsh7Irj3QKmytUdZw8EaDm6XoA0/lPeYMpUnhCgdV472qZ/j5Whgl6vqqvKUF1gaOlMY/8NMBNt2lHku3/V4dfwT6OhhxcrVo3VasZtiJr6MmbYo98bUL9FRg9CO0xfKzDyIdkRfOCZjMSQ+izbj860/326r/Nqa+TfajEUZARg+d+T7ZqLNJOezASGEy7jyge/rSqlOOKeaHgMmu7CuKk1ZQlDBs3Nvs0ag6m4s+ByfW9EevYvsCjEz90PMDRDwIsqr8D5zrTVkLAedCV5DL+zwuBqFBqPuhWNjx4F7d1Sdj5ztce+JdpzPN/e+jh4Nlgaowj454JwDoGPGgcdwVJ2C5zbouHvAPOt8DiCEcAmXBX+t9S2uKrs2UO6dUe6diz4wZSZgR1vbFzE/F5RS6ID3IGEqOnMXWJo4A63PXRg+E3MfG/gu5Bh2qdw7otw75jpGmylo+0nwGgOWRsW4KucDaEgtvJ2+94GOL0Z5QojSkhm+FUBrG9q2tfTplsla8jD2TmfahByUzwSU/zQMt1YX1ZmZf33J74C2O7uiyHQ+DI6/F536HQCmmY6ZNB2tglHWFlllaXT6Ymc6iZx1JL0LsaMh+W2UW+sir0EpBT63gtcNucvJWI22bXLWk7nf+Wwha/KaEMI1JPhXhLQf0LG3gH1vkYfqjBX5r2lrnnOer1MubEr5Gm3bAoZPrtm5Wmeio/qik17N/w3AcxjK2hxl1IGQX8HjSnBr59wXfz+kvA2xo9G2zc5tjpPo+Icg9Xu0GYeZ+CJm2kJI+8Z51+81BvJ5bpEfw3cqhme/3NecOA2d+DrYVqNjRkPGimKVJYQoPZnkVRE8h6GUL1iLvjvWCU+BtXWe/nPlOTjv3XDaT+A4hdYJ4Pc0OmUGqs77YO0AnteCpRk6sisEvovy6It2RILhj/K59UIZqV9Bxp/g/5Qz4ZvjDHgMd3bjZLVXWcMhaBZY24H9AKTOA/+O4DUa5TsV7HvRUUMh6GuUtTjdP7mpoC9BWQEPlN8TUJxJbUKIMpHgXwGcaZNHFO/YoG/BKOaC5r4PQ/xE8LkXrG3A0gCUr7N7xe/faDMabGvQRl3QpvMhruM02tIQ5fewsz7Pa5wPcY1QdMYm0EmogGdQWZk7zeSPQXli+NzmrNO9M4RtcH6SsbZFWULQZoBzNJPycj5LUJ7ZXUbFumZL2IUXPvKoSIiKIN0+VYyyhmcH3qIYnr1RocvBaABxt4K1NTp9MQA67l6InYDyfx5ix6GTZ2Ut9GKBlBlobV6oz+dWlDIwvEc4V/PKWX/GSshYhTZjMRNfRDsiUYYvuHeCrAfAyu1SjODZKEswOv5+dELetYS1bTNmzK1oMxEzbSlm3N3O+QU5jzFTMWNvQ2esKfG/mxCiZOTOv5pTlnrg2QttTobMreA469zhNcr5nMDwc745pLwOQXPAayw4ItFJr4FHX5TH5YWXH5Q1RDVzi7O7x2MgWMIw/J/L//jAD7MeJl/EjHU+XNbpYJ4E+2HATu7/gpnOTyaO6CJHLgkhykaVZQRKeevWrZvesmVLZTejRtH2k+jUBZD6AQT8F8NroHP0UWQvcO+BUecjtG072rYB5TO50HkF2kxGGb6Y6SvAthbl96SkZBCiClBKbdValyiHunT7VGFa29H2I2UrI34qpE4HSz2UR3d0+nLADYwmkOksW6f9AimfAAXn8wec3T3gzEeUvhDIf/0AbT/sHLJZwbTOqPA6haiuJPi7kM7cg077rfQFpH6Ljh5RpjcAFfAy+D4APndB2nfo+CngOIYK/hS8rsWM7A2+96FCl6OUe6FlaTMRnTob3K8Aa3uc3Tb5HBf/CDr+/mK1z4wZg5nwbEkvK2+d9kPo893Q6YuKPlgIIX3+rqRTZkDG6qyhnqXoHvHMSrtgCS9d/VqDtTWG2yXO12YyytoGLE2c7XHvgnYcQhk+RQZ+AGxr0YnTwOu2rDkH6ZBPbh4V+KYzhURxWFuAtWXxrsd+HB03CRXwH5R7l9w7jXrgNdI5HFUIUSQJ/i6k/F8GM77U/eI6YzkAhirdr0knPuOcMBW6GqWUs9smxwNe5dEL5dGr+AV6DEYFNwFrG5R6LM9uM/5RsIRj+E0tdpFGwLTi16+szvQQyi3vLsPX+SlHCFEs0u3jQsrwLdWkJwDtOAeJr0Fq7mUZzaQPMOPuKeCcM5jR16Ezdzo3eFwFnqPK7aGsUgbKrW3B5TnOgXm+XOrKt35LQ4yQ+aisTzJCiNKT