kmeansfromscratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-Means from scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le but de ce notebook est de recoder successivement un algorithme K-Means à partir d'un nombre de clusters $k$ et une matrice de données $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On ouvre pour tester le fichier `dataset_1.csv` qui contient deux variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On importe les bibliothèques nécessaires."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On ouvre le fichier et on illustre ses données sur un scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>normalized_age</th>\n",
       "      <th>normalized_salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.680267</td>\n",
       "      <td>-0.016342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.809518</td>\n",
       "      <td>0.798483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.661372</td>\n",
       "      <td>-0.577667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.257307</td>\n",
       "      <td>-0.155552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.698017</td>\n",
       "      <td>0.174561</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   normalized_age  normalized_salary\n",
       "0        0.680267          -0.016342\n",
       "1        3.809518           0.798483\n",
       "2       -1.661372          -0.577667\n",
       "3       -0.257307          -0.155552\n",
       "4        0.698017           0.174561"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"dataset_1.csv\", index_col=\"Unnamed: 0\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Salaire')"
      ]
     },
     "execution_count": 8,
     "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(df.iloc[:,0], df.iloc[:,1])\n",
    "plt.title(\"Age vs salaire\")\n",
    "plt.xlabel(\"Age\")\n",
    "plt.ylabel(\"Salaire\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque qu'on peut placer au moins 2 clusters. Pour palcer un cluster, on a plusieurs méthodes à notre disposition.\n",
    "\n",
    "On peut commencer par une **méthode aléatoire** qui consiste à placer des points dans les limites des données. On peut convertir cette dataframe en une matrice Numpy et voir où se situent les extremum pour chaque variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maxima de X :\n",
      "[4.69090369 4.850055  ]\n",
      "Minima de X :\n",
      "[-8.096229   -1.19017548]\n"
     ]
    }
   ],
   "source": [
    "X =np.array(df)\n",
    "\n",
    "X_max= np.max(X, axis=0)\n",
    "X_min = np.min(X, axis=0)\n",
    "\n",
    "print(\"Maxima de X :\")\n",
    "print(X_max)\n",
    "print(\"Minima de X :\")\n",
    "print(X_min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut donc garder un nombre initial $k$ et lancer les centroïdes initiaux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.29467476 -0.16983681]\n",
      " [-5.98696084  3.73802748]\n",
      " [ 0.55583641  0.19755707]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Salaire')"
      ]
     },
     "execution_count": 10,
     "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": [
    "k = 3\n",
    "#Pur hasard\n",
    "random_centroids  = np.random.random((k,X_min.shape[0])) * (np.tile(X_max,(k,1)) - np.tile(X_min,(k,1))) + np.tile(X_min,(k,1))\n",
    "#Selon les données\n",
    "centroids = X[np.random.choice(X.shape[0],k),:]\n",
    "print(centroids)\n",
    "\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.scatter(centroids[:,0], centroids[:,1], marker=\"X\", color=\"red\")\n",
    "plt.title(\"Age vs salaire\")\n",
    "plt.xlabel(\"Age\")\n",
    "plt.ylabel(\"Salaire\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A partir de ces premiers clusters, on peut calculer la distance pour chaque point et assigner un label au point le plus proche. Pour calculer la distance, on peut utiliser la distance **euclidienne** ou la distance de **Manhattan**.\n",
    "\n",
    "Partons sur la distance euclidienne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre de points dans le cluster 0 :\n",
      "212\n",
      "Nombre de points dans le cluster 1 :\n",
      "500\n",
      "Nombre de points dans le cluster 2 :\n",
      "288\n"
     ]
    }
   ],
   "source": [
    "#Initialisation de la matrice\n",
    "labels = np.zeros((X.shape[0], k))\n",
    "for cluster in range(k):\n",
    "    labels[:,cluster] = np.sqrt(np.sum((X - centroids[cluster,:])**2,axis=1))\n",
    "labels=np.argmin(labels, axis=1)\n",
    "\n",
    "for i in range(k):\n",
    "    print(f\"Nombre de points dans le cluster {i} :\")\n",
    "    print(labels[labels==i].size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Salaire')"
      ]
     },
     "execution_count": 12,
     "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": [
    "for i in range(k):\n",
    "    plt.scatter(X[labels==i][:,0], X[labels==i][:,1])\n",
    "plt.scatter(centroids[:,0], centroids[:,1], marker=\"X\", color=\"red\")\n",
    "plt.title(\"Age vs salaire\")\n",
    "plt.xlabel(\"Age\")\n",
    "plt.ylabel(\"Salaire\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le hasard peut être très ou pas convaincant du tout. La prochaine étape est donc de recentrer les centroïdes en fédinissant la moyenne des points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Les centroïdes ne sont pas alignés\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Salaire')"
      ]
     },
     "execution_count": 13,
     "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": [
    "new_centroids = np.zeros(centroids.shape)\n",
