09_probabilistic_Gaussian_Clustering.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probabilistic Clustering with Gaussian Mixture Models "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### In `K-Means` we assume that variance of the clusters is equal, however, in the cases were variances vary, `GMM` can be used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Simple Example using simulation of heights of both women and men \n",
    "\n",
    "import numpy as np \n",
    "N = 1000\n",
    "m_height_men = 72 #Mean height of men\n",
    "m_height_women = 66 #mean height of women\n",
    "std_men = 2 #standard deviation of men height\n",
    "std_women = 2 #standard deviation of women height"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ffa1787b20>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "men = np.random.normal(m_height_men, std_men, N)\n",
    "women = np.random.normal(m_height_women, std_women, N)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "ax.set_title(\"Histogram of Heights\")\n",
    "ax.hist(men, alpha=0.5, label=\"Men\")\n",
    "ax.hist(women, alpha=0.5, label=\"Women\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating test and train samples \n",
    "\n",
    "random_samples = np.random.choice([True, False],size=men.size)\n",
    "men_test = men[random_samples]\n",
    "men_train = men[~random_samples]\n",
    "women_test = women[random_samples]\n",
    "women_train = women[~random_samples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Getting empirical distribution of the heights of both men and women \n",
    "\n",
    "from scipy import stats \n",
    "men_pdf = stats.norm(men_train.mean(),men_train.std())\n",
    "women_pdf = stats.norm(women_train.mean(), women_train.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.033085369053765426"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Next, we will calculate based on the likelihood that the data point was generated from either distribution, and the most likely distribution will get the appropriate label assigned \n",
    "\n",
    "men_pdf.pdf(men[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19033782241577527"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "women_pdf.pdf(women[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets assume situations when the men's probability is higher \n",
    "\n",
    "guess_men = np.ones_like(men_test)\n",
    "guess_men[men_pdf.pdf(men_test) < women_pdf.pdf(men_test)] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9342915811088296"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#guees_men will be 1 if we are correct, and close to 0 if we are not, taking the mean of the vector and get the accuracy \n",
    "guess_men.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "guess_women = np.ones_like(women_test)\n",
    "guess_women[women_pdf.pdf(women_test) > women_pdf.pdf(women_test)] = 0 \n",
    "guess_women.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ffb396d790>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#If we allow the variance to differ between groups \n",
    "\n",
    "std_men = 2 \n",
    "std_women = 4\n",
    "\n",
    "men = np.random.normal(m_height_men, std_men, N)\n",
    "women = np.random.normal(m_height_women, std_women, N)\n",
    "\n",
    "\n",
    "\n",
    "men_test = men[random_samples]\n",
    "men_train = men[~random_samples]\n",
    "women_test = women[random_samples]\n",
    "women_train = women[~random_samples]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "ax.set_title(\"Histogram of Heights\")\n",
    "ax.hist(men_train, alpha=0.5, label=\"Men\")\n",
    "ax.hist(women_train, alpha=0.5, label=\"Women\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#CREATING PDF\n",
    "\n",
    "men_pdf = stats.norm(men_train.mean(), men_train.std())\n",
    "women_pdf = stats.norm(women_train.mean(), women_train.std())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\konar\\AppData\\Local\\Temp\\ipykernel_13388\\1629018551.py:4: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"k\" (-> color=(0.0, 0.0, 0.0, 1)). The keyword argument will take precedence.\n",
      "  plt.plot(x, men_pdf.pdf(x), 'k',linewidth=2, color='blue',label='Men')\n",
      "C:\\Users\\konar\\AppData\\Local\\Temp\\ipykernel_13388\\1629018551.py:5: UserWarning: color is redundantly defined by the 'color' keyword argument and the fmt string \"k\" (-> color=(0.0, 0.0, 0.0, 1)). The keyword argument will take precedence.\n",
      "  plt.plot(x, women_pdf.pdf(x),'k', linewidth=2, color='green',label='Women')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ffb44923a0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(50,80,300)\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"PDF of Heights\")\n",
    "plt.plot(x, men_pdf.pdf(x), 'k',linewidth=2, color='blue',label='Men')\n",
    "plt.plot(x, women_pdf.pdf(x),'k', linewidth=2, color='green',label='Women')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1ffb462d7c0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "class_A = np.random.normal(0,1,size=(100,2))\n",
    "class_B = np.random.normal(4, 1.5, size=(100,2))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,5))\n",
    "plt.title(\"Random 2D Normal Draws\")\n",
    "ax.scatter(class_A[:,0],class_A[:,1],label='A',c='r')\n",
    "ax.scatter(class_B[:,0],class_B[:,1],label='B')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Let's do `GMM` with scikit now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'covariance_type': 'full',\n",
       " 'init_params': 'kmeans',\n",
       " 'max_iter': 100,\n",
       " 'means_init': None,\n",
       " 'n_components': 1,\n",
       " 'n_init': 1,\n",
       " 'precisions_init': None,\n",
       " 'random_state': None,\n",
       " 'reg_covar': 1e-06,\n",
       " 'tol': 0.001,\n",
       " 'verbose': 0,\n",
       " 'verbose_interval': 10,\n",
       " 'warm_start': False,\n",
       " 'weights_init': None}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.mixture import GaussianMixture \n",
    "gmm = GaussianMixture()\n",
    "\n",
    "X = np.row_stack((class_A, class_B))\n",
    "y = np.hstack((np.ones(100), np.zeros(100)))\n",
    "\n",
    "\n",
    "train = np.random.choice([True, False],200)\n",
    "gmm.fit(X[train])\n",
    "gmm.get_params()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0], dtype=int64)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gmm.predict(X[train])[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.09858459, -0.09169468],\n",
       "       [-1.65217131,  2.41911118],\n",
       "       [-0.5897825 ,  1.00045122],\n",
       "       [ 0.25167112,  0.17502491],\n",
       "       [ 0.87847771,  0.56666034]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[train][:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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