PCA - Teoría.ipynb

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    "<h1 style=\"color:darkblue;\">PCA - Teoría</h1>\n",
    "\n",
    "### Introducción\n",
    "El análisis de componentes principales es una técnica de reducción de dimensionalidad en la cual se toma una matriz de datos y se busca generar una nueva mátriz en la cual se hallen aquellos componentes, ordenados de mayor a menor, que expliquen el máximo de varianza de los datos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algoritmo\n",
    "La idea intuitiva detrás del algoritmo es bastante simple:\n",
    "- Primeramente, se toma una matriz de datos $D_{m\\times n}$ que tiene $m$ instanscias en $\\mathbb{R}^n$\n",
    "- Se le resta la media de cada columna a $D$, por lo que se obtiene $D'$ correspondiente a los datos centrados\n",
    "- Se obtiene a matriz de covarianza de $D'$, $\\Sigma =$ cov($D'$)\n",
    "- Se calculan los autovalores de $\\Sigma$ de tal manera que $eig(\\Sigma) = \\{ \\Sigma_1, \\Sigma_2,...\\Sigma_n \\}$ se agrupan de mayor a menor segun el orden dado por el autovalor de cada autovector.\n",
    "\n",
    "### Ejemplo\n",
    "nota: los datos corresponden a diversos indicadores de países, pero para el ejemplo no es necesario conocerlos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import scipy.linalg as la\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>X5</th>\n",
       "      <th>X6</th>\n",
       "      <th>X7</th>\n",
       "      <th>X8</th>\n",
       "      <th>X9</th>\n",
       "      <th>X10</th>\n",
       "      <th>X11</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>30</td>\n",
       "      <td>41</td>\n",
       "      <td>2199</td>\n",
       "      <td>3903</td>\n",
       "      <td>12</td>\n",
       "      <td>94</td>\n",
       "      <td>53</td>\n",
       "      <td>0.0</td>\n",
       "      <td>341</td>\n",
       "      <td>1.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>124</td>\n",
       "      <td>46</td>\n",
       "      <td>4422</td>\n",
       "      <td>955</td>\n",
       "      <td>6</td>\n",
       "      <td>57</td>\n",
       "      <td>19</td>\n",
       "      <td>0.7</td>\n",
       "      <td>89</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.3</td>\n",
       "      <td>21</td>\n",
       "      <td>13</td>\n",
       "      <td>133540</td>\n",
       "      <td>91019</td>\n",
       "      <td>96</td>\n",
       "      <td>497</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4566</td>\n",
       "      <td>13.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.5</td>\n",
       "      <td>34</td>\n",
       "      <td>24</td>\n",
       "      <td>44609</td>\n",
       "      <td>19883</td>\n",
       "      <td>42</td>\n",
       "      <td>180</td>\n",
       "      <td>2</td>\n",
       "      <td>0.8</td>\n",
       "      <td>906</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.3</td>\n",
       "      <td>22</td>\n",
       "      <td>31</td>\n",
       "      <td>278431</td>\n",
       "      <td>65962</td>\n",
       "      <td>160</td>\n",
       "      <td>1043</td>\n",
       "      <td>22</td>\n",
       "      <td>0.1</td>\n",
       "      <td>1504</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "    X1   X2  X3      X4     X5   X6    X7  X8   X9   X10   X11\n",
       "0  1.0   30  41    2199   3903   12    94  53  0.0   341   1.2\n",
       "1  3.0  124  46    4422    955    6    57  19  0.7    89   0.5\n",
       "2  4.3   21  13  133540  91019   96   497   1  0.0  4566  13.1\n",
       "3  2.5   34  24   44609  19883   42   180   2  0.8   906   3.0\n",
       "4  1.3   22  31  278431  65962  160  1043  22  0.1  1504   3.5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Datos\n",
    "D = pd.read_excel(\"Datasets/paises_mundo.xlsx\")\n",
    "D.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X4</th>\n",
       "      <th>X5</th>\n",
       "      <th>X6</th>\n",
       "      <th>X7</th>\n",
