PCA_FROM_SCRATCH.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "# <center>$Machine   Learning   From   Scratch$</center>\n",
    "# <center><span style='background:yellow'> PCA (Análise de Componentes Principais)</span></center>\n",
    "<center>$Rafael Pavan$</center>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "## 1. Introdução\n",
    "\n",
    "    \n",
    "Análise de Componentes Principais (PCA) é um dos métodos para redução de dimensionalidade. A redução de dimensionalidade é feita através do cálculo de autovetores e autovalores sobre a matriz de covariância dos atributos dos dados. Com estes dados, é possı́vel projetar as amostras em espaços dimensionais menores, além reconstruı́-los de forma aproximada para as dimensões originais.\n",
    "        \n",
    "Em muitas vezes pode ser comum a redução da quantidade de atributos. Essa redução pode ser feita para: \n",
    "    - Reduzir o volume de informação para os recursos computacionais disponı́veis;\n",
    "    - Descrever as amostras num espaço dimensional possı́vel de ser visualizado graficamente.\n",
    "    \n",
    "Deve-se ter cuidado ao realizar a dimensão de dimensionalidade, uma vez que esta também diminui a variância explicada dos dados. A análise neste tutorial será feita para apenas dois atributos, no entanto, o método é replicável para qualquer quantidade."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "rcParams['font.family'] = 'sans-serif'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "## 2. Importando e Pré-Visualizando os Dados\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1 = pd.read_csv('Dados.csv', sep=',', index_col=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>f1</th>\n",
       "      <th>f2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.366636</td>\n",
       "      <td>1.389113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.504032</td>\n",
       "      <td>3.854178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.655682</td>\n",
       "      <td>4.411995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.765235</td>\n",
       "      <td>4.715414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.846560</td>\n",
       "      <td>4.175506</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         f1        f2\n",
       "0  3.366636  1.389113\n",
       "1  2.504032  3.854178\n",
       "2  1.655682  4.411995\n",
       "3  3.765235  4.715414\n",
       "4  4.846560  4.175506"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [[3.36663556 1.38911268]\n",
      " [2.50403207 3.8541781 ]\n",
      " [1.65568187 4.41199472]\n",
      " [3.76523467 4.71541365]\n",
      " [4.84656011 4.17550645]]\n"
     ]
    }
   ],
   "source": [
    "X = df1.iloc[:,:].values\n",
    "\n",
    "print('X:', X[0:5,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,10))\n",
    "\n",
    "plt.scatter( X[:,0], X[:,1], marker='o', label = 'Dados', color='purple', s=90) \n",
    "\n",
    "plt.title('Dados',fontsize='x-large')\n",
    "\n",
    "plt.xlabel('X1',fontsize='x-large')\n",
    "\n",
    "plt.ylabel('X2',fontsize='x-large')\n",
    "\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "## 2. Normalização\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "Atributos com escalas diferentes podem gerar um $bias$ na análise. Assim, devem ser normalizados de forma que a média ($\\mu$) seja igual a 0 e desvio padrão ($\\sigma$) igual a 1.\n",
    "    \n",
    "\n",
    "<center>$X$Normalizado = ($X$ - $\\mu$) / $\\sigma$</center>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normaliza(X):\n",
    "    \"\"\"\n",
    "    Normaliza os atributos.\n",
    "    \n",
    "    Entrada: X não normalizado.\n",
    "    Saída: X normalizado.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    m, n = X.shape \n",
    "    \n",
    "    X_norm = np.zeros( (m,n) ) \n",
    "    \n",
    "    mu = 0 \n",
    "    \n",
    "    sigma = 1\n",
    "    \n",
    "    mu = X.mean(axis=0)\n",
    "    \n",
    "    sigma = X.std(axis=0,ddof=1)\n",
    "    \n",
    "    colu, lin = 0, 0\n",
    "    \n",
    "    for colu in range(X.shape[1]):\n",
    "    \n",
    "        for lin in range(X.shape[0]):\n",
    "    \n",
    "            X_norm[lin,colu]=(X[lin,colu]-mu[colu])/(sigma[colu])   \n",
    "    \n",
    "    \n",
    "    return X_norm, mu, sigma\n",