    "for cluster in range(k):\n",
    "    new_centroids[cluster,:] = np.mean(X[labels==cluster],axis=0)\n",
    "\n",
    "if (new_centroids!=centroids).all():\n",
    "    print(\"Les centroïdes ne sont pas alignés\")\n",
    "else:\n",
    "    print(\"Les centroïdes sont alignés\")\n",
    "    \n",
    "for i in range(k):\n",
    "    plt.scatter(X[labels==i][:,0], X[labels==i][:,1])\n",
    "plt.scatter(centroids[:,0], centroids[:,1], marker=\"X\", color=\"red\")\n",
    "plt.scatter(new_centroids[:,0], new_centroids[:,1], marker=\"D\", color=\"black\")\n",
    "plt.title(\"Age vs salaire\")\n",
    "plt.xlabel(\"Age\")\n",
    "plt.ylabel(\"Salaire\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va donc réassigner les nouveaux centroïdes aux vieux centroïdes jusqu'à ce qu'ils ne bougent plus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On a déterminé les centroïdes au bout de 1 itérations.\n"
     ]
    }
   ],
   "source": [
    "nbr_of_iterations = 0\n",
    "threshold = 1000\n",
    "\n",
    "while (np.round(new_centroids, 3)!=np.round(centroids,3)).all():\n",
    "    centroids = new_centroids\n",
    "    nbr_of_iterations += 1\n",
    "    labels = np.zeros((X.shape[0], k))\n",
    "    for cluster in range(k):\n",
    "        labels[:,cluster] = np.sqrt(np.sum((X - centroids[cluster,:])**2,axis=1))\n",
    "    labels=np.argmin(labels, axis=1)\n",
    "    new_centroids = np.zeros(centroids.shape)\n",
    "    for cluster in range(k):\n",
    "        new_centroids[cluster,:] = np.mean(X[labels==cluster],axis=0)\n",
    "\n",
    "if nbr_of_iterations<=threshold:\n",
    "    print(f\"On a déterminé les centroïdes au bout de {nbr_of_iterations} itérations.\")\n",
    "else:\n",
    "    print(\"Limite maximale d'itérations atteinte\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Salaire')"
      ]
     },
     "execution_count": 15,
     "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": [
    "for i in range(k):\n",
    "    plt.scatter(X[labels==i][:,0], X[labels==i][:,1])\n",
    "plt.scatter(new_centroids[:,0], new_centroids[:,1], marker=\"X\", color=\"red\")\n",
    "plt.title(\"Age vs salaire\")\n",
    "plt.xlabel(\"Age\")\n",
    "plt.ylabel(\"Salaire\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test de la classe\n",
    "\n",
    "On importe la classe crée dans le fichier `clustering.py`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# from clustering import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#On rouvre les données\n",
    "df = pd.read_csv(\"dataset_1.csv\", index_col=\"Unnamed: 0\")\n",
    "X =np.array(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class KMeans:\n",
    "    def __init__(self, X, k, cluster_init_method=\"random_data\", metrics=\"euclidean\", threshold=1000):\n",
    "        self.X = np.array(X) if X.__class__.__name__!= 'ndarray' else X\n",
    "        self.k = k\n",
    "        self.parameters = {\n",
    "            'cluster_init_method': cluster_init_method,\n",
    "            'metrics': metrics,\n",
    "            'threshold': threshold\n",
    "        }\n",
    "        self.centroids, self.labels = self.place_centroids()\n",
    "\n",
    "    def __initialize_centroids(self, bounds):\n",
    "        if self.parameters['cluster_init_method'] == 'pure_random':\n",
    "            return np.random.random((self.k,bounds[0].shape[0])) * (np.tile(bounds[1],(self.k,1)) - np.tile(bounds[0],(self.k,1))) + np.tile(bounds[0],(self.k,1))\n",
    "        elif self.parameters['cluster_init_method'] == 'random_data':\n",
    "            return self.X[np.random.choice(self.X.shape[0],self.k),:]\n",
    "\n",
    "    def __assign_labels(self, centroids):\n",
    "        labels = np.zeros((self.X.shape[0], self.k))\n",
    "        for cluster in range(self.k):\n",
    "            labels[:,cluster] = np.sqrt(np.sum((self.X - centroids[cluster,:])**2,axis=1))\n",
    "        labels=np.argmin(labels, axis=1)\n",
    "        return labels\n",
    "    \n",
    "    def __compute_next_iter(self, centroids):\n",
    "        next_centroid = np.zeros(centroids.shape)\n",
    "        labels = self.__assign_labels(centroids)\n",
    "        for cluster in range(self.k):\n",
    "            next_centroid[cluster,:] = np.mean(self.X[labels==cluster],axis=0)\n",
    "        return next_centroid\n",
    "\n",
    "    def place_centroids(self):\n",
    "        X_bounds = (np.min(self.X, axis=0), np.max(self.X, axis=0))\n",
    "        init_centroids = self.__initialize_centroids(X_bounds)\n",
    "        curr_centroids = self.__compute_next_iter(init_centroids)\n",
    "        nbr_of_iterations = 0\n",
    "        while (np.round(curr_centroids,3)!=np.round(init_centroids,3)).all():\n",
    "            nbr_of_iterations += 1\n",
    "            curr_centroids = self.__compute_next_iter(curr_centroids)\n",
    "            if nbr_of_iterations == self.parameters['threshold']:\n",
    "                break       \n",
    "        return curr_centroids, labels\n",
    "    \n",
    "    def render_data_2d(self):\n",
    "        for i in range(self.k):\n",
    "            plt.scatter(self.X[self.labels==i][:,0], self.X[self.labels==i][:,1])\n",
    "        plt.scatter(self.centroids[:,0], self.centroids[:,1], marker=\"X\", color=\"red\")\n",
    "        plt.title(\"2D render\")\n",
    "        plt.xlabel(\"X\")\n",
    "        plt.ylabel(\"Y\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "kmeans = KMeans(X,3)\n",
    "kmeans.render_data_2d()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}