       "      <th>X8</th>\n",
       "      <th>X9</th>\n",
       "      <th>X10</th>\n",
       "      <th>X11</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.870833</td>\n",
       "      <td>-9.0625</td>\n",
       "      <td>3.71875</td>\n",
       "      <td>-114388.416667</td>\n",
       "      <td>-65358.322917</td>\n",
       "      <td>-153.125</td>\n",
       "      <td>-415.84375</td>\n",
       "      <td>25.666667</td>\n",
       "      <td>-0.553125</td>\n",
       "      <td>-1513.427083</td>\n",
       "      <td>-3.354167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.129167</td>\n",
       "      <td>84.9375</td>\n",
       "      <td>8.71875</td>\n",
       "      <td>-112165.416667</td>\n",
       "      <td>-68306.322917</td>\n",
       "      <td>-159.125</td>\n",
       "      <td>-452.84375</td>\n",
       "      <td>-8.333333</td>\n",
       "      <td>0.146875</td>\n",
       "      <td>-1765.427083</td>\n",
       "      <td>-4.054167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.429167</td>\n",
       "      <td>-18.0625</td>\n",
       "      <td>-24.28125</td>\n",
       "      <td>16952.583333</td>\n",
       "      <td>21757.677083</td>\n",
       "      <td>-69.125</td>\n",
       "      <td>-12.84375</td>\n",
       "      <td>-26.333333</td>\n",
       "      <td>-0.553125</td>\n",
       "      <td>2711.572917</td>\n",
       "      <td>8.545833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.629167</td>\n",
       "      <td>-5.0625</td>\n",
       "      <td>-13.28125</td>\n",
       "      <td>-71978.416667</td>\n",
       "      <td>-49378.322917</td>\n",
       "      <td>-123.125</td>\n",
       "      <td>-329.84375</td>\n",
       "      <td>-25.333333</td>\n",
       "      <td>0.246875</td>\n",
       "      <td>-948.427083</td>\n",
       "      <td>-1.554167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.570833</td>\n",
       "      <td>-17.0625</td>\n",
       "      <td>-6.28125</td>\n",
       "      <td>161843.583333</td>\n",
       "      <td>-3299.322917</td>\n",
       "      <td>-5.125</td>\n",
       "      <td>533.15625</td>\n",
       "      <td>-5.333333</td>\n",
       "      <td>-0.453125</td>\n",
       "      <td>-350.427083</td>\n",
       "      <td>-1.054167</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "         X1       X2        X3             X4            X5       X6  \\\n",
       "0 -0.870833  -9.0625   3.71875 -114388.416667 -65358.322917 -153.125   \n",
       "1  1.129167  84.9375   8.71875 -112165.416667 -68306.322917 -159.125   \n",
       "2  2.429167 -18.0625 -24.28125   16952.583333  21757.677083  -69.125   \n",
       "3  0.629167  -5.0625 -13.28125  -71978.416667 -49378.322917 -123.125   \n",
       "4 -0.570833 -17.0625  -6.28125  161843.583333  -3299.322917   -5.125   \n",
       "\n",
       "          X7         X8        X9          X10       X11  \n",
       "0 -415.84375  25.666667 -0.553125 -1513.427083 -3.354167  \n",
       "1 -452.84375  -8.333333  0.146875 -1765.427083 -4.054167  \n",
       "2  -12.84375 -26.333333 -0.553125  2711.572917  8.545833  \n",
       "3 -329.84375 -25.333333  0.246875  -948.427083 -1.554167  \n",
       "4  533.15625  -5.333333 -0.453125  -350.427083 -1.054167  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#datos centrados - Dp = D' --> \"D prima\"\n",
    "Dp = D - D.mean()\n",
    "Dp.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Matriz de Covarianza\n",
    "Sigma = Dp.cov() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Autovalores y Autovectores\n",
    "eigvals, eigvecs = la.eig(Sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Auto vectores y datos centrados \n",
    "t_eigvecs = eigvecs.T\n",
    "t_Dp = Dp.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Componentes principales\n",
    "pca = t_eigvecs.dot(t_Dp)\n",
    "pca = pca.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Tabla de PCA\n",