    "\n",
    "X_norm, mu, sigma = normaliza(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "\n",
    "## 3. Análise de Componentes Principais (PCA)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "\n",
    "Embora o entendimento da análise seja complexo, a sua implementação matemática é fácil. O primeiro passo para o PCA, é calcular a matriz covariância dos dados:\n",
    "\n",
    "$$\\psi = \\frac{1}{m}X^{T}X$$\n",
    "\n",
    "- $X$ é a matriz de dados;\n",
    "- $X^{T}$ é a matriz transposta de X;\n",
    "- $m$ é a quantidade de objetos; \n",
    "- $\\psi$ é a matriz quadrada ($n \\times n$) resultante.\n",
    "    \n",
    "Uma vez encontrada a matriz de covariância dos dados, é necessário realizar sua decomposição em valores singulares (SVD). Para realizar a fatoração, será utilizada a função np.linalg.svd. Esta função decompõe a matriz de covariância em um produto escalar de três matrizes, sendo que uma delas contém todos os componentes principais necessários.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pca(X):\n",
    "    \"\"\"\n",
    "    \n",
    "    Executa a analise de componentes principais na matriz de dados X.\n",
    "\n",
    "    Entrada: Dados X.\n",
    "    Saída: Autovetores (U) e Autovalores (S).\n",
    "    \n",
    "    \"\"\"\n",
    "\n",
    "    m, n = X.shape \n",
    "    U = np.zeros( [n,n] ) \n",
    "    S = np.zeros( n )  \n",
    "    \n",
    "    # Calcula a matriz de covariância\n",
    "    \n",
    "    psi=np.zeros([n,n])\n",
    "    psi=(1/m)*np.dot(X.T,X)\n",
    "    \n",
    "    # Realiza a decomposição SVD (Single Values Decomposition)\n",
    "    \n",
    "    U, S, V = np.linalg.svd(psi)\n",
    "    \n",
    "\n",
    "    return U, S \n",
    "    \n",
    "    \n",
    "\n",
    "U, S = pca(X_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "As setas indicam as componentes principais, ou seja, direções de máxima variação dos dados. Como os dados possuiam apenas dois atributos, há apenas duas componentes. A componente vermelha é a que apresenta maior significância:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X2')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,10))\n",
    "\n",
    "plt.scatter( X[:,0], X[:,1], marker='o', label = 'Dados', color='blue', s=90) \n",
    "\n",
    "plt.arrow( x=mu[0], y=mu[1], dx=2 * S[0] * U[0, 0], dy=2 * S[0] * U[1, 0], head_width=0.10, color='red')\n",
    "\n",
    "plt.arrow( x=mu[0], y=mu[1], dx=2 * S[1] * U[0, 1], dy=2 * S[1] * U[1, 1], head_width=0.10, color='orange') \n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.title('PCA - Análise de Componentes Principais',fontsize='x-large')\n",
    "\n",
    "plt.xlabel('X1',fontsize='x-large')\n",
    "\n",
    "plt.ylabel('X2',fontsize='x-large')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "Ao realizar a Análise de Componentes Principais, deve-se atentar para a quantidade de variância explicada necessária, uma vez que a técnica nada mais é do que a **preservação dos eixos que descrevem a maior quantidade de variância dos dados**, garantindo a perda de pouca informação. Assim, pode-se calcular quantas componentes você deve utilizar para atender a demanda de variância previamente dimensionada. A variância explicada por cada componente pode ser calculada por:\n",
    "    \n",
    "$$V_{Exp} = \\frac{S}{\\sum_{i=1}^{n} (S_i)}$$ \n",
    "    \n",
    "Onde:\n",
    "\n",
    "- $V_{Exp}$ : Vetor de Variância Explicada Para Cada Componente;\n",
    "    \n",
    "- $S$ : Vetor de Auto-Valores;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Porcentagem de variância explicada pela primeira componente: 56.45%\n",
      "Porcentagem de variância explicada pela segunda componente: 43.55%\n"
     ]
    }
   ],
   "source": [
    "def var_expl(S):\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    Calcula a variância explicada de cada componente.\n",
    "\n",
    "    Entrada: Vetor de Autovalores (S).\n",
    "    Saída: Vetor de Variância Explicada (var).\n",
    "    \n",
    "    \"\"\"\n",
    "\n",
    "    var = S/(np.sum(S))\n",
    "    \n",
    "    return var\n",
    "\n",
    "var=var_expl(S)\n",
    "\n",
    "print('Porcentagem de variância explicada pela primeira componente: %1.2f%%' %(var[0]*100))\n",
    "print('Porcentagem de variância explicada pela segunda componente: %1.2f%%' %(var[1]*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "\n",