4F9lmc6uDP9nLtqemd2los1k56Sqf2g76BR06nzM2NtRHv0w/P+vxDVrMxX9z5BRQGesc666lfJZ4Sfa9zuHdFYgbduKmfBCkYvXCyFyk+BfQcz0ZZgJTxY7uZuyNMAI+x3D47Jc2w2/BzGCPgVAJ3+IjhmDNuOc51jDMUIXg6U+/4zE0Vo7cwDlky9IaztmwhPojA25tyc+h44enh1QdcrHzhQQGesKb7P/UyifScW6vrxt0ejMXSUO4tq2AdJ/hRKsaSCEkOBfcTJ3QMYaChohU1I6YwOk/wZ+j4EKzLXP8J2EEfRVVvdMBiS/mZ2186JCIP1PdOZ256ib+McBZ6ZQ/J5xLt1o2+ycuBW6ElXn08LbBOiUmZj2yOJfhyMabdsOtvXomJsgY2mxz3W29V5U2LoLw1D5Z4jssRKVI0RtI8G/ghh+D6NCV6LyeVhZGlpngHkWUr4ptE9fKU9UyBKUf96UC8rwQYWtx/C927mQS+YOtBmPcmuH8hoCad+j05aik99H6eSinx3Yj4BtC0QPKHB4qtbpmAnPZc8D0ElvoWNvQbt1QPk/C+6FzzjOe30q70il1K+dn1zsx0tUlhC1iQT/ClSes2GVR19w6wnWpmjHuQK7S7TWKEtYngCp7Ycxkz9Ha4fzGK9rnQuomElZbfVCha0G75ucmT9teWdea63RaT9nPx8w/B5EBc8Bn8kFL+5ixjqzkWZud9bjdz+qznQMwx/lPTbXHXypeQ5G+T3mTDYnhMiXpHeoQGbsJLC2wPB/FO2IAjMK5Va2cenacRodNRjl94izuybnvowV6PiHUEFzURct9mImvQspnwIGuF2CcdEyk7nKMRNA+ed589KOGHRUX/C5E8PvoeK3WaeXaiF4M3UupHyBCv4BZXiX+HwhaipJ71DVKc/spGc68SV07PgCHwBrx2nMmHHozIOFl2nUBd/7nQnXLmaJAI9+aJ2Eth/O3RTfKRDyByh/wNkVpc0EzMg+ziCb81gjIN9PLcoS7AzEvncX2DytbdkZRLPPK0Xgd54YBJawrNz/QoiykL+iCmTU+V/2z8rv/8AxtuCuIDPVmaFTJxVaplJWlG/+I2yUtSkq8F3M6OFoDFTIrznOc0NZ60PdHOmTlSe4dUCVYEaxcmtT6H4dPRTcLkUFvpP/fjMWnfQOyneKM0NpIQyvq8Hr6mK3TQhRMLnzryTKGo52nMRMW5L/freWGGEr8qYxKE1dAW+iAl4v+jjlgVHno5LN+i2K5yiwn8CML6BbyH4S0uY7VwgTQlQYufOvTClfOLsxvAa5tBrl1rZM55sp30D6fKjzGYbhX+Txzm4ehVIKw+8+TJ2cb45/rW1gPwShK1CWkDK1UQhRMnLnX4lU8A+oOp9UdjOKptzAzITInpjJHxR5uI6+Fh35T/poMPyfwPB7MO+BmTvQic+gbOvzlmE/gS5iUpkQovQk+FciZXgXmk3TjL0VM/E/JS7XTHwNM63g1MbaTEEXN+smYHjfCIFvOF84ipG7x+MKwLvoOty6oYK+QXsMRNu25nr4rZPfQsdPKfaMaCFEyUjwr8qMEDBCS35exhKwrS5wt44ego5/pGRNcWsJHiMgbb6zu6awY/0fx6i7CsNrENpMLPA4pRTKvRMqfYFzQXj7hTxFyu9pVNBsWSlMCBeRPv8qzAh8u1TnqZA/oLBVcH0mgKUl2rYFrG1Rhk/xyvV/GOzXFS/3P6Az1qPj7oQ6n6EuylGUi+cQlPIA64VnE8oSCpZSvPEJIYpF7vyrKa3TMOPuRds259mnlFHoHbPhcwfKGuFMqxA3pdjJ1JSlXuFB/GLWVuA9Hi6aYJanXMMf5TUSJeP3hagwZQr+SqkblVK7lVKmUqrbRfueUEodUkrtV0oNLlsza5diBWOd5nxgWsL8NdpMds7YtTQGz2GQuRWysoKWN2UJxvB/EmUEuaR8IUTplfXOfxdwHbAq50alVDtgLNAeGAJ8qJSylLGuGkubCZjxDznXoc3YiI7sgrbtKPQcZQRhhK3F8L6hZHXFTULHjHH2twe8gQpbWa7DLHXmnkpZvF0IUTJlCv5a671a6/z+0kcCc7TWGVrro8AhoEdZ6qrRzGjncov2Y2BtBB5XZuXkL3/K927wvc/5szJQRhDatgMzsh86c2+R5+f3sFdrjXZEO3+Ofxid8KjzZ0eMc2Ux26ZyvAIhRHlwVSdrQyDnCiGnsraJLFrbAcMZgK3NIWwrSjnfiwtKhVAelEffvI+