src/main.ipynb

{
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   "cell_type": "markdown",
   "metadata": {
    "id": "VgGSNxgZGFhj"
   },
   "source": [
    "# Étape 1 : Concepts de base\n",
    "\n",
    "## 1. Question conceptuelle\n",
    "\n",
    "> Expliquez en une phrase ce qu'est un perceptron.\n",
    "\n",
    "Un perceptron est un modèle de neurone artificiel qui effectue une classification binaire en combinant linéairement des entrées pondérées, puis en appliquant une fonction d'activation pour produire une sortie.\n",
    "\n",
    "## 2. Exercice manuel\n",
    "\n",
    "> Une donnée `X = [2, 3]`, un vecteur de poids `w = [0.5, 1.5]` et un biais `b = -2` sont donnés. Calculez la sortie du perceptron avec une fonction sigmoïde.\n",
    "```\n",
    "z = w(T)X + b\n",
    "y(pred) = a(z)\n",
    "```\n",
    "Que se passe-t-il si vous augmentez le biais b ? Essayez avec `b = 0` et `b = 2`.\n",
    "\n",
    "La formule donnée est : `z = w(T)X + b`\n",
    "Avec `w = [0.5, 1.5]`, `X = [2, 3]` et `b = -2`, nous avons :\n",
    "\n",
    "`z = (0.5 \\* 2) + (1.5 \\* 3) + (-2)`\n",
    "\n",
    "`z = 1 + 4.5 - 2`\n",
    "\n",
    "`z = 3.5`\n",
    "\n",
    "La fonction sigmoïde est définie comme :\n",
    "\n",
    "`a(z) = 1 / 1 + e^(-z)`\n",
    "\n",
    "En remplançant `z = 3.5`, nous obtenons :\n",
    "\n",
    "`a(3.5) = 1 / 1 + e^(-3.5)`\n",
    "\n",
    "Le résultat numérique est environ :\n",
    "\n",
    "`a(3.5) = 0.9707`\n",
    "\n",
    "L'effet de l'augmentation du biais `b` dans le cas où `b = 0` :\n",
    "\n",
    "`z = 5.5`\n",
    "`a(5.5) = 0.9959`\n",
    "\n",
    "L'effet de l'augmentation du biais `b` dans le cas où `b = 2` :\n",
    "\n",
    "`z = 7.5`\n",
    "`a(7.5) = 0.9994`\n",
    "\n",
    "Lorsque le biais `b` augmente, `z` augmente également, ce qui pousse la sortie du perceptron `y(pred)` plus près de 1 (la saturation de la sigmoïde).\n",
    "A l'inverse, diminuer `b` entraîne une sortie proche de 0. Le biais contrôle donc la tendance du perceptron à activer ou non une sortie."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "66lrj2l8VWxj"
   },
   "source": [
    "# Étape 2 : Génération et visualisation des données\n",
    "\n",
    "> 1. Générer des données linéairement séparables avec make_blobs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "R13Q5CT9Ve5C"
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "X, y = make_blobs(n_samples=100, centers=2, cluster_std=1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XQwfzg7yXECL"
   },
   "source": [
    "> 2. Affichez ces données avec matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 565
    },
    "id": "QNEgh7VpWPmo",
    "outputId": "861a5405-f8a2-4d41-9cc3-1ab0465573be"
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, cmap='viridis', edgecolors='k')\n",
    "plt.xlabel('Fonctionnalité 1')\n",
    "plt.ylabel('Fonctionnalité 2')\n",
    "plt.title('Données linéairement séparables')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5v6Ftda3X1N2"
   },
   "source": [
    "> Combien de points appartiennent à chaque classe ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "fYggV3OdYIBF",
    "outputId": "e1cf6622-eae7-46b7-ee02-567263cb72f7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre de points dans la classe 0 : 50\n",
      "Nombre de points dans la classe 1 : 50\n"
     ]
    }
   ],
   "source": [
    "class_0 = sum(1 for label in y if label == 0)\n",
    "class_1 = sum(1 for label in y if label == 1)\n",
    "\n",
    "print(f\"Nombre de points dans la classe 0 : {class_0}\")\n",
    "print(f\"Nombre de points dans la classe 1 : {class_1}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZfAzj3MQZ7le"
   },
   "source": [
    "> Pensez-vous que le perceptron peut séparer ces données ?\n",
    "\n",
    "Oui, le perceptron peut séparer ces données si elles sont linéairement séparables, ce qui semble être le cas ici, étant donné que nous avons utilisé des paramètres de génération qui favorisent cette séparation (clusters bien définis avec une faible dispersion relative grâce à `cluster_std=1.5`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jxS3GBm7bIPL"
   },
   "source": [
    "# Étape 3 : Implémentation de la fonction sigmoïde\n",
    "\n",
    "> 1. Implémentez la fonction sigmoïde :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "RrNgazh5bPab"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "def sigmoid(z):\n",