    "A primeira componente é a que explica a maior parte da variância, com 56.45%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "\n",
    "Uma vez identificada a quantidade de componentes necessárias para atingir o objetivo pré-estabelecido de variância, os dados são então projetados nesta. No tutorial, iremos projetá-los sobre a componente vermelha, de variância de 56.45%, diminuindo o espaço dimensional de 2 para 1 dimensão.\n",
    "    \n",
    "A projeção é dada pelo simples produto escalar:\n",
    "    \n",
    "$$X_{Projetado} = X \\cdot W_{d}$$ \n",
    "    \n",
    "Onde:\n",
    "\n",
    "- $X_{Projetado}$ : Dados Projetados nas $N$ Componentes Escolhidas;\n",
    "\n",
    "    \n",
    "- $X$ : Conjunto de Dados;\n",
    "\n",
    "    \n",
    "- $W_{d}$ : Matriz de Auto-Vetores nas $N$ Componentes Escolhidas;\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "Uma vez projetados os dados, é possível recuperá-los nas dimensões originais. Para isso, utiliza-se a seguinte equação:\n",
    "    \n",
    "$$X_{Recuperado} = X_{Projetado} \\cdot W^{T}$$ \n",
    "    \n",
    "Onde:\n",
    "\n",
    "- $X_{Projetado}$ : Dados Projetados nas $N$ Componentes Escolhidas;\n",
    "\n",
    "    \n",
    "- $X_{Recuperado}$ : Dados recuperados para a Dimensão Original com Perdas;\n",
    "\n",
    "    \n",
    "- $W^{T}$ : Matriz de Auto-Vetores nas $N$ Componentes Escolhidas Transposta;\n",
    " \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cinco Primeiros Dados Projetados: \n",
      "[[ 2.23379119]\n",
      " [ 1.24841604]\n",
      " [ 1.35905894]\n",
      " [ 0.10600508]\n",
      " [-0.13399883]]\n"
     ]
    }
   ],
   "source": [
    "def projecao(X, U, N): \n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    Projeta os dados X, nas N componentes principais.\n",
    "    \n",
    "    Entrada: Dados (X), Auto-Vetores (U), Número de Componentes (N).\n",
    "    Saída: Dados Projetados (Z).\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    Z = np.zeros( [X.shape[0],N] )   \n",
    "    \n",
    "    Z = np.dot(X,U[:,0:N])\n",
    "    \n",
    "    return Z\n",
    "\n",
    "N = 1\n",
    "Z = projecao(X_norm, U, N)\n",
    "\n",
    "print('Cinco Primeiros Dados Projetados: ')\n",
    "\n",
    "print(Z[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def recuperacao(Z, U, N): \n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    Recupera os dados X com perdas, nas componentes originais.\n",
    "    \n",
    "    Entrada: Dados Projetados (Z), Auto-Vetores (U), Número de Componentes (N).\n",
    "    Saída: Dados Projetados (K).\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    K = np.zeros( [Z.shape[0], U.shape[0]] ) \n",
    "    \n",
    "    K = np.dot(Z,U[:,0:N].T)\n",
    "\n",
    "    return K\n",
    "\n",
    "N = 1\n",
    "K = recuperacao(Z, U, N) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X2')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,10))\n",
    "\n",
    "plt.scatter( X_norm[:,0], X_norm[:,1], marker='o', color='blue', s=90) \n",
    "\n",
    "plt.scatter( K[:,0], K[:,1], marker='o', color='red', s=90)\n",
    "\n",
    "\n",
    "for i in range( X_norm.shape[0] ):\n",
    "    plt.plot( [X_norm[i,0],K[i,0]], [X_norm[i,1],K[i,1]], linestyle='--', color='gray') \n",
    "    \n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.title('PCA - Recuperação dos Dados Originais (Com Perdas)',fontsize='x-large')\n",
    "\n",
    "plt.xlabel('X1',fontsize='x-large')\n",
    "\n",
    "plt.ylabel('X2',fontsize='x-large')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style='font-family:serif'>\n",
    "    \n",
    "O gráfico acima representa a recuperação dos dados originais, com perdas. As bolinhas de cor azul representam os dados originais, do início do tutorial. As vermelhas, os dados que foram projetados e em seguida recuperados. Nota-se que a projeção ocorreu apenas no eixo vermelho (de maior variância), excluindo-se a componente laranja. Ao recuperá-los, a variância da componente laranja não foi levada em consideração, o que gerou as perdas na descrição do comportamento dos dados. A distância entre cada dado original e sua versão recuperada é demarcada pela linha tracejada cinza."
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}