CDV9nBkxVeEZNbduCjp0AQZ+h3HO8l2csQcc/DEHfoOq8z4V7Coeze6qI0UFCiIpXZPBXSi0F8ku68pTW+ueyNkApNQmYBBAeXvycMtWdjrkejHqooI8BsgN/eTLTlkDGH6iA1wotX1mbo4K/KbpASzh4Dnd+z8mtM/hMBGvzXCmZlSUMFVrwfAMhROUpMvhrra8qRbmngcY5XjfK2pZf+TOAGeBM6VyKuqonz2FghLm2Dvse5wNdHJTHwC5lCUMFvpr/dr+Hc23TZjw68XmU71SUtUWZ6xZClC9XDfX8BRirlPJQSjUFWgLS8ZuD4TsZw3u0a+vwexAj9M9yWz2sRMwYyFgFspqWEFVSmfr8lVKjgfeAUOA3pdR2rfVgrfVupdQ8YA/ORWun6JKuzC1KTKcvB2WgPPpVdlNyPMeQGbpCVEVlCv5a6/nA/AL2TQOmlaV8UTI6+W3AWiWCP5TvspVCiPIlM3xrEBX0JSroi2Idq81EzKiBmKk/OIdqZmx0LgovhKgVJPjXIMqogzICinmwO1giUJa6YN+NjpvgXFRFCFErSDKVSqC1g6ImPGut0YnPg/vlGC5Y7EUpT1TQzAvtCXgTPPqUez1CiKpJ7vwrmLafREd2Q6ctKOJIEzJWQuYWl7dJKQvKaxjK8HN5XUKIqkHu/CuaUQc8BkIRY9+VskDocnloKoRwCQn+FUwZvqjAN4t3rAR+IYSLSLdPDWLGP4SZ+m1lN0MIUQ3InX9NYj8BRoPKboUQohqQ4F+DGCE/VHYThBDVhHT7CCFELSTBXwghaiEJ/kIIUQtJ8BelojPWYSa/X9nNEEKUkgR/USo6/TdInY3WZvY2M+VzzOhr8l3nVwhRtUjwF6Wi/F9Ehf6Ze3lIIwSMesh/KyGqPhnqKUrFmZjOK9c2w2sEeI2onAYJIUpEbtGEEKIWkuAvhBC1kAR/IYSohST4CyFELSTBXwghaiEJ/kIIUQtJ8BdCiFpIgr8QQtRCEvyFEKIWkuAvhBC1kAR/IYSohST4CyFELVSm4K+UulEptVspZSqluuXY3kQplaaU2p71Nb3sTRVCCFFeyprVcxdwHfBxPvsOa607lbF8IYQQLlCm4K+13guglCqf1gghhKgQrszn31QptQ1IBJ7WWq/O7yCl1CRgUtbLDKXULhe2qbKFANGV3QgXkuur3mry9dXkawNoXdITigz+SqmlQL18dj2ltf65gNPOAuFa6xilVFfgJ6VUe6114sUHaq1nADOy6tqite528TE1hVxf9SbXV33V5GsD5/WV9Jwig7/W+qqSFqq1zgAysn7eqpQ6DLQCStxAIYQQ5c8lQz2VUqHKuc4fSqlmQEvgiCvqEkIIUXJlHeo5Wil1CugF/KaUWpy1qy+wUym1HfgeuFtrHVuMImeUpT3VgFxf9SbXV33V5GuDUlyf0lq7oiFCCCGqMJnhK4QQtZAEfyGEqIWqRPCv6WkiCrq+rH1PKKUOKaX2K6UGV1Yby4tS6nml1Okcv7Nhld2mslJKDcn6/RxSSj1e2e0pb0qpY0qpv7N+X9V+RJ5SaqZSKjLnnCGlVJBS6g+l1MGs73Uqs41lUcD1lfjvrkoEfy6kiViVz77DWutOWV93V3C7yku+16eUageMBdoDQ4AP/xklVc29k+N3trCyG1MWWb+PD4ChQDtgXNbvraYZkPX7qglj4b/A+feU0+PAMq11S2BZ1uvq6gvyXh+U8O+uSgR/rfVerfX+ym6HqxRyfSOBOVrrDK31UeAQ0KNiWyeK0AM4pLU+orW2AXNw/t5EFaW1XgVcPLpwJDAr6+dZwKiKbFN5KuD6SqxKBP8iNFVKbVNKrVRK9ansxpSzhsDJHK9PZW2r7qYqpXZmfTytth+vs9TU31FOGliilNqalW6lJqqrtT6b9fM5oG5lNsZFSvR3V2HBXym1VCm1K5+vwu6i/kkT0Rl4GPhGKeVfMS0umVJeX7VUxLV+BDQHOuH8/b1VmW0VxXKF1roLzq6tKUqpvpXdIFfSzvHtNW2Me4n/7lyZ2C2Xmp4mojTXB5wGGud43ShrW5VW3GtVSn0CLHBxc1ytWv6OSkJrfTrre6RSaj7Orq78nr9VZ+eVUvW11meVUvWByMpuUHnSWp//5+fi/t1V6W6fWpAm4hdgrFLKQynVFOf1barkNpVJ1h/WP0bjfNhdnW0GWiqlmiql3HE+oP+lkttUbpRSPkopv39+BgZR/X9n+fkFuC3r59uAgpJSVkul+bursDv/wiilRgPvAaE400Rs11oPxpkm4kWlVCZgUvw0EVVKQdentd6tlJoH7AHswBSttaMy21oOXldKdcL5sfoYMLlSW1NGWmu7UmoqsBiwADO11rsruVnlqS4wXznX5LAC32itf6/cJpWNUupboD8QkpV+5jngVWCeUmoicBy4qfJaWDYFXF//kv7dSXoHIYSohap0t48QQgjXkOAvhBC1kAR/IYSohST4CyFELSTBXwghaiEJ/kIIUQtJ8BdCiFro/wG4G0fbgbbX8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1],c=y,s=0.5)\n",
    "plt.scatter(mu[:,0],mu[:,1],c='r')\n",
    "plt.xlim([-15,15])\n",
    "plt.ylim([-15,15])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72c61642",
   "metadata": {},
   "source": [
    "the red points are our initial clusters centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "59708a51",
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialize prior probabilities\n",
    "p = np.zeros((k,1))\n",
    "for i in range(k):\n",
    "    p[i] = 1/k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "8b1fdaee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize covariance matrices\n",
    "sigma = np.zeros((k,n,n))\n",
    "for i in range(k):\n",
    "    sigma[i] = np.eye(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "4eb2f1c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# our Multivariate Gaussian function\n",
    "from numpy.linalg import multi_dot\n",
    "def MultiGaussian(x,mu,cov):\n",
    "    invcov = np.linalg.inv(cov)\n",
    "    detcov = np.linalg.det(cov)\n",
    "    n = x.shape[1]\n",
    "    f=[]\n",
    "    denom = ((np.sqrt(2*np.pi))**n)*(np.sqrt(detcov))\n",
    "    for i in range(len(X)):\n",
    "        Q = (multi_dot([(x[i]-mu),invcov,(x[i]-mu).T]))/2\n",
    "        f.append(np.exp(-Q)/denom)\n",
    "    \n",
    "    \n",
    "    return np.array(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "5544eadb",
   "metadata": {},
   "outputs": [],
   "source": [
    "#EM steps\n",
    "f = np.zeros((k,m))\n",
    "num = np.zeros((k,m))\n",
    "Xbar= np.zeros((k,m,n))\n",
    "new_sigma = np.zeros((k,n,n))\n",
    "for iteration in range(200):\n",
    "    for i in range(k):\n",
    "        f[i] = MultiGaussian(X,mu[i],sigma[i])\n",
    "        num[i] = f[i]*p[i]\n",
    "    denom = np.sum(num,axis=0,keepdims=True)\n",
    "    w = (num/denom).T #weights\n",
    "    sumw = (np.sum(w,axis=0,keepdims=True)).T #sum of weights\n",