    "  return 1 / (1 + math.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2iLvu4rbbfFv"
   },
   "source": [
    "> 2. Testez-la avec une série de valeurs de z."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "p7FbZwmTbT8k",
    "outputId": "8a5f38ef-c1c7-47d3-f48c-87e9c36143fe"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-5, 0.0066928509242848554),\n",
       " (-2, 0.11920292202211755),\n",
       " (0, 0.5),\n",
       " (2, 0.8807970779778823),\n",
       " (5, 0.9933071490757153)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z_values = [-5, -2, 0, 2, 5]\n",
    "sigmoid_results = [(z, sigmoid(z)) for z in z_values]\n",
    "\n",
    "sigmoid_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NuAZ_NzAcLJA"
   },
   "source": [
    "> Quelle est la sortie pour z = 0 ? Pourquoi ?\n",
    "\n",
    "Pour `z = 0`, la sortie de la fonction sigmoïde est :\n",
    "\n",
    "`sigmoid(0) = 1/1+e^(-0)`\n",
    "\n",
    "`sigmoid(0) = 1/1+1 = 1/2 = 0.5`\n",
    "\n",
    "> Tracez la courbe de la sigmoïde pour z entre -10 et 10. Que remarquez\n",
    "vous ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 564
    },
    "id": "Rn8jc3Ejc6qV",
    "outputId": "139f6f35-6254-4fb3-ac00-be3dfca99375"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def sigmoid(z):\n",
    "  return 1 / (1 + np.exp(-z))\n",
    "\n",
    "z_values = np.linspace(-10, 10)\n",
    "sigmoid_results = sigmoid(z_values)\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(z_values, sigmoid_results, label='Sigmoïde', color='blue')\n",
    "plt.axhline(y=0.5, color='red', linestyle='--', label='y = 0.5')\n",
    "plt.axvline(x=0, color='green', linestyle='--', label='z = 0')\n",
    "plt.title('Courbe de la fonction Sigmoïde')\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('Sigmoïde(z)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ptCEloGQgVCZ"
   },
   "source": [
    "Le sigmoïde est idéale pour convertir une valeur scalaire en une probabilité, mais elle est limitée par se valeurs extrêmes qui tendent à saturer à 0 ou 1.\n",
    "\n",
    "# Étape 4 : Fonction coût\n",
    "\n",
    "> 1. Implémentez la fonction coût logistique binaire :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "mxINHNxGhLQD"
   },
   "outputs": [],
   "source": [
    "def cost_function(y, y_pred):\n",
    "  epsilon = 1e-15\n",
    "\n",
    "  y_pred = np.clip(y_pred, epsilon, 1 - epsilon)\n",
    "  cost = -np.mean(y * np.log(y_pred) + (1 - y) * np.log(1 - y_pred))\n",
    "\n",
    "  return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pkSyYqMjj7Wz"
   },
   "source": [
    "> 2. Testez-la avec\n",
    "`y = [1, 0, 1, 0]` et `y(pred) =[0.9, 0.1, 0.8, 0.2].` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ruyGtq0JkSiw",
    "outputId": "9fb40ef0-2418-41ac-f0ca-44024269dedf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.164252033486018"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_og = np.array([1, 0, 1, 0])\n",
    "y_pred = np.array([0.9, 0.1, 0.8, 0.2])\n",
    "\n",
    "cost = cost_function(y_og, y_pred)\n",
    "cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1WSAY0rPlEPN"
   },
   "source": [
    "> Que se passe-t-il si les prédictions `y(pred)` sont proches des étiquettes `y` ? Et\n",
    "si elles sont très éloignées ?\n",
    "\n",
    "Cela montre que les prédictions sont assez proches des étiqquettes rééelles, ce qui correspond à un faible coût."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "El8Csvq9mMH-"
   },
   "source": [
    "# Étape 5 : Descente de gradient\n",
    "\n",
    "> 1. Implémentez une étape de la descente de gradient. Utilisez les formules pour\n",
    "mettre à jour `w` et `b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "tWEwl7yDmxEx"
   },
   "outputs": [],
   "source": [
    "def gradient_descent_step(X, y, w, b, alpha):\n",
    "    m = len(y)\n",
    "    z = np.dot(X, w) + b\n",
    "    y_pred = sigmoid(z)\n",
    "\n",
    "    dw = (1 / m) * np.dot(X.T, (y_pred - y))\n",
    "    db = (1 / m) * np.sum(y_pred - y)\n",
    "\n",
    "    w -= dw * alpha\n",
    "    b -= db * alpha\n",
    "\n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1CI2aJnsq8yp"
   },
   "source": [
    "> Qu'arrive-t-il aux poids si le taux d'apprentissage `α` est trop grand ?                             \n",
    "Essayez `α` = 0.1, 1, et 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "h9TnGY2frM9Z",