    "cols = [\"P1\",\"P2\",\"P3\",\"P4\",\"P5\",\"P6\",\"P7\",\"P8\",\"P9\",\"P10\",\"P11\"]\n",
    "PCA = pd.DataFrame(data=pca, columns=cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P1     0.90345\n",
      "P2     0.09647\n",
      "P3     0.00007\n",
      "P4     0.00000\n",
      "P5     0.00000\n",
      "P6     0.00000\n",
      "P7     0.00000\n",
      "P8     0.00000\n",
      "P9     0.00000\n",
      "P10    0.00000\n",
      "P11    0.00000\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#Proporcion de varianza explicada\n",
    "prop_var = PCA.var() / sum(PCA.var())\n",
    "print(round(prop_var,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> En este caso el primer componente explica el 90% de la varianza y el segundo el 9.65%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,5))\n",
    "plt.suptitle(\"Componentes\")\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.bar(cols,prop_var)\n",
    "plt.xlabel(\"Componente Principal\")\n",
    "plt.ylabel(\"Varianza explicada\")\n",
    "plt.grid(alpha=0.5)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(np.linspace(1,11,11), prop_var, color=\"red\")\n",
    "plt.xlabel(\"Componente Principal\")\n",
    "plt.ylabel(\"Varianza explicada\")\n",
    "plt.grid(alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "P1     0.903454\n",
       "P2     0.999927\n",
       "P3     0.999995\n",
       "P4     1.000000\n",
       "P5     1.000000\n",
       "P6     1.000000\n",
       "P7     1.000000\n",
       "P8     1.000000\n",
       "P9     1.000000\n",
       "P10    1.000000\n",
       "P11    1.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#proporcion de varianza acumulada\n",
    "cum_var = prop_var.cumsum()\n",
    "cum_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#PCA con sklearn\n",
    "from sklearn.decomposition import PCA as skPCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "sk_pca = skPCA(n_components=11).fit(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,5))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(np.linspace(1,11,11), sk_pca.explained_variance_ratio_, color=\"red\")\n",
    "plt.title(\"sklear\")\n",
    "plt.xlabel(\"Componente Principal\")\n",
    "plt.ylabel(\"Varianza explicada\")\n",
    "plt.grid(alpha=0.5)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(np.linspace(1,11,11), prop_var, color=\"red\")\n",
    "plt.title(\"My model\")\n",
    "plt.xlabel(\"Componente Principal\")\n",
    "plt.ylabel(\"Varianza explicada\")\n",
    "plt.grid(alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P1     0.0\n",
      "P2     0.0\n",
      "P3    -0.0\n",
      "P4     0.0\n",
      "P5     0.0\n",
      "P6    -0.0\n",
      "P7    -0.0\n",
      "P8    -0.0\n",
      "P9     0.0\n",
      "P10    0.0\n",
      "P11   -0.0\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "#Diferencia entre los calculos paso a paso y sklearn\n",
    "error = sk_pca.explained_variance_ratio_ - prop_var\n",
    "print(round(error,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Finalmente, el modelo casi desde cero en Python resultó bastante similar al modelo de sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Fuentes:\n",
    "- Amat Rodrigo (2017) Análisis de Componentes Principales (Principal Component Analysis, PCA) y t-SNE. Extraído el 09 de septiembre 2020 de: https://www.cienciadedatos.net/documentos/35_principal_component_analysis\n",
    "- Baillo Moreno & Grane Chavez (2008) 100 problemas de estadistica multivariante (Implementados en Matlab). Delta, Publicaciones Universitarias. Primera Edición. Madrid España. \n",
    "- VanderPlas J. (s.f.) In Depth: Principal Component Analysis.  Python Data Science Handbook. Extraído el 09 de septiembre 2020 de: https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html\n",
    "- UnADM (s.f.) Unidad 2 Minería de Datos. Computación II. Universidad Abierta y a Distancia de México. Clave 05142423/06142423"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}