    "    new_p = (sumw/m) # new prior probability\n",
    "    new_mu = np.dot(w.T,X)/sumw # new centers\n",
    "    for i in range(k):\n",
    "        Xbar[i] = X - new_mu[i]\n",
    "        new_sigma[i] = np.cov(Xbar[i].T,aweights=(w[:,i]/sumw[i]).flatten(), bias=True) # new covariance\n",
    "    mu = new_mu\n",
    "    sigma = new_sigma\n",
    "    p = new_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "800a2977",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-15.0, 15.0)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1],c=y,s=0.5)\n",
    "plt.scatter(mu[:,0],mu[:,1],c='r')\n",
    "plt.xlim([-15,15])\n",
    "plt.ylim([-15,15])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20283dbe",
   "metadata": {},
   "source": [
    "finial clusters centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6cc6691f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-6.4837452 , -6.74083782],\n",
       "       [ 4.56848945,  1.93913877],\n",
       "       [-2.517623  ,  9.04765746]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu #calculated center of clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "ec63510d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.50919762,  9.01428613],\n",
       "       [ 4.63987884,  1.97316968],\n",
       "       [-6.87962719, -6.88010959]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centers # true center of clusters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d532ae15",
   "metadata": {},
   "source": [
    "pretty close ha? that's feels good :)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8cf1ad3",
   "metadata": {},
   "source": [
    "#### GMM in scikit learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "db9543d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.mixture import GaussianMixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "5fa052d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.517623  ,  9.04765746],\n",
       "       [-6.4837452 , -6.74083782],\n",
       "       [ 4.56848945,  1.93913877]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=3,random_state=42)\n",
    "gmm.fit(X)\n",
    "gmm.means_"
   ]
  }
 ],
 "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}