    "outputId": "add0c548-e815-44cf-e434-8acad7c75d89"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0.1: (array([-0.47556584, -0.30947906]), -1.9619202922022119),\n",
       " 1: (array([-4.75565837, -3.09479059]), -1.6192029220221178),\n",
       " 10: (array([-47.55658367, -30.94790593]), 1.807970779778823)}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = {}\n",
    "initial_b = -2\n",
    "initial_w = np.zeros(X.shape[1])\n",
    "\n",
    "for alpha in [0.1, 1, 10]:\n",
    "  w, b = initial_w.copy(), initial_b\n",
    "  w, b = gradient_descent_step(X, y, w, b, alpha)\n",
    "\n",
    "  results[alpha] = (w, b)\n",
    "\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eOguvqoQuFdF"
   },
   "source": [
    "# Étape 6 : Entraînement du perceptron\n",
    "\n",
    "> 1. Implémentez une boucle complète d’entraînement pour optimiser les poids et\n",
    "biais sur plusieurs itérations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EFyZHGE5ucle",
    "outputId": "0a220bda-ea78-4c24-ee46-6465ccdad3d9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Poids optimisés : [-0.74085344 -0.32272285]\n",
      "Biais optimisé : -1.9747532251708997\n"
     ]
    }
   ],
   "source": [
    "def train_model(X, y, w, b, alpha, num_iterations):\n",
    "  costs = []\n",
    "\n",
    "  for i in range(num_iterations):\n",
    "    w, b = gradient_descent_step(X, y, w, b, alpha)\n",
    "\n",
    "    z = np.dot(X, w) + b\n",
    "    y_pred = sigmoid(z)\n",
    "\n",
    "    cost = cost_function(y, y_pred)\n",
    "    costs.append(cost)\n",
    "\n",
    "  return w, b, costs\n",
    "\n",
    "w_opt, b_opt, costs = train_model(X, y, initial_w, initial_b, 0.1, 100)\n",
    "\n",
    "print(f\"Poids optimisés : {w_opt}\")\n",
    "print(f\"Biais optimisé : {b_opt}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FGw4HOpJvv9V"
   },
   "source": [
    "> Après combien d’itérations le coût commence-t-il à se stabiliser ? Pourquoi ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "RbDakMEHv9gW",
    "outputId": "71b1f236-8c1c-49ae-8a9d-6757dbd56b8e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point de stabilité : 27 itérations\n"
     ]
    }
   ],
   "source": [
    "def find_stabilization_point(costs, threshold=1e-4):\n",
    "    for i in range(1, len(costs)):\n",
    "        if abs(costs[i] - costs[i - 1]) < threshold:\n",
    "            return i\n",
    "    return len(costs)\n",
    "\n",
    "stabilization_point = find_stabilization_point(costs)\n",
    "\n",
    "print(f\"Point de stabilité : {stabilization_point} itérations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QJ2fYqDoyZId"
   },
   "source": [
    "# Étape 7 : Évaluation\n",
    "\n",
    "> 1. Implémentez une fonction predict pour prédire les étiquettes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qdP-rqd_yfCg",
    "outputId": "566689fc-7202-483f-e0a8-ef827d4c6acb"
   },
   "outputs": [],
   "source": [
    "def predict(X, w, b):\n",
    "  z = np.dot(X, w) + b\n",
    "  y_pred = sigmoid(z)\n",
    "  y_pred = (y_pred >= 0.5).astype(int)\n",
    "\n",
    "  return y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RqxCVROozfs9"
   },
   "source": [
    "> 2. Évaluez la précision sur le jeu de données."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vbZGAxKjz1a_",
    "outputId": "c7a9259b-b20b-48c3-ea3a-0518e51142cd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1,\n",
       "       0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1,\n",
       "       0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0,\n",
       "       0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0,\n",
       "       1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = predict(X, w_opt, b_opt)\n",
    "output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QOOpHdpwz4Ct"
   },
   "source": [
    "> Votre perceptron est-il parfait ? Pourquoi pourrait-il échouer dans certains\n",
    "cas ?\n",
    "\n",
    "Non, un percerptron n'est pas parfait et peut éechouer dans certain cas.\n",
    "\n",
    "> Comment pourriez-vous améliorer ce modèle ?\n",
    "\n",
    "En combinant des modèles plus avancés (réseaux de neurones, SVM) avec un bon prétraitement des données, une régularisation et des optimisation modernes, il est possible d'améliorer considérablement la performance et la robustesse d'un modèle initial basé sur un perceptron."
   ]
  }
 ],
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